KILLED proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF).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), 264 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 2734 ms] (14) BOUNDS(1, INF) (15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (16) CpxTRS (17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (18) CpxRelTRS (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 50 ms] (20) CpxRelTRS (21) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxWeightedTrs (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CpxTypedWeightedTrs (25) CompletionProof [UPPER BOUND(ID), 0 ms] (26) CpxTypedWeightedCompleteTrs (27) NarrowingProof [BOTH BOUNDS(ID, ID), 7575 ms] (28) CpxTypedWeightedCompleteTrs (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CpxRNTS (33) CompletionProof [UPPER BOUND(ID), 0 ms] (34) CpxTypedWeightedCompleteTrs (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 16 ms] (36) CpxRNTS (37) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (38) CdtProblem (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 1 ms] (40) CdtProblem (41) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (46) CdtProblem (47) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 4 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (66) CdtProblem (67) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 37 ms] (70) CdtProblem (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 2 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 40 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 12 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 70 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 3 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 205 ms] (148) CdtProblem (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 53 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 254 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 514 ms] (156) CdtProblem (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 35 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 537 ms] (160) CdtProblem (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 39 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 340 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 82 ms] (166) CdtProblem ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(U11(tt, M, N)) -> mark(U12(tt, M, N)) active(U12(tt, M, N)) -> mark(s(plus(N, M))) active(plus(N, 0)) -> mark(N) active(plus(N, s(M))) -> mark(U11(tt, M, N)) mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)) mark(tt) -> active(tt) mark(U12(X1, X2, X3)) -> active(U12(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, X3) -> U11(X1, X2, X3) U11(X1, mark(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, mark(X3)) -> U11(X1, X2, X3) U11(active(X1), X2, X3) -> U11(X1, X2, X3) U11(X1, active(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, active(X3)) -> U11(X1, X2, X3) U12(mark(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, mark(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, mark(X3)) -> U12(X1, X2, X3) U12(active(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, active(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, active(X3)) -> U12(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: FULL ---------------------------------------- (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, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(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, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U12(x_1, x_2, x_3) -> U12(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 (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(U11(tt, M, N)) -> mark(U12(tt, M, N)) active(U12(tt, M, N)) -> mark(s(plus(N, M))) active(plus(N, 0)) -> mark(N) active(plus(N, s(M))) -> mark(U11(tt, M, N)) mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)) mark(tt) -> active(tt) mark(U12(X1, X2, X3)) -> active(U12(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, X3) -> U11(X1, X2, X3) U11(X1, mark(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, mark(X3)) -> U11(X1, X2, X3) U11(active(X1), X2, X3) -> U11(X1, X2, X3) U11(X1, active(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, active(X3)) -> U11(X1, X2, X3) U12(mark(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, mark(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, mark(X3)) -> U12(X1, X2, X3) U12(active(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, active(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, active(X3)) -> U12(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, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(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, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U12(x_1, x_2, x_3) -> U12(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: FULL ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(U11(tt, M, N)) -> mark(U12(tt, M, N)) active(U12(tt, M, N)) -> mark(s(plus(N, M))) active(plus(N, 0)) -> mark(N) active(plus(N, s(M))) -> mark(U11(tt, M, N)) mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)) mark(tt) -> active(tt) mark(U12(X1, X2, X3)) -> active(U12(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, X3) -> U11(X1, X2, X3) U11(X1, mark(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, mark(X3)) -> U11(X1, X2, X3) U11(active(X1), X2, X3) -> U11(X1, X2, X3) U11(X1, active(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, active(X3)) -> U11(X1, X2, X3) U12(mark(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, mark(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, mark(X3)) -> U12(X1, X2, X3) U12(active(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, active(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, active(X3)) -> U12(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, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(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, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U12(x_1, x_2, x_3) -> U12(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: FULL ---------------------------------------- (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 (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(U11(tt, M, N)) -> mark(U12(tt, M, N)) active(U12(tt, M, N)) -> mark(s(plus(N, M))) active(plus(N, 0)) -> mark(N) active(plus(N, s(M))) -> mark(U11(tt, M, N)) mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)) mark(tt) -> active(tt) mark(U12(X1, X2, X3)) -> active(U12(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, X3) -> U11(X1, X2, X3) U11(X1, mark(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, mark(X3)) -> U11(X1, X2, X3) U11(active(X1), X2, X3) -> U11(X1, X2, X3) U11(X1, active(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, active(X3)) -> U11(X1, X2, X3) U12(mark(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, mark(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, mark(X3)) -> U12(X1, X2, X3) U12(active(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, active(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, active(X3)) -> U12(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, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(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, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U12(x_1, x_2, x_3) -> U12(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: FULL ---------------------------------------- (7) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (8) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(U11(tt, M, N)) -> mark(U12(tt, M, N)) active(U12(tt, M, N)) -> mark(s(plus(N, M))) active(plus(N, 0')) -> mark(N) active(plus(N, s(M))) -> mark(U11(tt, M, N)) mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)) mark(tt) -> active(tt) mark(U12(X1, X2, X3)) -> active(U12(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, X3) -> U11(X1, X2, X3) U11(X1, mark(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, mark(X3)) -> U11(X1, X2, X3) U11(active(X1), X2, X3) -> U11(X1, X2, X3) U11(X1, active(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, active(X3)) -> U11(X1, X2, X3) U12(mark(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, mark(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, mark(X3)) -> U12(X1, X2, X3) U12(active(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, active(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, active(X3)) -> U12(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, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(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, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U12(x_1, x_2, x_3) -> U12(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: FULL ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: TRS: Rules: active(U11(tt, M, N)) -> mark(U12(tt, M, N)) active(U12(tt, M, N)) -> mark(s(plus(N, M))) active(plus(N, 0')) -> mark(N) active(plus(N, s(M))) -> mark(U11(tt, M, N)) mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)) mark(tt) -> active(tt) mark(U12(X1, X2, X3)) -> active(U12(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, X3) -> U11(X1, X2, X3) U11(X1, mark(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, mark(X3)) -> U11(X1, X2, X3) U11(active(X1), X2, X3) -> U11(X1, X2, X3) U11(X1, active(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, active(X3)) -> U11(X1, X2, X3) U12(mark(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, mark(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, mark(X3)) -> U12(X1, X2, X3) U12(active(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, active(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, active(X3)) -> U12(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, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(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, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U12(x_1, x_2, x_3) -> U12(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_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus tt :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus U12 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus s :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus 0' :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encArg :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_active :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_U12 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_s :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_active :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_tt :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_U12 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_s :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_0 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus hole_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus1_4 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus2_4 :: Nat -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus ---------------------------------------- (11) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: active, mark, U12, s, plus, U11, encArg They will be analysed ascendingly in the following order: active = mark U12 < active s < active plus < active U11 < active active < encArg U12 < mark s < mark plus < mark U11 < mark mark < encArg U12 < encArg s < encArg plus < encArg U11 < encArg ---------------------------------------- (12) Obligation: TRS: Rules: active(U11(tt, M, N)) -> mark(U12(tt, M, N)) active(U12(tt, M, N)) -> mark(s(plus(N, M))) active(plus(N, 0')) -> mark(N) active(plus(N, s(M))) -> mark(U11(tt, M, N)) mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)) mark(tt) -> active(tt) mark(U12(X1, X2, X3)) -> active(U12(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, X3) -> U11(X1, X2, X3) U11(X1, mark(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, mark(X3)) -> U11(X1, X2, X3) U11(active(X1), X2, X3) -> U11(X1, X2, X3) U11(X1, active(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, active(X3)) -> U11(X1, X2, X3) U12(mark(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, mark(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, mark(X3)) -> U12(X1, X2, X3) U12(active(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, active(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, active(X3)) -> U12(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, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(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, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U12(x_1, x_2, x_3) -> U12(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_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus tt :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus U12 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus s :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus 0' :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encArg :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_active :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_U12 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_s :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_active :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_tt :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_U12 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_s :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_0 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus hole_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus1_4 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus2_4 :: Nat -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus Generator Equations: gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus2_4(0) <=> tt gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus2_4(+(x, 1)) <=> cons_active(gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus2_4(x)) The following defined symbols remain to be analysed: U12, active, mark, s, plus, U11, encArg They will be analysed ascendingly in the following order: active = mark U12 < active s < active plus < active U11 < active active < encArg U12 < mark s < mark plus < mark U11 < mark mark < encArg U12 < encArg s < encArg plus < encArg U11 < encArg ---------------------------------------- (13) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus2_4(+(1, n390_4))) -> *3_4, rt in Omega(0) Induction Base: encArg(gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus2_4(+(1, 0))) Induction Step: encArg(gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus2_4(+(1, +(n390_4, 1)))) ->_R^Omega(0) active(encArg(gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus2_4(+(1, n390_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 (full) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(U11(tt, M, N)) -> mark(U12(tt, M, N)) active(U12(tt, M, N)) -> mark(s(plus(N, M))) active(plus(N, 0)) -> mark(N) active(plus(N, s(M))) -> mark(U11(tt, M, N)) mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)) mark(tt) -> active(tt) mark(U12(X1, X2, X3)) -> active(U12(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, X3) -> U11(X1, X2, X3) U11(X1, mark(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, mark(X3)) -> U11(X1, X2, X3) U11(active(X1), X2, X3) -> U11(X1, X2, X3) U11(X1, active(X2), X3) -> U11(X1, X2, X3) U11(X1, X2, active(X3)) -> U11(X1, X2, X3) U12(mark(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, mark(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, mark(X3)) -> U12(X1, X2, X3) U12(active(X1), X2, X3) -> U12(X1, X2, X3) U12(X1, active(X2), X3) -> U12(X1, X2, X3) U12(X1, X2, active(X3)) -> U12(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, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(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, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U12(x_1, x_2, x_3) -> U12(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: FULL ---------------------------------------- (17) NonCtorToCtorProof (UPPER BOUND(ID)) transformed non-ctor to ctor-system ---------------------------------------- (18) Obligation: The Runtime Complexity (full) 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) mark(c_U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3)) plus(X1, c_mark(X2)) -> plus(X1, X2) U12(X1, c_active(X2), X3) -> U12(X1, X2, X3) plus(c_active(X1), X2) -> plus(X1, X2) mark(c_s(X)) -> active(s(mark(X))) U12(c_mark(X1), X2, X3) -> U12(X1, X2, X3) active(c_U12(tt, M, N)) -> mark(s(plus(N, M))) U11(X1, c_mark(X2), X3) -> U11(X1, X2, X3) U11(c_active(X1), X2, X3) -> U11(X1, X2, X3) s(c_active(X)) -> s(X) active(c_plus(N, c_s(M))) -> mark(U11(tt, M, N)) active(c_U11(tt, M, N)) -> mark(U12(tt, M, N)) U12(X1, X2, c_mark(X3)) -> U12(X1, X2, X3) U11(X1, c_active(X2), X3) -> U11(X1, X2, X3) U12(c_active(X1), X2, X3) -> U12(X1, X2, X3) U11(c_mark(X1), X2, X3) -> U11(X1, X2, X3) mark(c_U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)) s(c_mark(X)) -> s(X) plus(c_mark(X1), X2) -> plus(X1, X2) U11(X1, X2, c_mark(X3)) -> U11(X1, X2, X3) U12(X1, X2, c_active(X3)) -> U12(X1, X2, X3) active(c_plus(N, 0)) -> mark(N) U11(X1, X2, c_active(X3)) -> U11(X1, X2, X3) plus(X1, c_active(X2)) -> plus(X1, X2) mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) U12(X1, c_mark(X2), X3) -> U12(X1, X2, X3) 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, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(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, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U12(x_1, x_2, x_3) -> U12(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) active(x0) -> c_active(x0) plus(x0, x1) -> c_plus(x0, x1) U12(x0, x1, x2) -> c_U12(x0, x1, x2) U11(x0, x1, x2) -> c_U11(x0, x1, x2) mark(x0) -> c_mark(x0) Rewrite Strategy: FULL ---------------------------------------- (19) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. As the TRS is a non-duplicating overlay system, we have rc = irc. ---------------------------------------- (20) 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) mark(c_U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3)) plus(X1, c_mark(X2)) -> plus(X1, X2) U12(X1, c_active(X2), X3) -> U12(X1, X2, X3) plus(c_active(X1), X2) -> plus(X1, X2) mark(c_s(X)) -> active(s(mark(X))) U12(c_mark(X1), X2, X3) -> U12(X1, X2, X3) active(c_U12(tt, M, N)) -> mark(s(plus(N, M))) U11(X1, c_mark(X2), X3) -> U11(X1, X2, X3) U11(c_active(X1), X2, X3) -> U11(X1, X2, X3) s(c_active(X)) -> s(X) active(c_plus(N, c_s(M))) -> mark(U11(tt, M, N)) active(c_U11(tt, M, N)) -> mark(U12(tt, M, N)) U12(X1, X2, c_mark(X3)) -> U12(X1, X2, X3) U11(X1, c_active(X2), X3) -> U11(X1, X2, X3) U12(c_active(X1), X2, X3) -> U12(X1, X2, X3) U11(c_mark(X1), X2, X3) -> U11(X1, X2, X3) mark(c_U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)) s(c_mark(X)) -> s(X) plus(c_mark(X1), X2) -> plus(X1, X2) U11(X1, X2, c_mark(X3)) -> U11(X1, X2, X3) U12(X1, X2, c_active(X3)) -> U12(X1, X2, X3) active(c_plus(N, 0)) -> mark(N) U11(X1, X2, c_active(X3)) -> U11(X1, X2, X3) plus(X1, c_active(X2)) -> plus(X1, X2) mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) U12(X1, c_mark(X2), X3) -> U12(X1, X2, X3) 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, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U12(x_1, x_2, x_3)) -> U12(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, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U12(x_1, x_2, x_3) -> U12(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) active(x0) -> c_active(x0) plus(x0, x1) -> c_plus(x0, x1) U12(x0, x1, x2) -> c_U12(x0, x1, x2) U11(x0, x1, x2) -> c_U11(x0, x1, x2) mark(x0) -> c_mark(x0) Rewrite Strategy: INNERMOST ---------------------------------------- (21) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (22) 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] mark(c_U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3)) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] U12(X1, c_active(X2), X3) -> U12(X1, X2, X3) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] U12(c_mark(X1), X2, X3) -> U12(X1, X2, X3) [1] active(c_U12(tt, M, N)) -> mark(s(plus(N, M))) [1] U11(X1, c_mark(X2), X3) -> U11(X1, X2, X3) [1] U11(c_active(X1), X2, X3) -> U11(X1, X2, X3) [1] s(c_active(X)) -> s(X) [1] active(c_plus(N, c_s(M))) -> mark(U11(tt, M, N)) [1] active(c_U11(tt, M, N)) -> mark(U12(tt, M, N)) [1] U12(X1, X2, c_mark(X3)) -> U12(X1, X2, X3) [1] U11(X1, c_active(X2), X3) -> U11(X1, X2, X3) [1] U12(c_active(X1), X2, X3) -> U12(X1, X2, X3) [1] U11(c_mark(X1), X2, X3) -> U11(X1, X2, X3) [1] mark(c_U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)) [1] s(c_mark(X)) -> s(X) [1] plus(c_mark(X1), X2) -> plus(X1, X2) [1] U11(X1, X2, c_mark(X3)) -> U11(X1, X2, X3) [1] U12(X1, X2, c_active(X3)) -> U12(X1, X2, X3) [1] active(c_plus(N, 0)) -> mark(N) [1] U11(X1, X2, c_active(X3)) -> U11(X1, X2, X3) [1] plus(X1, c_active(X2)) -> plus(X1, X2) [1] mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) [1] U12(X1, c_mark(X2), X3) -> U12(X1, X2, X3) [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, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_U12(x_1, x_2, x_3)) -> U12(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, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_tt -> tt [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_U12(x_1, x_2, x_3) -> U12(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] active(x0) -> c_active(x0) [0] plus(x0, x1) -> c_plus(x0, x1) [0] U12(x0, x1, x2) -> c_U12(x0, x1, x2) [0] U11(x0, x1, x2) -> c_U11(x0, x1, x2) [0] mark(x0) -> c_mark(x0) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (23) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (24) 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] mark(c_U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3)) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] U12(X1, c_active(X2), X3) -> U12(X1, X2, X3) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] U12(c_mark(X1), X2, X3) -> U12(X1, X2, X3) [1] active(c_U12(tt, M, N)) -> mark(s(plus(N, M))) [1] U11(X1, c_mark(X2), X3) -> U11(X1, X2, X3) [1] U11(c_active(X1), X2, X3) -> U11(X1, X2, X3) [1] s(c_active(X)) -> s(X) [1] active(c_plus(N, c_s(M))) -> mark(U11(tt, M, N)) [1] active(c_U11(tt, M, N)) -> mark(U12(tt, M, N)) [1] U12(X1, X2, c_mark(X3)) -> U12(X1, X2, X3) [1] U11(X1, c_active(X2), X3) -> U11(X1, X2, X3) [1] U12(c_active(X1), X2, X3) -> U12(X1, X2, X3) [1] U11(c_mark(X1), X2, X3) -> U11(X1, X2, X3) [1] mark(c_U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)) [1] s(c_mark(X)) -> s(X) [1] plus(c_mark(X1), X2) -> plus(X1, X2) [1] U11(X1, X2, c_mark(X3)) -> U11(X1, X2, X3) [1] U12(X1, X2, c_active(X3)) -> U12(X1, X2, X3) [1] active(c_plus(N, 0)) -> mark(N) [1] U11(X1, X2, c_active(X3)) -> U11(X1, X2, X3) [1] plus(X1, c_active(X2)) -> plus(X1, X2) [1] mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) [1] U12(X1, c_mark(X2), X3) -> U12(X1, X2, X3) [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, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_U12(x_1, x_2, x_3)) -> U12(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, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_tt -> tt [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_U12(x_1, x_2, x_3) -> U12(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] active(x0) -> c_active(x0) [0] plus(x0, x1) -> c_plus(x0, x1) [0] U12(x0, x1, x2) -> c_U12(x0, x1, x2) [0] U11(x0, x1, x2) -> c_U11(x0, x1, x2) [0] mark(x0) -> c_mark(x0) [0] The TRS has the following type information: mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus tt :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus 0 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus c_U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus c_mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus c_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus c_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus c_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus c_U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encArg :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus cons_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_tt :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus encode_0 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus Rewrite Strategy: INNERMOST ---------------------------------------- (25) 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_3 encode_tt encode_mark_1 encode_U12_3 encode_s_1 encode_plus_2 encode_0 s_1 active_1 plus_2 U12_3 U11_3 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, v2) -> null_encode_U11 [0] encode_tt -> null_encode_tt [0] encode_mark(v0) -> null_encode_mark [0] encode_U12(v0, v1, v2) -> null_encode_U12 [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] active(v0) -> null_active [0] plus(v0, v1) -> null_plus [0] U12(v0, v1, v2) -> null_U12 [0] U11(v0, v1, v2) -> 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_s, null_encode_plus, null_encode_0, null_s, null_active, null_plus, null_U12, null_U11, null_mark ---------------------------------------- (26) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: mark(tt) -> active(tt) [1] mark(0) -> active(0) [1] mark(c_U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3)) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] U12(X1, c_active(X2), X3) -> U12(X1, X2, X3) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] U12(c_mark(X1), X2, X3) -> U12(X1, X2, X3) [1] active(c_U12(tt, M, N)) -> mark(s(plus(N, M))) [1] U11(X1, c_mark(X2), X3) -> U11(X1, X2, X3) [1] U11(c_active(X1), X2, X3) -> U11(X1, X2, X3) [1] s(c_active(X)) -> s(X) [1] active(c_plus(N, c_s(M))) -> mark(U11(tt, M, N)) [1] active(c_U11(tt, M, N)) -> mark(U12(tt, M, N)) [1] U12(X1, X2, c_mark(X3)) -> U12(X1, X2, X3) [1] U11(X1, c_active(X2), X3) -> U11(X1, X2, X3) [1] U12(c_active(X1), X2, X3) -> U12(X1, X2, X3) [1] U11(c_mark(X1), X2, X3) -> U11(X1, X2, X3) [1] mark(c_U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)) [1] s(c_mark(X)) -> s(X) [1] plus(c_mark(X1), X2) -> plus(X1, X2) [1] U11(X1, X2, c_mark(X3)) -> U11(X1, X2, X3) [1] U12(X1, X2, c_active(X3)) -> U12(X1, X2, X3) [1] active(c_plus(N, 0)) -> mark(N) [1] U11(X1, X2, c_active(X3)) -> U11(X1, X2, X3) [1] plus(X1, c_active(X2)) -> plus(X1, X2) [1] mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) [1] U12(X1, c_mark(X2), X3) -> U12(X1, X2, X3) [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, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_U12(x_1, x_2, x_3)) -> U12(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, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_tt -> tt [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_U12(x_1, x_2, x_3) -> U12(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] active(x0) -> c_active(x0) [0] plus(x0, x1) -> c_plus(x0, x1) [0] U12(x0, x1, x2) -> c_U12(x0, x1, x2) [0] U11(x0, x1, x2) -> c_U11(x0, x1, x2) [0] mark(x0) -> c_mark(x0) [0] encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_U11(v0, v1, v2) -> null_encode_U11 [0] encode_tt -> null_encode_tt [0] encode_mark(v0) -> null_encode_mark [0] encode_U12(v0, v1, v2) -> null_encode_U12 [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] active(v0) -> null_active [0] plus(v0, v1) -> null_plus [0] U12(v0, v1, v2) -> null_U12 [0] U11(v0, v1, v2) -> null_U11 [0] mark(v0) -> null_mark [0] The TRS has the following type information: mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark tt :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark 0 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark c_U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> 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tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark cons_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> 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tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark cons_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark cons_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_tt :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_0 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encArg :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_tt :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_0 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark Rewrite Strategy: INNERMOST ---------------------------------------- (27) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (28) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: mark(tt) -> active(tt) [1] mark(0) -> active(0) [1] mark(c_U12(tt, X2, X3)) -> active(U12(active(tt), X2, X3)) [2] mark(c_U12(0, X2, X3)) -> active(U12(active(0), X2, X3)) [2] mark(c_U12(c_U12(X1', X2', X3'), X2, X3)) -> active(U12(active(U12(mark(X1'), X2', X3')), X2, X3)) [2] mark(c_U12(c_s(X'), X2, X3)) -> active(U12(active(s(mark(X'))), X2, X3)) [2] mark(c_U12(c_U11(X1'', X2'', X3''), X2, X3)) -> active(U12(active(U11(mark(X1''), X2'', X3'')), X2, X3)) [2] mark(c_U12(c_plus(X11, X21), X2, X3)) -> active(U12(active(plus(mark(X11), mark(X21))), X2, X3)) [2] mark(c_U12(X1, X2, X3)) -> active(U12(c_mark(X1), X2, X3)) [1] mark(c_U12(X1, X2, X3)) -> active(U12(null_mark, X2, X3)) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] U12(X1, c_active(X2), X3) -> U12(X1, X2, X3) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(tt)) -> active(s(active(tt))) [2] mark(c_s(0)) -> active(s(active(0))) [2] mark(c_s(c_U12(X12, X22, X31))) -> active(s(active(U12(mark(X12), X22, X31)))) [2] mark(c_s(c_s(X''))) -> active(s(active(s(mark(X''))))) [2] mark(c_s(c_U11(X13, X23, X32))) -> active(s(active(U11(mark(X13), X23, X32)))) [2] mark(c_s(c_plus(X14, X24))) -> active(s(active(plus(mark(X14), mark(X24))))) [2] mark(c_s(X)) -> active(s(c_mark(X))) [1] mark(c_s(X)) -> active(s(null_mark)) [1] U12(c_mark(X1), X2, X3) -> U12(X1, X2, X3) [1] active(c_U12(tt, c_mark(X25), N)) -> mark(s(plus(N, X25))) [2] active(c_U12(tt, M, c_active(X15))) -> mark(s(plus(X15, M))) [2] active(c_U12(tt, M, c_mark(X16))) -> mark(s(plus(X16, M))) [2] active(c_U12(tt, c_active(X26), N)) -> mark(s(plus(N, X26))) [2] active(c_U12(tt, M, N)) -> mark(s(c_plus(N, M))) [1] active(c_U12(tt, M, N)) -> mark(s(null_plus)) [1] U11(X1, c_mark(X2), X3) -> U11(X1, X2, X3) [1] U11(c_active(X1), X2, X3) -> U11(X1, X2, X3) [1] s(c_active(X)) -> s(X) [1] active(c_plus(N, c_s(c_mark(X27)))) -> mark(U11(tt, X27, N)) [2] active(c_plus(N, c_s(c_active(X28)))) -> mark(U11(tt, X28, N)) [2] active(c_plus(c_mark(X33), c_s(M))) -> mark(U11(tt, M, X33)) [2] active(c_plus(c_active(X34), c_s(M))) -> mark(U11(tt, M, X34)) [2] active(c_plus(N, c_s(M))) -> mark(c_U11(tt, M, N)) [1] active(c_plus(N, c_s(M))) -> mark(null_U11) [1] active(c_U11(tt, c_active(X29), N)) -> mark(U12(tt, X29, N)) [2] active(c_U11(tt, M, c_mark(X35))) -> mark(U12(tt, M, X35)) [2] active(c_U11(tt, M, c_active(X36))) -> mark(U12(tt, M, X36)) [2] active(c_U11(tt, c_mark(X210), N)) -> mark(U12(tt, X210, N)) [2] active(c_U11(tt, M, N)) -> mark(c_U12(tt, M, N)) [1] active(c_U11(tt, M, N)) -> mark(null_U12) [1] U12(X1, X2, c_mark(X3)) -> U12(X1, X2, X3) [1] U11(X1, c_active(X2), X3) -> U11(X1, X2, X3) [1] U12(c_active(X1), X2, X3) -> U12(X1, X2, X3) [1] U11(c_mark(X1), X2, X3) -> U11(X1, X2, X3) [1] mark(c_U11(tt, X2, X3)) -> active(U11(active(tt), X2, X3)) [2] mark(c_U11(0, X2, X3)) -> active(U11(active(0), X2, X3)) [2] mark(c_U11(c_U12(X17, X211, X37), X2, X3)) -> active(U11(active(U12(mark(X17), X211, X37)), X2, X3)) [2] mark(c_U11(c_s(X4), X2, X3)) -> active(U11(active(s(mark(X4))), X2, X3)) [2] mark(c_U11(c_U11(X18, X212, X38), X2, X3)) -> active(U11(active(U11(mark(X18), X212, X38)), X2, X3)) [2] mark(c_U11(c_plus(X19, X213), X2, X3)) -> active(U11(active(plus(mark(X19), mark(X213))), X2, X3)) [2] mark(c_U11(X1, X2, X3)) -> active(U11(c_mark(X1), X2, X3)) [1] mark(c_U11(X1, X2, X3)) -> active(U11(null_mark, X2, X3)) [1] s(c_mark(X)) -> s(X) [1] plus(c_mark(X1), X2) -> plus(X1, X2) [1] U11(X1, X2, c_mark(X3)) -> U11(X1, X2, X3) [1] U12(X1, X2, c_active(X3)) -> U12(X1, X2, X3) [1] active(c_plus(N, 0)) -> mark(N) [1] U11(X1, X2, c_active(X3)) -> U11(X1, X2, X3) [1] plus(X1, c_active(X2)) -> plus(X1, X2) [1] mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) [1] U12(X1, c_mark(X2), X3) -> U12(X1, X2, X3) [1] encArg(tt) -> tt [0] encArg(0) -> 0 [0] encArg(cons_active(tt)) -> active(tt) [0] encArg(cons_active(0)) -> active(0) [0] encArg(cons_active(cons_active(x_1'))) -> active(active(encArg(x_1'))) [0] encArg(cons_active(cons_mark(x_1''))) -> active(mark(encArg(x_1''))) [0] encArg(cons_active(cons_U11(x_11, x_2', x_3'))) -> active(U11(encArg(x_11), encArg(x_2'), encArg(x_3'))) [0] encArg(cons_active(cons_U12(x_12, x_2'', x_3''))) -> active(U12(encArg(x_12), encArg(x_2''), encArg(x_3''))) [0] encArg(cons_active(cons_s(x_13))) -> active(s(encArg(x_13))) [0] encArg(cons_active(cons_plus(x_14, x_21))) -> active(plus(encArg(x_14), encArg(x_21))) [0] encArg(cons_active(x_1)) -> active(null_encArg) [0] encArg(cons_mark(tt)) -> mark(tt) [0] encArg(cons_mark(0)) -> mark(0) [0] encArg(cons_mark(cons_active(x_15))) -> mark(active(encArg(x_15))) [0] encArg(cons_mark(cons_mark(x_16))) -> mark(mark(encArg(x_16))) [0] encArg(cons_mark(cons_U11(x_17, x_22, x_31))) -> mark(U11(encArg(x_17), encArg(x_22), encArg(x_31))) [0] encArg(cons_mark(cons_U12(x_18, x_23, x_32))) -> mark(U12(encArg(x_18), encArg(x_23), encArg(x_32))) [0] encArg(cons_mark(cons_s(x_19))) -> mark(s(encArg(x_19))) [0] encArg(cons_mark(cons_plus(x_110, x_24))) -> mark(plus(encArg(x_110), encArg(x_24))) [0] encArg(cons_mark(x_1)) -> mark(null_encArg) [0] encArg(cons_U11(x_1, x_2, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_U12(x_1, x_2, x_3)) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_s(tt)) -> s(tt) [0] encArg(cons_s(0)) -> s(0) [0] encArg(cons_s(cons_active(x_11103))) -> s(active(encArg(x_11103))) [0] encArg(cons_s(cons_mark(x_11104))) -> s(mark(encArg(x_11104))) [0] encArg(cons_s(cons_U11(x_11105, x_2551, x_3367))) -> s(U11(encArg(x_11105), encArg(x_2551), encArg(x_3367))) [0] encArg(cons_s(cons_U12(x_11106, x_2552, x_3368))) -> s(U12(encArg(x_11106), encArg(x_2552), encArg(x_3368))) [0] encArg(cons_s(cons_s(x_11107))) -> s(s(encArg(x_11107))) [0] encArg(cons_s(cons_plus(x_11108, x_2553))) -> s(plus(encArg(x_11108), encArg(x_2553))) [0] encArg(cons_s(x_1)) -> s(null_encArg) [0] encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0] encode_active(tt) -> active(tt) [0] encode_active(0) -> active(0) [0] encode_active(cons_active(x_11169)) -> active(active(encArg(x_11169))) [0] encode_active(cons_mark(x_11170)) -> active(mark(encArg(x_11170))) [0] encode_active(cons_U11(x_11171, x_2584, x_3389)) -> active(U11(encArg(x_11171), encArg(x_2584), encArg(x_3389))) [0] encode_active(cons_U12(x_11172, x_2585, x_3390)) -> active(U12(encArg(x_11172), encArg(x_2585), encArg(x_3390))) [0] encode_active(cons_s(x_11173)) -> active(s(encArg(x_11173))) [0] encode_active(cons_plus(x_11174, x_2586)) -> active(plus(encArg(x_11174), encArg(x_2586))) [0] encode_active(x_1) -> active(null_encArg) [0] encode_U11(x_1, x_2, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_tt -> tt [0] encode_mark(tt) -> mark(tt) [0] encode_mark(0) -> mark(0) [0] encode_mark(cons_active(x_11721)) -> mark(active(encArg(x_11721))) [0] encode_mark(cons_mark(x_11722)) -> mark(mark(encArg(x_11722))) [0] encode_mark(cons_U11(x_11723, x_2860, x_3573)) -> mark(U11(encArg(x_11723), encArg(x_2860), encArg(x_3573))) [0] encode_mark(cons_U12(x_11724, x_2861, x_3574)) -> mark(U12(encArg(x_11724), encArg(x_2861), encArg(x_3574))) [0] encode_mark(cons_s(x_11725)) -> mark(s(encArg(x_11725))) [0] encode_mark(cons_plus(x_11726, x_2862)) -> mark(plus(encArg(x_11726), encArg(x_2862))) [0] encode_mark(x_1) -> mark(null_encArg) [0] encode_U12(x_1, x_2, x_3) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_s(tt) -> s(tt) [0] encode_s(0) -> s(0) [0] encode_s(cons_active(x_12273)) -> s(active(encArg(x_12273))) [0] encode_s(cons_mark(x_12274)) -> s(mark(encArg(x_12274))) [0] encode_s(cons_U11(x_12275, x_21136, x_3757)) -> s(U11(encArg(x_12275), encArg(x_21136), encArg(x_3757))) [0] encode_s(cons_U12(x_12276, x_21137, x_3758)) -> s(U12(encArg(x_12276), encArg(x_21137), encArg(x_3758))) [0] encode_s(cons_s(x_12277)) -> s(s(encArg(x_12277))) [0] encode_s(cons_plus(x_12278, x_21138)) -> s(plus(encArg(x_12278), encArg(x_21138))) [0] encode_s(x_1) -> s(null_encArg) [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] active(x0) -> c_active(x0) [0] plus(x0, x1) -> c_plus(x0, x1) [0] U12(x0, x1, x2) -> c_U12(x0, x1, x2) [0] U11(x0, x1, x2) -> c_U11(x0, x1, x2) [0] mark(x0) -> c_mark(x0) [0] encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_U11(v0, v1, v2) -> null_encode_U11 [0] encode_tt -> null_encode_tt [0] encode_mark(v0) -> null_encode_mark [0] encode_U12(v0, v1, v2) -> null_encode_U12 [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] active(v0) -> null_active [0] plus(v0, v1) -> null_plus [0] U12(v0, v1, v2) -> null_U12 [0] U11(v0, v1, v2) -> null_U11 [0] mark(v0) -> null_mark [0] The TRS has the following type information: mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark tt :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark 0 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark c_U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark c_mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark c_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark c_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark c_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark c_U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encArg :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark cons_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark cons_mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark cons_U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark cons_U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark cons_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark cons_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_tt :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_0 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encArg :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_tt :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_0 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark Rewrite Strategy: INNERMOST ---------------------------------------- (29) 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_s => 0 null_encode_plus => 0 null_encode_0 => 0 null_s => 0 null_active => 0 null_plus => 0 null_U12 => 0 null_U11 => 0 null_mark => 0 ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: U11(z, z', z'') -{ 1 }-> U11(X1, X2, X3) :|: X1 >= 0, X3 >= 0, z' = 1 + X2, X2 >= 0, z = X1, z'' = X3 U11(z, z', z'') -{ 1 }-> U11(X1, X2, X3) :|: X1 >= 0, z = 1 + X1, X3 >= 0, X2 >= 0, z' = X2, z'' = X3 U11(z, z', z'') -{ 1 }-> U11(X1, X2, X3) :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = 1 + X3 U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 U11(z, z', z'') -{ 0 }-> 1 + x0 + x1 + x2 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1, z'' = x2, x2 >= 0 U12(z, z', z'') -{ 1 }-> U12(X1, X2, X3) :|: X1 >= 0, X3 >= 0, z' = 1 + X2, X2 >= 0, z = X1, z'' = X3 U12(z, z', z'') -{ 1 }-> U12(X1, X2, X3) :|: X1 >= 0, z = 1 + X1, X3 >= 0, X2 >= 0, z' = X2, z'' = X3 U12(z, z', z'') -{ 1 }-> U12(X1, X2, X3) :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = 1 + X3 U12(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 U12(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 + N + 0, N >= 0 active(z) -{ 2 }-> mark(s(plus(N, X25))) :|: z = 1 + 1 + (1 + X25) + N, X25 >= 0, N >= 0 active(z) -{ 2 }-> mark(s(plus(N, X26))) :|: z = 1 + 1 + (1 + X26) + N, X26 >= 0, N >= 0 active(z) -{ 2 }-> mark(s(plus(X15, M))) :|: z = 1 + 1 + M + (1 + X15), M >= 0, X15 >= 0 active(z) -{ 2 }-> mark(s(plus(X16, M))) :|: X16 >= 0, M >= 0, z = 1 + 1 + M + (1 + X16) active(z) -{ 1 }-> mark(s(0)) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 1 }-> mark(s(1 + N + M)) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 2 }-> mark(U12(1, M, X35)) :|: z = 1 + 1 + M + (1 + X35), X35 >= 0, M >= 0 active(z) -{ 2 }-> mark(U12(1, M, X36)) :|: X36 >= 0, M >= 0, z = 1 + 1 + M + (1 + X36) active(z) -{ 2 }-> mark(U12(1, X210, N)) :|: z = 1 + 1 + (1 + X210) + N, X210 >= 0, N >= 0 active(z) -{ 2 }-> mark(U12(1, X29, N)) :|: X29 >= 0, z = 1 + 1 + (1 + X29) + N, N >= 0 active(z) -{ 2 }-> mark(U11(1, M, X33)) :|: z = 1 + (1 + X33) + (1 + M), X33 >= 0, M >= 0 active(z) -{ 2 }-> mark(U11(1, M, X34)) :|: z = 1 + (1 + X34) + (1 + M), M >= 0, X34 >= 0 active(z) -{ 2 }-> mark(U11(1, X27, N)) :|: z = 1 + N + (1 + (1 + X27)), X27 >= 0, N >= 0 active(z) -{ 2 }-> mark(U11(1, X28, N)) :|: X28 >= 0, z = 1 + N + (1 + (1 + X28)), N >= 0 active(z) -{ 1 }-> mark(0) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(0) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 1 }-> mark(1 + 1 + M + N) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(1 + 1 + M + N) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 active(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 encArg(z) -{ 0 }-> s(s(encArg(x_11107))) :|: z = 1 + (1 + x_11107), x_11107 >= 0 encArg(z) -{ 0 }-> s(plus(encArg(x_11108), encArg(x_2553))) :|: z = 1 + (1 + x_11108 + x_2553), x_11108 >= 0, x_2553 >= 0 encArg(z) -{ 0 }-> s(mark(encArg(x_11104))) :|: z = 1 + (1 + x_11104), x_11104 >= 0 encArg(z) -{ 0 }-> s(active(encArg(x_11103))) :|: z = 1 + (1 + x_11103), x_11103 >= 0 encArg(z) -{ 0 }-> s(U12(encArg(x_11106), encArg(x_2552), encArg(x_3368))) :|: z = 1 + (1 + x_11106 + x_2552 + x_3368), x_3368 >= 0, x_11106 >= 0, x_2552 >= 0 encArg(z) -{ 0 }-> s(U11(encArg(x_11105), encArg(x_2551), encArg(x_3367))) :|: z = 1 + (1 + x_11105 + x_2551 + x_3367), x_2551 >= 0, x_11105 >= 0, x_3367 >= 0 encArg(z) -{ 0 }-> s(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> s(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> s(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> mark(s(encArg(x_19))) :|: z = 1 + (1 + x_19), x_19 >= 0 encArg(z) -{ 0 }-> mark(plus(encArg(x_110), encArg(x_24))) :|: z = 1 + (1 + x_110 + x_24), x_24 >= 0, x_110 >= 0 encArg(z) -{ 0 }-> mark(mark(encArg(x_16))) :|: x_16 >= 0, z = 1 + (1 + x_16) encArg(z) -{ 0 }-> mark(active(encArg(x_15))) :|: x_15 >= 0, z = 1 + (1 + x_15) encArg(z) -{ 0 }-> mark(U12(encArg(x_18), encArg(x_23), encArg(x_32))) :|: x_32 >= 0, z = 1 + (1 + x_18 + x_23 + x_32), x_23 >= 0, x_18 >= 0 encArg(z) -{ 0 }-> mark(U11(encArg(x_17), encArg(x_22), encArg(x_31))) :|: z = 1 + (1 + x_17 + x_22 + x_31), x_17 >= 0, x_31 >= 0, x_22 >= 0 encArg(z) -{ 0 }-> mark(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> mark(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> mark(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> active(s(encArg(x_13))) :|: z = 1 + (1 + x_13), x_13 >= 0 encArg(z) -{ 0 }-> active(plus(encArg(x_14), encArg(x_21))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_21), x_21 >= 0 encArg(z) -{ 0 }-> active(mark(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0 encArg(z) -{ 0 }-> active(active(encArg(x_1'))) :|: z = 1 + (1 + x_1'), x_1' >= 0 encArg(z) -{ 0 }-> active(U12(encArg(x_12), encArg(x_2''), encArg(x_3''))) :|: z = 1 + (1 + x_12 + x_2'' + x_3''), x_2'' >= 0, x_12 >= 0, x_3'' >= 0 encArg(z) -{ 0 }-> active(U11(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3') encArg(z) -{ 0 }-> active(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> active(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> active(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> U12(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encArg(z) -{ 0 }-> U11(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, 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', z'') -{ 0 }-> U11(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_U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_U12(z, z', z'') -{ 0 }-> U12(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_U12(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_active(z) -{ 0 }-> active(s(encArg(x_11173))) :|: z = 1 + x_11173, x_11173 >= 0 encode_active(z) -{ 0 }-> active(plus(encArg(x_11174), encArg(x_2586))) :|: x_11174 >= 0, x_2586 >= 0, z = 1 + x_11174 + x_2586 encode_active(z) -{ 0 }-> active(mark(encArg(x_11170))) :|: x_11170 >= 0, z = 1 + x_11170 encode_active(z) -{ 0 }-> active(active(encArg(x_11169))) :|: x_11169 >= 0, z = 1 + x_11169 encode_active(z) -{ 0 }-> active(U12(encArg(x_11172), encArg(x_2585), encArg(x_3390))) :|: x_3390 >= 0, z = 1 + x_11172 + x_2585 + x_3390, x_11172 >= 0, x_2585 >= 0 encode_active(z) -{ 0 }-> active(U11(encArg(x_11171), encArg(x_2584), encArg(x_3389))) :|: x_11171 >= 0, x_2584 >= 0, x_3389 >= 0, z = 1 + x_11171 + x_2584 + x_3389 encode_active(z) -{ 0 }-> active(1) :|: z = 1 encode_active(z) -{ 0 }-> active(0) :|: z = 0 encode_active(z) -{ 0 }-> active(0) :|: x_1 >= 0, z = x_1 encode_active(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_mark(z) -{ 0 }-> mark(s(encArg(x_11725))) :|: z = 1 + x_11725, x_11725 >= 0 encode_mark(z) -{ 0 }-> mark(plus(encArg(x_11726), encArg(x_2862))) :|: z = 1 + x_11726 + x_2862, x_2862 >= 0, x_11726 >= 0 encode_mark(z) -{ 0 }-> mark(mark(encArg(x_11722))) :|: z = 1 + x_11722, x_11722 >= 0 encode_mark(z) -{ 0 }-> mark(active(encArg(x_11721))) :|: z = 1 + x_11721, x_11721 >= 0 encode_mark(z) -{ 0 }-> mark(U12(encArg(x_11724), encArg(x_2861), encArg(x_3574))) :|: x_2861 >= 0, x_11724 >= 0, x_3574 >= 0, z = 1 + x_11724 + x_2861 + x_3574 encode_mark(z) -{ 0 }-> mark(U11(encArg(x_11723), encArg(x_2860), encArg(x_3573))) :|: x_11723 >= 0, x_3573 >= 0, x_2860 >= 0, z = 1 + x_11723 + x_2860 + x_3573 encode_mark(z) -{ 0 }-> mark(1) :|: z = 1 encode_mark(z) -{ 0 }-> mark(0) :|: z = 0 encode_mark(z) -{ 0 }-> mark(0) :|: x_1 >= 0, z = x_1 encode_mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_plus(z, z') -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_s(z) -{ 0 }-> s(s(encArg(x_12277))) :|: z = 1 + x_12277, x_12277 >= 0 encode_s(z) -{ 0 }-> s(plus(encArg(x_12278), encArg(x_21138))) :|: x_21138 >= 0, z = 1 + x_12278 + x_21138, x_12278 >= 0 encode_s(z) -{ 0 }-> s(mark(encArg(x_12274))) :|: z = 1 + x_12274, x_12274 >= 0 encode_s(z) -{ 0 }-> s(active(encArg(x_12273))) :|: z = 1 + x_12273, x_12273 >= 0 encode_s(z) -{ 0 }-> s(U12(encArg(x_12276), encArg(x_21137), encArg(x_3758))) :|: z = 1 + x_12276 + x_21137 + x_3758, x_21137 >= 0, x_3758 >= 0, x_12276 >= 0 encode_s(z) -{ 0 }-> s(U11(encArg(x_12275), encArg(x_21136), encArg(x_3757))) :|: x_12275 >= 0, z = 1 + x_12275 + x_21136 + x_3757, x_21136 >= 0, x_3757 >= 0 encode_s(z) -{ 0 }-> s(1) :|: z = 1 encode_s(z) -{ 0 }-> s(0) :|: z = 0 encode_s(z) -{ 0 }-> s(0) :|: x_1 >= 0, z = x_1 encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_tt -{ 0 }-> 1 :|: encode_tt -{ 0 }-> 0 :|: mark(z) -{ 2 }-> active(s(active(s(mark(X''))))) :|: z = 1 + (1 + X''), X'' >= 0 mark(z) -{ 2 }-> active(s(active(plus(mark(X14), mark(X24))))) :|: z = 1 + (1 + X14 + X24), X14 >= 0, X24 >= 0 mark(z) -{ 2 }-> active(s(active(U12(mark(X12), X22, X31)))) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22 + X31), X31 >= 0 mark(z) -{ 2 }-> active(s(active(U11(mark(X13), X23, X32)))) :|: X32 >= 0, z = 1 + (1 + X13 + X23 + X32), X13 >= 0, X23 >= 0 mark(z) -{ 2 }-> active(s(active(1))) :|: z = 1 + 1 mark(z) -{ 2 }-> active(s(active(0))) :|: z = 1 + 0 mark(z) -{ 1 }-> active(s(0)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(s(1 + X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(plus(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> active(U12(active(s(mark(X'))), X2, X3)) :|: z = 1 + (1 + X') + X2 + X3, X3 >= 0, X' >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U12(active(plus(mark(X11), mark(X21))), X2, X3)) :|: X11 >= 0, X21 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X11 + X21) + X2 + X3 mark(z) -{ 2 }-> active(U12(active(U12(mark(X1'), X2', X3')), X2, X3)) :|: X3' >= 0, X2' >= 0, z = 1 + (1 + X1' + X2' + X3') + X2 + X3, X1' >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U12(active(U11(mark(X1''), X2'', X3'')), X2, X3)) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + X3, X3'' >= 0, X3 >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U12(active(1), X2, X3)) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U12(active(0), X2, X3)) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 1 }-> active(U12(0, X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> active(U12(1 + X1, X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(s(mark(X4))), X2, X3)) :|: z = 1 + (1 + X4) + X2 + X3, X3 >= 0, X4 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(plus(mark(X19), mark(X213))), X2, X3)) :|: X19 >= 0, X213 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X19 + X213) + X2 + X3 mark(z) -{ 2 }-> active(U11(active(U12(mark(X17), X211, X37)), X2, X3)) :|: X37 >= 0, X17 >= 0, X3 >= 0, X211 >= 0, z = 1 + (1 + X17 + X211 + X37) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(U11(mark(X18), X212, X38)), X2, X3)) :|: X212 >= 0, X38 >= 0, X18 >= 0, X3 >= 0, z = 1 + (1 + X18 + X212 + X38) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(1), X2, X3)) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(0), X2, X3)) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 1 }-> active(U11(0, X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> active(U11(1 + X1, X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> active(1) :|: z = 1 mark(z) -{ 1 }-> active(0) :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 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 ---------------------------------------- (31) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: U11(z, z', z'') -{ 1 }-> U11(z, z', z'' - 1) :|: z >= 0, z'' - 1 >= 0, z' >= 0 U11(z, z', z'') -{ 1 }-> U11(z, z' - 1, z'') :|: z >= 0, z'' >= 0, z' - 1 >= 0 U11(z, z', z'') -{ 1 }-> U11(z - 1, z', z'') :|: z - 1 >= 0, z'' >= 0, z' >= 0 U11(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 U11(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z >= 0, z' >= 0, z'' >= 0 U12(z, z', z'') -{ 1 }-> U12(z, z', z'' - 1) :|: z >= 0, z'' - 1 >= 0, z' >= 0 U12(z, z', z'') -{ 1 }-> U12(z, z' - 1, z'') :|: z >= 0, z'' >= 0, z' - 1 >= 0 U12(z, z', z'') -{ 1 }-> U12(z - 1, z', z'') :|: z - 1 >= 0, z'' >= 0, z' >= 0 U12(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 U12(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z >= 0, z' >= 0, z'' >= 0 active(z) -{ 2 }-> mark(s(plus(N, X25))) :|: z = 1 + 1 + (1 + X25) + N, X25 >= 0, N >= 0 active(z) -{ 2 }-> mark(s(plus(N, X26))) :|: z = 1 + 1 + (1 + X26) + N, X26 >= 0, N >= 0 active(z) -{ 2 }-> mark(s(plus(X15, M))) :|: z = 1 + 1 + M + (1 + X15), M >= 0, X15 >= 0 active(z) -{ 2 }-> mark(s(plus(X16, M))) :|: X16 >= 0, M >= 0, z = 1 + 1 + M + (1 + X16) active(z) -{ 1 }-> mark(s(0)) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 1 }-> mark(s(1 + N + M)) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 2 }-> mark(U12(1, M, X35)) :|: z = 1 + 1 + M + (1 + X35), X35 >= 0, M >= 0 active(z) -{ 2 }-> mark(U12(1, M, X36)) :|: X36 >= 0, M >= 0, z = 1 + 1 + M + (1 + X36) active(z) -{ 2 }-> mark(U12(1, X210, N)) :|: z = 1 + 1 + (1 + X210) + N, X210 >= 0, N >= 0 active(z) -{ 2 }-> mark(U12(1, X29, N)) :|: X29 >= 0, z = 1 + 1 + (1 + X29) + N, N >= 0 active(z) -{ 2 }-> mark(U11(1, M, X33)) :|: z = 1 + (1 + X33) + (1 + M), X33 >= 0, M >= 0 active(z) -{ 2 }-> mark(U11(1, M, X34)) :|: z = 1 + (1 + X34) + (1 + M), M >= 0, X34 >= 0 active(z) -{ 2 }-> mark(U11(1, X27, N)) :|: z = 1 + N + (1 + (1 + X27)), X27 >= 0, N >= 0 active(z) -{ 2 }-> mark(U11(1, X28, N)) :|: X28 >= 0, z = 1 + N + (1 + (1 + X28)), N >= 0 active(z) -{ 1 }-> mark(0) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(0) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 1 }-> mark(z - 1) :|: z - 1 >= 0 active(z) -{ 1 }-> mark(1 + 1 + M + N) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(1 + 1 + M + N) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 0 }-> 0 :|: z >= 0 active(z) -{ 0 }-> 1 + z :|: z >= 0 encArg(z) -{ 0 }-> s(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(plus(encArg(x_11108), encArg(x_2553))) :|: z = 1 + (1 + x_11108 + x_2553), x_11108 >= 0, x_2553 >= 0 encArg(z) -{ 0 }-> s(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(U12(encArg(x_11106), encArg(x_2552), encArg(x_3368))) :|: z = 1 + (1 + x_11106 + x_2552 + x_3368), x_3368 >= 0, x_11106 >= 0, x_2552 >= 0 encArg(z) -{ 0 }-> s(U11(encArg(x_11105), encArg(x_2551), encArg(x_3367))) :|: z = 1 + (1 + x_11105 + x_2551 + x_3367), x_2551 >= 0, x_11105 >= 0, x_3367 >= 0 encArg(z) -{ 0 }-> s(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> s(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> s(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> mark(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(plus(encArg(x_110), encArg(x_24))) :|: z = 1 + (1 + x_110 + x_24), x_24 >= 0, x_110 >= 0 encArg(z) -{ 0 }-> mark(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(U12(encArg(x_18), encArg(x_23), encArg(x_32))) :|: x_32 >= 0, z = 1 + (1 + x_18 + x_23 + x_32), x_23 >= 0, x_18 >= 0 encArg(z) -{ 0 }-> mark(U11(encArg(x_17), encArg(x_22), encArg(x_31))) :|: z = 1 + (1 + x_17 + x_22 + x_31), x_17 >= 0, x_31 >= 0, x_22 >= 0 encArg(z) -{ 0 }-> mark(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> mark(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> mark(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> active(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(plus(encArg(x_14), encArg(x_21))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_21), x_21 >= 0 encArg(z) -{ 0 }-> active(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(U12(encArg(x_12), encArg(x_2''), encArg(x_3''))) :|: z = 1 + (1 + x_12 + x_2'' + x_3''), x_2'' >= 0, x_12 >= 0, x_3'' >= 0 encArg(z) -{ 0 }-> active(U11(encArg(x_11), encArg(x_2'), encArg(x_3'))) :|: x_11 >= 0, x_3' >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2' + x_3') encArg(z) -{ 0 }-> active(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> active(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> active(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> U12(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encArg(z) -{ 0 }-> U11(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encode_0 -{ 0 }-> 0 :|: encode_U11(z, z', z'') -{ 0 }-> U11(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0 encode_U11(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 encode_U12(z, z', z'') -{ 0 }-> U12(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0 encode_U12(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 encode_active(z) -{ 0 }-> active(s(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(plus(encArg(x_11174), encArg(x_2586))) :|: x_11174 >= 0, x_2586 >= 0, z = 1 + x_11174 + x_2586 encode_active(z) -{ 0 }-> active(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(active(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(U12(encArg(x_11172), encArg(x_2585), encArg(x_3390))) :|: x_3390 >= 0, z = 1 + x_11172 + x_2585 + x_3390, x_11172 >= 0, x_2585 >= 0 encode_active(z) -{ 0 }-> active(U11(encArg(x_11171), encArg(x_2584), encArg(x_3389))) :|: x_11171 >= 0, x_2584 >= 0, x_3389 >= 0, z = 1 + x_11171 + x_2584 + x_3389 encode_active(z) -{ 0 }-> active(1) :|: z = 1 encode_active(z) -{ 0 }-> active(0) :|: z = 0 encode_active(z) -{ 0 }-> active(0) :|: z >= 0 encode_active(z) -{ 0 }-> 0 :|: z >= 0 encode_mark(z) -{ 0 }-> mark(s(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(plus(encArg(x_11726), encArg(x_2862))) :|: z = 1 + x_11726 + x_2862, x_2862 >= 0, x_11726 >= 0 encode_mark(z) -{ 0 }-> mark(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(active(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(U12(encArg(x_11724), encArg(x_2861), encArg(x_3574))) :|: x_2861 >= 0, x_11724 >= 0, x_3574 >= 0, z = 1 + x_11724 + x_2861 + x_3574 encode_mark(z) -{ 0 }-> mark(U11(encArg(x_11723), encArg(x_2860), encArg(x_3573))) :|: x_11723 >= 0, x_3573 >= 0, x_2860 >= 0, z = 1 + x_11723 + x_2860 + x_3573 encode_mark(z) -{ 0 }-> mark(1) :|: z = 1 encode_mark(z) -{ 0 }-> mark(0) :|: z = 0 encode_mark(z) -{ 0 }-> mark(0) :|: z >= 0 encode_mark(z) -{ 0 }-> 0 :|: z >= 0 encode_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_s(z) -{ 0 }-> s(s(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(plus(encArg(x_12278), encArg(x_21138))) :|: x_21138 >= 0, z = 1 + x_12278 + x_21138, x_12278 >= 0 encode_s(z) -{ 0 }-> s(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(active(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(U12(encArg(x_12276), encArg(x_21137), encArg(x_3758))) :|: z = 1 + x_12276 + x_21137 + x_3758, x_21137 >= 0, x_3758 >= 0, x_12276 >= 0 encode_s(z) -{ 0 }-> s(U11(encArg(x_12275), encArg(x_21136), encArg(x_3757))) :|: x_12275 >= 0, z = 1 + x_12275 + x_21136 + x_3757, x_21136 >= 0, x_3757 >= 0 encode_s(z) -{ 0 }-> s(1) :|: z = 1 encode_s(z) -{ 0 }-> s(0) :|: z = 0 encode_s(z) -{ 0 }-> s(0) :|: z >= 0 encode_s(z) -{ 0 }-> 0 :|: z >= 0 encode_tt -{ 0 }-> 1 :|: encode_tt -{ 0 }-> 0 :|: mark(z) -{ 2 }-> active(s(active(s(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(s(active(plus(mark(X14), mark(X24))))) :|: z = 1 + (1 + X14 + X24), X14 >= 0, X24 >= 0 mark(z) -{ 2 }-> active(s(active(U12(mark(X12), X22, X31)))) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22 + X31), X31 >= 0 mark(z) -{ 2 }-> active(s(active(U11(mark(X13), X23, X32)))) :|: X32 >= 0, z = 1 + (1 + X13 + X23 + X32), X13 >= 0, X23 >= 0 mark(z) -{ 2 }-> active(s(active(1))) :|: z = 1 + 1 mark(z) -{ 2 }-> active(s(active(0))) :|: z = 1 + 0 mark(z) -{ 1 }-> active(s(0)) :|: z - 1 >= 0 mark(z) -{ 1 }-> active(s(1 + (z - 1))) :|: z - 1 >= 0 mark(z) -{ 1 }-> active(plus(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> active(U12(active(s(mark(X'))), X2, X3)) :|: z = 1 + (1 + X') + X2 + X3, X3 >= 0, X' >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U12(active(plus(mark(X11), mark(X21))), X2, X3)) :|: X11 >= 0, X21 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X11 + X21) + X2 + X3 mark(z) -{ 2 }-> active(U12(active(U12(mark(X1'), X2', X3')), X2, X3)) :|: X3' >= 0, X2' >= 0, z = 1 + (1 + X1' + X2' + X3') + X2 + X3, X1' >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U12(active(U11(mark(X1''), X2'', X3'')), X2, X3)) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + X3, X3'' >= 0, X3 >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U12(active(1), X2, X3)) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U12(active(0), X2, X3)) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 1 }-> active(U12(0, X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> active(U12(1 + X1, X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(s(mark(X4))), X2, X3)) :|: z = 1 + (1 + X4) + X2 + X3, X3 >= 0, X4 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(plus(mark(X19), mark(X213))), X2, X3)) :|: X19 >= 0, X213 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X19 + X213) + X2 + X3 mark(z) -{ 2 }-> active(U11(active(U12(mark(X17), X211, X37)), X2, X3)) :|: X37 >= 0, X17 >= 0, X3 >= 0, X211 >= 0, z = 1 + (1 + X17 + X211 + X37) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(U11(mark(X18), X212, X38)), X2, X3)) :|: X212 >= 0, X38 >= 0, X18 >= 0, X3 >= 0, z = 1 + (1 + X18 + X212 + X38) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(1), X2, X3)) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(0), X2, X3)) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 1 }-> active(U11(0, X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> active(U11(1 + X1, X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> active(1) :|: z = 1 mark(z) -{ 1 }-> active(0) :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 1 + z :|: z >= 0 plus(z, z') -{ 1 }-> plus(z, z' - 1) :|: z >= 0, z' - 1 >= 0 plus(z, z') -{ 1 }-> plus(z - 1, z') :|: z - 1 >= 0, z' >= 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0 s(z) -{ 1 }-> s(z - 1) :|: z - 1 >= 0 s(z) -{ 0 }-> 0 :|: z >= 0 s(z) -{ 0 }-> 1 + z :|: z >= 0 ---------------------------------------- (33) 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, v2) -> null_encode_U11 [0] encode_tt -> null_encode_tt [0] encode_mark(v0) -> null_encode_mark [0] encode_U12(v0, v1, v2) -> null_encode_U12 [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] active(v0) -> null_active [0] plus(v0, v1) -> null_plus [0] U12(v0, v1, v2) -> null_U12 [0] U11(v0, v1, v2) -> 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_s, null_encode_plus, null_encode_0, null_s, null_active, null_plus, null_U12, null_U11, null_mark ---------------------------------------- (34) 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] mark(c_U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3)) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] U12(X1, c_active(X2), X3) -> U12(X1, X2, X3) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] U12(c_mark(X1), X2, X3) -> U12(X1, X2, X3) [1] active(c_U12(tt, M, N)) -> mark(s(plus(N, M))) [1] U11(X1, c_mark(X2), X3) -> U11(X1, X2, X3) [1] U11(c_active(X1), X2, X3) -> U11(X1, X2, X3) [1] s(c_active(X)) -> s(X) [1] active(c_plus(N, c_s(M))) -> mark(U11(tt, M, N)) [1] active(c_U11(tt, M, N)) -> mark(U12(tt, M, N)) [1] U12(X1, X2, c_mark(X3)) -> U12(X1, X2, X3) [1] U11(X1, c_active(X2), X3) -> U11(X1, X2, X3) [1] U12(c_active(X1), X2, X3) -> U12(X1, X2, X3) [1] U11(c_mark(X1), X2, X3) -> U11(X1, X2, X3) [1] mark(c_U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)) [1] s(c_mark(X)) -> s(X) [1] plus(c_mark(X1), X2) -> plus(X1, X2) [1] U11(X1, X2, c_mark(X3)) -> U11(X1, X2, X3) [1] U12(X1, X2, c_active(X3)) -> U12(X1, X2, X3) [1] active(c_plus(N, 0)) -> mark(N) [1] U11(X1, X2, c_active(X3)) -> U11(X1, X2, X3) [1] plus(X1, c_active(X2)) -> plus(X1, X2) [1] mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) [1] U12(X1, c_mark(X2), X3) -> U12(X1, X2, X3) [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, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_U12(x_1, x_2, x_3)) -> U12(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, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_tt -> tt [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_U12(x_1, x_2, x_3) -> U12(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] active(x0) -> c_active(x0) [0] plus(x0, x1) -> c_plus(x0, x1) [0] U12(x0, x1, x2) -> c_U12(x0, x1, x2) [0] U11(x0, x1, x2) -> c_U11(x0, x1, x2) [0] mark(x0) -> c_mark(x0) [0] encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_U11(v0, v1, v2) -> null_encode_U11 [0] encode_tt -> null_encode_tt [0] encode_mark(v0) -> null_encode_mark [0] encode_U12(v0, v1, v2) -> null_encode_U12 [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] active(v0) -> null_active [0] plus(v0, v1) -> null_plus [0] U12(v0, v1, v2) -> null_U12 [0] U11(v0, v1, v2) -> null_U11 [0] mark(v0) -> null_mark [0] The TRS has the following type information: mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark tt :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark active :: 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tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> 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tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark c_U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> 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tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark cons_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> 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tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark cons_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark cons_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_tt :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark -> tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark encode_0 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encArg :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_tt :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_encode_0 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_s :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_active :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_plus :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_U12 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_U11 :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark null_mark :: tt:0:c_U12:c_mark:c_active:c_s:c_plus:c_U11:cons_active:cons_mark:cons_U11:cons_U12:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_s:null_encode_plus:null_encode_0:null_s:null_active:null_plus:null_U12:null_U11:null_mark Rewrite Strategy: INNERMOST ---------------------------------------- (35) 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_s => 0 null_encode_plus => 0 null_encode_0 => 0 null_s => 0 null_active => 0 null_plus => 0 null_U12 => 0 null_U11 => 0 null_mark => 0 ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: U11(z, z', z'') -{ 1 }-> U11(X1, X2, X3) :|: X1 >= 0, X3 >= 0, z' = 1 + X2, X2 >= 0, z = X1, z'' = X3 U11(z, z', z'') -{ 1 }-> U11(X1, X2, X3) :|: X1 >= 0, z = 1 + X1, X3 >= 0, X2 >= 0, z' = X2, z'' = X3 U11(z, z', z'') -{ 1 }-> U11(X1, X2, X3) :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = 1 + X3 U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 U11(z, z', z'') -{ 0 }-> 1 + x0 + x1 + x2 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1, z'' = x2, x2 >= 0 U12(z, z', z'') -{ 1 }-> U12(X1, X2, X3) :|: X1 >= 0, X3 >= 0, z' = 1 + X2, X2 >= 0, z = X1, z'' = X3 U12(z, z', z'') -{ 1 }-> U12(X1, X2, X3) :|: X1 >= 0, z = 1 + X1, X3 >= 0, X2 >= 0, z' = X2, z'' = X3 U12(z, z', z'') -{ 1 }-> U12(X1, X2, X3) :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = 1 + X3 U12(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 U12(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 + N + 0, N >= 0 active(z) -{ 1 }-> mark(s(plus(N, M))) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 1 }-> mark(U12(1, M, N)) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 1 }-> mark(U11(1, M, N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 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 }-> active(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> U12(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encArg(z) -{ 0 }-> U11(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, 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', z'') -{ 0 }-> U11(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_U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_U12(z, z', z'') -{ 0 }-> U12(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_U12(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_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 :|: 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(U12(mark(X1), X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> active(U11(mark(X1), X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> active(1) :|: z = 1 mark(z) -{ 1 }-> active(0) :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 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. ---------------------------------------- (37) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(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, z2) -> U11(encArg(z0), encArg(z1), encArg(z2)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_U12(z0, z1, z2) -> U12(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(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, z2)) -> c4(U11'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U12(z0, z1, z2)) -> c5(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ACTIVE(z0) -> c8(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_U11(z0, z1, z2) -> c9(U11'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCODE_TT -> c10 ENCODE_MARK(z0) -> c11(MARK(encArg(z0)), ENCARG(z0)) ENCODE_U12(z0, z1, z2) -> c12(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCODE_S(z0) -> c13(S(encArg(z0)), ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c14(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_0 -> c15 S(z0) -> c16 S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(z0) -> c19 ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, z1) -> c24 PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, z1, z2) -> c29 U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, z1, z2) -> c36 U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(z0) -> c43 MARK(tt) -> c44(ACTIVE(tt)) MARK(0) -> c45(ACTIVE(0)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44(ACTIVE(tt)) MARK(0) -> c45(ACTIVE(0)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) K tuples:none Defined Rule Symbols: mark_1, plus_2, U12_3, active_1, U11_3, s_1, encArg_1, encode_active_1, encode_U11_3, encode_tt, encode_mark_1, encode_U12_3, encode_s_1, encode_plus_2, encode_0 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_TT, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_0, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1 Compound Symbols: c, c1, c2_2, c3_2, c4_4, c5_4, c6_2, c7_3, c8_2, c9_4, c10, c11_2, c12_4, c13_2, c14_3, c15, c16, c17_1, c18_1, c19, c20_3, c21_2, c22_2, c23_1, c24, c25_1, c26_1, c27_1, c28_1, c29, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43, c44_1, c45_1, c46_3, c47_3, c48_3, c49_4 ---------------------------------------- (39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: S(z0) -> c16 ENCARG(0) -> c1 ENCODE_0 -> c15 U11'(z0, z1, z2) -> c36 ACTIVE(z0) -> c19 ENCARG(tt) -> c U12'(z0, z1, z2) -> c29 ENCODE_TT -> c10 PLUS(z0, z1) -> c24 MARK(z0) -> c43 ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(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, z2) -> U11(encArg(z0), encArg(z1), encArg(z2)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_U12(z0, z1, z2) -> U12(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(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, z2)) -> c4(U11'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U12(z0, z1, z2)) -> c5(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ACTIVE(z0) -> c8(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_U11(z0, z1, z2) -> c9(U11'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCODE_MARK(z0) -> c11(MARK(encArg(z0)), ENCARG(z0)) ENCODE_U12(z0, z1, z2) -> c12(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCODE_S(z0) -> c13(S(encArg(z0)), ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c14(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44(ACTIVE(tt)) MARK(0) -> c45(ACTIVE(0)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44(ACTIVE(tt)) MARK(0) -> c45(ACTIVE(0)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) K tuples:none Defined Rule Symbols: mark_1, plus_2, U12_3, active_1, U11_3, s_1, encArg_1, encode_active_1, encode_U11_3, encode_tt, encode_mark_1, encode_U12_3, encode_s_1, encode_plus_2, encode_0 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1 Compound Symbols: c2_2, c3_2, c4_4, c5_4, c6_2, c7_3, c8_2, c9_4, c11_2, c12_4, c13_2, c14_3, c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44_1, c45_1, c46_3, c47_3, c48_3, c49_4 ---------------------------------------- (41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(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, z2) -> U11(encArg(z0), encArg(z1), encArg(z2)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_U12(z0, z1, z2) -> U12(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(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, z2)) -> c4(U11'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U12(z0, z1, z2)) -> c5(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ACTIVE(z0) -> c8(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_U11(z0, z1, z2) -> c9(U11'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCODE_MARK(z0) -> c11(MARK(encArg(z0)), ENCARG(z0)) ENCODE_U12(z0, z1, z2) -> c12(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCODE_S(z0) -> c13(S(encArg(z0)), ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c14(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: mark_1, plus_2, U12_3, active_1, U11_3, s_1, encArg_1, encode_active_1, encode_U11_3, encode_tt, encode_mark_1, encode_U12_3, encode_s_1, encode_plus_2, encode_0 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1 Compound Symbols: c2_2, c3_2, c4_4, c5_4, c6_2, c7_3, c8_2, c9_4, c11_2, c12_4, c13_2, c14_3, c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45 ---------------------------------------- (43) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(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, z2) -> U11(encArg(z0), encArg(z1), encArg(z2)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_U12(z0, z1, z2) -> U12(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(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, z2)) -> c4(U11'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U12(z0, z1, z2)) -> c5(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_ACTIVE(z0) -> c(ENCARG(z0)) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U11(z0, z1, z2) -> c(ENCARG(z0)) ENCODE_U11(z0, z1, z2) -> c(ENCARG(z1)) ENCODE_U11(z0, z1, z2) -> c(ENCARG(z2)) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_MARK(z0) -> c(ENCARG(z0)) ENCODE_U12(z0, z1, z2) -> c(U12'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U12(z0, z1, z2) -> c(ENCARG(z0)) ENCODE_U12(z0, z1, z2) -> c(ENCARG(z1)) ENCODE_U12(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: mark_1, plus_2, U12_3, active_1, U11_3, s_1, encArg_1, encode_active_1, encode_U11_3, encode_tt, encode_mark_1, encode_U12_3, encode_s_1, encode_plus_2, encode_0 Defined Pair Symbols: ENCARG_1, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c2_2, c3_2, c4_4, c5_4, c6_2, c7_3, c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1 ---------------------------------------- (45) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 11 leading nodes: ENCODE_ACTIVE(z0) -> c(ENCARG(z0)) ENCODE_U11(z0, z1, z2) -> c(ENCARG(z0)) ENCODE_U11(z0, z1, z2) -> c(ENCARG(z1)) ENCODE_U11(z0, z1, z2) -> c(ENCARG(z2)) ENCODE_MARK(z0) -> c(ENCARG(z0)) ENCODE_U12(z0, z1, z2) -> c(ENCARG(z0)) ENCODE_U12(z0, z1, z2) -> c(ENCARG(z1)) ENCODE_U12(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)) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(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, z2) -> U11(encArg(z0), encArg(z1), encArg(z2)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_U12(z0, z1, z2) -> U12(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(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, z2)) -> c4(U11'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U12(z0, z1, z2)) -> c5(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: mark_1, plus_2, U12_3, active_1, U11_3, s_1, encArg_1, encode_active_1, encode_U11_3, encode_tt, encode_mark_1, encode_U12_3, encode_s_1, encode_plus_2, encode_0 Defined Pair Symbols: ENCARG_1, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c2_2, c3_2, c4_4, c5_4, c6_2, c7_3, c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1 ---------------------------------------- (47) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_active(z0) -> active(encArg(z0)) encode_U11(z0, z1, z2) -> U11(encArg(z0), encArg(z1), encArg(z2)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_U12(z0, z1, z2) -> U12(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_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, z2)) -> c4(U11'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U12(z0, z1, z2)) -> c5(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c2_2, c3_2, c4_4, c5_4, c6_2, c7_3, c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1 ---------------------------------------- (49) 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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_U11(z0, z1, z2)) -> c4(U11'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U12(z0, z1, z2)) -> c5(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c3_2, c4_4, c5_4, c6_2, c7_3, c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2 ---------------------------------------- (51) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_active(0)) -> c2(ACTIVE(0), ENCARG(0)) ENCARG(cons_active(tt)) -> c2(ACTIVE(tt), ENCARG(tt)) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_U11(z0, z1, z2)) -> c4(U11'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U12(z0, z1, z2)) -> c5(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c3_2, c4_4, c5_4, c6_2, c7_3, c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2 ---------------------------------------- (53) 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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: ENCARG(cons_U11(z0, z1, z2)) -> c4(U11'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U12(z0, z1, z2)) -> c5(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c4_4, c5_4, c6_2, c7_3, c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2 ---------------------------------------- (55) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: ENCARG(cons_U11(z0, z1, z2)) -> c4(U11'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U12(z0, z1, z2)) -> c5(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c4_4, c5_4, c6_2, c7_3, c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U11(z0, z1, z2)) -> c4(U11'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) by ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1), ENCARG(tt)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1), ENCARG(0)) ENCARG(cons_U11(x0, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(tt), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(0), ENCARG(x2)) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(tt), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(0), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: ENCARG(cons_U12(z0, z1, z2)) -> c5(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1), ENCARG(tt)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1), ENCARG(0)) ENCARG(cons_U11(x0, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(tt), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(0), ENCARG(x2)) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(tt), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(0), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c5_4, c6_2, c7_3, c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: ENCARG(cons_U12(z0, z1, z2)) -> c5(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c5_4, c6_2, c7_3, c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U12(z0, z1, z2)) -> c5(U12'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) by ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1), ENCARG(tt)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1), ENCARG(0)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(tt), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(0), ENCARG(x2)) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(tt), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(0), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1), ENCARG(tt)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1), ENCARG(0)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(tt), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(0), ENCARG(x2)) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(tt), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(0), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c6_2, c7_3, c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c6_2, c7_3, c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) by ENCARG(cons_s(tt)) -> c6(S(tt), ENCARG(tt)) ENCARG(cons_s(0)) -> c6(S(0), ENCARG(0)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(tt)) -> c6(S(tt), ENCARG(tt)) ENCARG(cons_s(0)) -> c6(S(0), ENCARG(0)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c7_3, c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2 ---------------------------------------- (67) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_s(0)) -> c6(S(0), ENCARG(0)) ENCARG(cons_s(tt)) -> c6(S(tt), ENCARG(tt)) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c7_3, c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c17_1, c18_1, c20_3, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVE(c_U12(tt, z0, z1)) -> c20(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) by ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c17_1, c18_1, c21_2, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVE(c_plus(z0, c_s(z1))) -> c21(MARK(U11(tt, z1, z0)), U11'(tt, z1, z0)) by ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c17_1, c18_1, c22_2, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVE(c_U11(tt, z0, z1)) -> c22(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1)) by ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c46_3, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(c_U12(z0, z1, z2)) -> c46(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0)) by MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c47_3, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(c_s(z0)) -> c47(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) by MARK(c_s(x0)) -> c47(ACTIVE(c_s(mark(x0))), S(mark(x0)), MARK(x0)) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(ACTIVE(c_s(mark(x0))), S(mark(x0)), MARK(x0)) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(ACTIVE(c_s(mark(x0))), S(mark(x0)), MARK(x0)) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c48_3, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(c_U11(z0, z1, z2)) -> c48(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0)) by MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c49_4, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(c_plus(z0, z1)) -> c49(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) by MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4 ---------------------------------------- (89) 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, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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)))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(tt) -> c(ACTIVE(tt)) ENCODE_ACTIVE(0) -> c(ACTIVE(0)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4 ---------------------------------------- (91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_ACTIVE(tt) -> c(ACTIVE(tt)) ENCODE_ACTIVE(0) -> c(ACTIVE(0)) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_U11(z0, z1, z2) -> c(U11'(encArg(z0), encArg(z1), encArg(z2))) by ENCODE_U11(x0, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4 ---------------------------------------- (95) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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)))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4 ---------------------------------------- (97) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 2 leading nodes: ENCODE_MARK(tt) -> c(MARK(tt)) ENCODE_MARK(0) -> c(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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCODE_U12(z0, z1, z2) -> c(U12'(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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_U12(z0, z1, z2) -> c(U12'(encArg(z0), encArg(z1), encArg(z2))) by ENCODE_U12(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4 ---------------------------------------- (101) 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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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)))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4 ---------------------------------------- (103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_S(tt) -> c(S(tt)) ENCODE_S(0) -> c(S(0)) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c_1, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4 ---------------------------------------- (105) 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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 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, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1 ---------------------------------------- (107) 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(x0))) -> c2(ACTIVE(c_active(encArg(x0))), ENCARG(cons_active(x0))) 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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(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)))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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(x0))) -> c2(ACTIVE(c_active(encArg(x0))), ENCARG(cons_active(x0))) 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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1 ---------------------------------------- (109) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(0))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_1 ---------------------------------------- (111) 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(x0))) -> c2(ACTIVE(c_mark(encArg(x0))), ENCARG(cons_mark(x0))) 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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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)))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_active(cons_U11(z0, z1, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(0))) ENCARG(cons_active(cons_mark(x0))) -> c2(ACTIVE(c_mark(encArg(x0))), ENCARG(cons_mark(x0))) 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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_1 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_active(cons_U11(z0, z1, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(0))) 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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_1 ---------------------------------------- (115) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_active(cons_U11(z0, z1, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_1, c1_1 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_U11(z0, z1, z2))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) by ENCARG(cons_active(cons_U11(x0, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_1, c1_1 ---------------------------------------- (119) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_U12(z0, z1, z2))) -> c2(ACTIVE(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) by ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_1, c1_1 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) by ENCARG(cons_active(cons_s(x0))) -> c2(ACTIVE(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt)), ENCARG(cons_s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0)), ENCARG(cons_s(0))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(x0))) -> c2(ACTIVE(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt)), ENCARG(cons_s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0)), ENCARG(cons_s(0))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_1, c1_1 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c2_2, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_1, c1_1 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) by ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 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, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) by ENCARG(cons_mark(cons_active(x0))) -> c3(MARK(c_active(encArg(x0))), ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt)), ENCARG(cons_active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0)), ENCARG(cons_active(0))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(x0))) -> c3(MARK(c_active(encArg(x0))), ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt)), ENCARG(cons_active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0)), ENCARG(cons_active(0))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) by ENCARG(cons_mark(cons_mark(x0))) -> c3(MARK(c_mark(encArg(x0))), ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c3(MARK(mark(tt)), ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c3(MARK(mark(0)), ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(cons_U11(z0, z1, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(x0))) -> c3(MARK(c_mark(encArg(x0))), ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c3(MARK(mark(tt)), ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c3(MARK(mark(0)), ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1 ---------------------------------------- (133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(cons_U11(z0, z1, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(tt))) -> c3(MARK(mark(tt)), ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c3(MARK(mark(0)), ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1 ---------------------------------------- (135) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(cons_U11(z0, z1, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c8_1 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_mark(cons_U11(z0, z1, z2))) -> c3(MARK(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) by ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c8_1 ---------------------------------------- (139) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_mark(cons_U12(z0, z1, z2))) -> c3(MARK(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) by ENCARG(cons_mark(cons_U12(x0, x1, x2))) -> c3(MARK(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, tt))) -> c3(MARK(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_mark(cons_U12(x0, x1, 0))) -> c3(MARK(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_mark(cons_U12(x0, x1, cons_active(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_mark(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_s(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U12(x0, tt, x2))) -> c3(MARK(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_mark(cons_U12(x0, 0, x2))) -> c3(MARK(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_mark(cons_U12(x0, cons_active(z0), x2))) -> c3(MARK(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_mark(z0), x2))) -> c3(MARK(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_s(z0), x2))) -> c3(MARK(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U12(tt, x1, x2))) -> c3(MARK(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_mark(cons_U12(0, x1, x2))) -> c3(MARK(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_mark(cons_U12(cons_active(z0), x1, x2))) -> c3(MARK(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_mark(z0), x1, x2))) -> c3(MARK(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_s(z0), x1, x2))) -> c3(MARK(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ---------------------------------------- (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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, x2))) -> c3(MARK(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, tt))) -> c3(MARK(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_mark(cons_U12(x0, x1, 0))) -> c3(MARK(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_mark(cons_U12(x0, x1, cons_active(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_mark(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_s(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U12(x0, tt, x2))) -> c3(MARK(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_mark(cons_U12(x0, 0, x2))) -> c3(MARK(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_mark(cons_U12(x0, cons_active(z0), x2))) -> c3(MARK(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_mark(z0), x2))) -> c3(MARK(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_s(z0), x2))) -> c3(MARK(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U12(tt, x1, x2))) -> c3(MARK(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_mark(cons_U12(0, x1, x2))) -> c3(MARK(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_mark(cons_U12(cons_active(z0), x1, x2))) -> c3(MARK(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_mark(z0), x1, x2))) -> c3(MARK(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_s(z0), x1, x2))) -> c3(MARK(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c8_1 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) by ENCARG(cons_mark(cons_s(x0))) -> c3(MARK(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_mark(cons_s(tt))) -> c3(MARK(s(tt)), ENCARG(cons_s(tt))) ENCARG(cons_mark(cons_s(0))) -> c3(MARK(s(0)), ENCARG(cons_s(0))) ENCARG(cons_mark(cons_s(cons_active(z0)))) -> c3(MARK(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_mark(cons_s(cons_mark(z0)))) -> c3(MARK(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_mark(cons_s(cons_U11(z0, z1, z2)))) -> c3(MARK(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_U12(z0, z1, z2)))) -> c3(MARK(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_s(z0)))) -> c3(MARK(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_mark(cons_s(cons_plus(z0, z1)))) -> c3(MARK(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, x2))) -> c3(MARK(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, tt))) -> c3(MARK(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_mark(cons_U12(x0, x1, 0))) -> c3(MARK(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_mark(cons_U12(x0, x1, cons_active(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_mark(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_s(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U12(x0, tt, x2))) -> c3(MARK(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_mark(cons_U12(x0, 0, x2))) -> c3(MARK(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_mark(cons_U12(x0, cons_active(z0), x2))) -> c3(MARK(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_mark(z0), x2))) -> c3(MARK(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_s(z0), x2))) -> c3(MARK(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U12(tt, x1, x2))) -> c3(MARK(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_mark(cons_U12(0, x1, x2))) -> c3(MARK(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_mark(cons_U12(cons_active(z0), x1, x2))) -> c3(MARK(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_mark(z0), x1, x2))) -> c3(MARK(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_s(z0), x1, x2))) -> c3(MARK(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_s(x0))) -> c3(MARK(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_mark(cons_s(tt))) -> c3(MARK(s(tt)), ENCARG(cons_s(tt))) ENCARG(cons_mark(cons_s(0))) -> c3(MARK(s(0)), ENCARG(cons_s(0))) ENCARG(cons_mark(cons_s(cons_active(z0)))) -> c3(MARK(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_mark(cons_s(cons_mark(z0)))) -> c3(MARK(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_mark(cons_s(cons_U11(z0, z1, z2)))) -> c3(MARK(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_U12(z0, z1, z2)))) -> c3(MARK(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_s(z0)))) -> c3(MARK(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_mark(cons_s(cons_plus(z0, z1)))) -> c3(MARK(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c8_1 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 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, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, x2))) -> c3(MARK(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, tt))) -> c3(MARK(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_mark(cons_U12(x0, x1, 0))) -> c3(MARK(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_mark(cons_U12(x0, x1, cons_active(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_mark(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_s(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U12(x0, tt, x2))) -> c3(MARK(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_mark(cons_U12(x0, 0, x2))) -> c3(MARK(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_mark(cons_U12(x0, cons_active(z0), x2))) -> c3(MARK(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_mark(z0), x2))) -> c3(MARK(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_s(z0), x2))) -> c3(MARK(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U12(tt, x1, x2))) -> c3(MARK(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_mark(cons_U12(0, x1, x2))) -> c3(MARK(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_mark(cons_U12(cons_active(z0), x1, x2))) -> c3(MARK(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_mark(z0), x1, x2))) -> c3(MARK(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_s(z0), x1, x2))) -> c3(MARK(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_s(x0))) -> c3(MARK(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_mark(cons_s(cons_active(z0)))) -> c3(MARK(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_mark(cons_s(cons_mark(z0)))) -> c3(MARK(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_mark(cons_s(cons_U11(z0, z1, z2)))) -> c3(MARK(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_U12(z0, z1, z2)))) -> c3(MARK(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_s(z0)))) -> c3(MARK(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_mark(cons_s(cons_plus(z0, z1)))) -> c3(MARK(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_s(tt))) -> c3(MARK(s(tt))) ENCARG(cons_mark(cons_s(0))) -> c3(MARK(s(0))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_2, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c8_1 ---------------------------------------- (145) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) by ENCARG(cons_mark(cons_plus(x0, x1))) -> c3(MARK(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_mark(cons_plus(x0, tt))) -> c3(MARK(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_mark(cons_plus(x0, 0))) -> c3(MARK(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_mark(cons_plus(x0, cons_active(z0)))) -> c3(MARK(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_mark(z0)))) -> c3(MARK(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_s(z0)))) -> c3(MARK(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_plus(z0, z1)))) -> c3(MARK(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_plus(tt, x1))) -> c3(MARK(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_mark(cons_plus(0, x1))) -> c3(MARK(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_mark(cons_plus(cons_active(z0), x1))) -> c3(MARK(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_mark(cons_plus(cons_mark(z0), x1))) -> c3(MARK(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_mark(cons_plus(cons_U11(z0, z1, z2), x1))) -> c3(MARK(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_U12(z0, z1, z2), x1))) -> c3(MARK(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_s(z0), x1))) -> c3(MARK(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_mark(cons_plus(cons_plus(z0, z1), x1))) -> c3(MARK(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(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, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, x2))) -> c3(MARK(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, tt))) -> c3(MARK(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_mark(cons_U12(x0, x1, 0))) -> c3(MARK(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_mark(cons_U12(x0, x1, cons_active(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_mark(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_s(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U12(x0, tt, x2))) -> c3(MARK(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_mark(cons_U12(x0, 0, x2))) -> c3(MARK(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_mark(cons_U12(x0, cons_active(z0), x2))) -> c3(MARK(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_mark(z0), x2))) -> c3(MARK(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_s(z0), x2))) -> c3(MARK(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U12(tt, x1, x2))) -> c3(MARK(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_mark(cons_U12(0, x1, x2))) -> c3(MARK(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_mark(cons_U12(cons_active(z0), x1, x2))) -> c3(MARK(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_mark(z0), x1, x2))) -> c3(MARK(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_s(z0), x1, x2))) -> c3(MARK(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_s(x0))) -> c3(MARK(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_mark(cons_s(cons_active(z0)))) -> c3(MARK(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_mark(cons_s(cons_mark(z0)))) -> c3(MARK(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_mark(cons_s(cons_U11(z0, z1, z2)))) -> c3(MARK(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_U12(z0, z1, z2)))) -> c3(MARK(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_s(z0)))) -> c3(MARK(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_mark(cons_s(cons_plus(z0, z1)))) -> c3(MARK(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_s(tt))) -> c3(MARK(s(tt))) ENCARG(cons_mark(cons_s(0))) -> c3(MARK(s(0))) ENCARG(cons_mark(cons_plus(x0, x1))) -> c3(MARK(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_mark(cons_plus(x0, tt))) -> c3(MARK(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_mark(cons_plus(x0, 0))) -> c3(MARK(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_mark(cons_plus(x0, cons_active(z0)))) -> c3(MARK(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_mark(z0)))) -> c3(MARK(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_s(z0)))) -> c3(MARK(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_plus(z0, z1)))) -> c3(MARK(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_plus(tt, x1))) -> c3(MARK(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_mark(cons_plus(0, x1))) -> c3(MARK(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_mark(cons_plus(cons_active(z0), x1))) -> c3(MARK(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_mark(cons_plus(cons_mark(z0), x1))) -> c3(MARK(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_mark(cons_plus(cons_U11(z0, z1, z2), x1))) -> c3(MARK(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_U12(z0, z1, z2), x1))) -> c3(MARK(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_s(z0), x1))) -> c3(MARK(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_mark(cons_plus(cons_plus(z0, z1), x1))) -> c3(MARK(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c3_2, c8_1 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U11(x0, x1, cons_active(z0))) -> c4(U11'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) by ENCARG(cons_U11(x0, x1, cons_active(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_active(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(tt))) -> c4(U11'(encArg(x0), encArg(x1), active(tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(tt))) ENCARG(cons_U11(x0, x1, cons_active(0))) -> c4(U11'(encArg(x0), encArg(x1), active(0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(0))) ENCARG(cons_U11(x0, x1, cons_active(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), active(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, tt, cons_active(x2))) -> c4(U11'(encArg(x0), tt, active(encArg(x2))), ENCARG(x0), ENCARG(tt), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, 0, cons_active(x2))) -> c4(U11'(encArg(x0), 0, active(encArg(x2))), ENCARG(x0), ENCARG(0), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_active(z0), cons_active(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_active(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_active(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_active(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_active(x2))) ENCARG(cons_U11(tt, x1, cons_active(x2))) -> c4(U11'(tt, encArg(x1), active(encArg(x2))), ENCARG(tt), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(0, x1, cons_active(x2))) -> c4(U11'(0, encArg(x1), active(encArg(x2))), ENCARG(0), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_active(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_active(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_active(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_active(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), active(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_active(x2))) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, x2))) -> c3(MARK(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, tt))) -> c3(MARK(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_mark(cons_U12(x0, x1, 0))) -> c3(MARK(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_mark(cons_U12(x0, x1, cons_active(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_mark(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_s(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U12(x0, tt, x2))) -> c3(MARK(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_mark(cons_U12(x0, 0, x2))) -> c3(MARK(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_mark(cons_U12(x0, cons_active(z0), x2))) -> c3(MARK(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_mark(z0), x2))) -> c3(MARK(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_s(z0), x2))) -> c3(MARK(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U12(tt, x1, x2))) -> c3(MARK(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_mark(cons_U12(0, x1, x2))) -> c3(MARK(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_mark(cons_U12(cons_active(z0), x1, x2))) -> c3(MARK(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_mark(z0), x1, x2))) -> c3(MARK(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_s(z0), x1, x2))) -> c3(MARK(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_s(x0))) -> c3(MARK(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_mark(cons_s(cons_active(z0)))) -> c3(MARK(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_mark(cons_s(cons_mark(z0)))) -> c3(MARK(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_mark(cons_s(cons_U11(z0, z1, z2)))) -> c3(MARK(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_U12(z0, z1, z2)))) -> c3(MARK(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_s(z0)))) -> c3(MARK(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_mark(cons_s(cons_plus(z0, z1)))) -> c3(MARK(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_s(tt))) -> c3(MARK(s(tt))) ENCARG(cons_mark(cons_s(0))) -> c3(MARK(s(0))) ENCARG(cons_mark(cons_plus(x0, x1))) -> c3(MARK(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_mark(cons_plus(x0, tt))) -> c3(MARK(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_mark(cons_plus(x0, 0))) -> c3(MARK(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_mark(cons_plus(x0, cons_active(z0)))) -> c3(MARK(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_mark(z0)))) -> c3(MARK(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_s(z0)))) -> c3(MARK(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_plus(z0, z1)))) -> c3(MARK(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_plus(tt, x1))) -> c3(MARK(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_mark(cons_plus(0, x1))) -> c3(MARK(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_mark(cons_plus(cons_active(z0), x1))) -> c3(MARK(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_mark(cons_plus(cons_mark(z0), x1))) -> c3(MARK(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_mark(cons_plus(cons_U11(z0, z1, z2), x1))) -> c3(MARK(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_U12(z0, z1, z2), x1))) -> c3(MARK(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_s(z0), x1))) -> c3(MARK(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_mark(cons_plus(cons_plus(z0, z1), x1))) -> c3(MARK(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_U11(x0, x1, cons_active(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_active(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(tt))) -> c4(U11'(encArg(x0), encArg(x1), active(tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(tt))) ENCARG(cons_U11(x0, x1, cons_active(0))) -> c4(U11'(encArg(x0), encArg(x1), active(0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(0))) ENCARG(cons_U11(x0, x1, cons_active(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), active(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, tt, cons_active(x2))) -> c4(U11'(encArg(x0), tt, active(encArg(x2))), ENCARG(x0), ENCARG(tt), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, 0, cons_active(x2))) -> c4(U11'(encArg(x0), 0, active(encArg(x2))), ENCARG(x0), ENCARG(0), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_active(z0), cons_active(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_active(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_active(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_active(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_active(x2))) ENCARG(cons_U11(tt, x1, cons_active(x2))) -> c4(U11'(tt, encArg(x1), active(encArg(x2))), ENCARG(tt), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(0, x1, cons_active(x2))) -> c4(U11'(0, encArg(x1), active(encArg(x2))), ENCARG(0), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_active(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_active(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_active(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_active(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), active(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_active(x2))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c3_2, c8_1 ---------------------------------------- (149) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, x2))) -> c3(MARK(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, tt))) -> c3(MARK(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_mark(cons_U12(x0, x1, 0))) -> c3(MARK(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_mark(cons_U12(x0, x1, cons_active(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_mark(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_s(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U12(x0, tt, x2))) -> c3(MARK(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_mark(cons_U12(x0, 0, x2))) -> c3(MARK(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_mark(cons_U12(x0, cons_active(z0), x2))) -> c3(MARK(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_mark(z0), x2))) -> c3(MARK(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_s(z0), x2))) -> c3(MARK(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U12(tt, x1, x2))) -> c3(MARK(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_mark(cons_U12(0, x1, x2))) -> c3(MARK(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_mark(cons_U12(cons_active(z0), x1, x2))) -> c3(MARK(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_mark(z0), x1, x2))) -> c3(MARK(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_s(z0), x1, x2))) -> c3(MARK(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_s(x0))) -> c3(MARK(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_mark(cons_s(cons_active(z0)))) -> c3(MARK(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_mark(cons_s(cons_mark(z0)))) -> c3(MARK(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_mark(cons_s(cons_U11(z0, z1, z2)))) -> c3(MARK(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_U12(z0, z1, z2)))) -> c3(MARK(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_s(z0)))) -> c3(MARK(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_mark(cons_s(cons_plus(z0, z1)))) -> c3(MARK(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_s(tt))) -> c3(MARK(s(tt))) ENCARG(cons_mark(cons_s(0))) -> c3(MARK(s(0))) ENCARG(cons_mark(cons_plus(x0, x1))) -> c3(MARK(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_mark(cons_plus(x0, tt))) -> c3(MARK(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_mark(cons_plus(x0, 0))) -> c3(MARK(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_mark(cons_plus(x0, cons_active(z0)))) -> c3(MARK(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_mark(z0)))) -> c3(MARK(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_s(z0)))) -> c3(MARK(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_plus(z0, z1)))) -> c3(MARK(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_plus(tt, x1))) -> c3(MARK(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_mark(cons_plus(0, x1))) -> c3(MARK(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_mark(cons_plus(cons_active(z0), x1))) -> c3(MARK(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_mark(cons_plus(cons_mark(z0), x1))) -> c3(MARK(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_mark(cons_plus(cons_U11(z0, z1, z2), x1))) -> c3(MARK(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_U12(z0, z1, z2), x1))) -> c3(MARK(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_s(z0), x1))) -> c3(MARK(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_mark(cons_plus(cons_plus(z0, z1), x1))) -> c3(MARK(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_U11(x0, x1, cons_active(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_active(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), active(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_active(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_active(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_active(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_active(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_active(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_active(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_active(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_active(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), active(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(tt))) -> c4(U11'(encArg(x0), encArg(x1), active(tt)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, cons_active(0))) -> c4(U11'(encArg(x0), encArg(x1), active(0)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, cons_active(x2))) -> c4(U11'(encArg(x0), tt, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, 0, cons_active(x2))) -> c4(U11'(encArg(x0), 0, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(tt, x1, cons_active(x2))) -> c4(U11'(tt, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(0, x1, cons_active(x2))) -> c4(U11'(0, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c3_2, c8_1 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U11(x0, x1, cons_mark(z0))) -> c4(U11'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) by ENCARG(cons_U11(x0, x1, cons_mark(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_mark(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, x1, cons_mark(tt))) -> c4(U11'(encArg(x0), encArg(x1), mark(tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(tt))) ENCARG(cons_U11(x0, x1, cons_mark(0))) -> c4(U11'(encArg(x0), encArg(x1), mark(0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, x1, cons_mark(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), mark(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, tt, cons_mark(x2))) -> c4(U11'(encArg(x0), tt, mark(encArg(x2))), ENCARG(x0), ENCARG(tt), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, 0, cons_mark(x2))) -> c4(U11'(encArg(x0), 0, mark(encArg(x2))), ENCARG(x0), ENCARG(0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_active(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_mark(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(tt, x1, cons_mark(x2))) -> c4(U11'(tt, encArg(x1), mark(encArg(x2))), ENCARG(tt), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(0, x1, cons_mark(x2))) -> c4(U11'(0, encArg(x1), mark(encArg(x2))), ENCARG(0), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_mark(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_mark(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_mark(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_mark(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), mark(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_mark(x2))) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, x2))) -> c3(MARK(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, tt))) -> c3(MARK(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_mark(cons_U12(x0, x1, 0))) -> c3(MARK(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_mark(cons_U12(x0, x1, cons_active(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_mark(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_s(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U12(x0, tt, x2))) -> c3(MARK(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_mark(cons_U12(x0, 0, x2))) -> c3(MARK(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_mark(cons_U12(x0, cons_active(z0), x2))) -> c3(MARK(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_mark(z0), x2))) -> c3(MARK(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_s(z0), x2))) -> c3(MARK(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U12(tt, x1, x2))) -> c3(MARK(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_mark(cons_U12(0, x1, x2))) -> c3(MARK(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_mark(cons_U12(cons_active(z0), x1, x2))) -> c3(MARK(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_mark(z0), x1, x2))) -> c3(MARK(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_s(z0), x1, x2))) -> c3(MARK(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_s(x0))) -> c3(MARK(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_mark(cons_s(cons_active(z0)))) -> c3(MARK(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_mark(cons_s(cons_mark(z0)))) -> c3(MARK(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_mark(cons_s(cons_U11(z0, z1, z2)))) -> c3(MARK(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_U12(z0, z1, z2)))) -> c3(MARK(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_s(z0)))) -> c3(MARK(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_mark(cons_s(cons_plus(z0, z1)))) -> c3(MARK(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_s(tt))) -> c3(MARK(s(tt))) ENCARG(cons_mark(cons_s(0))) -> c3(MARK(s(0))) ENCARG(cons_mark(cons_plus(x0, x1))) -> c3(MARK(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_mark(cons_plus(x0, tt))) -> c3(MARK(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_mark(cons_plus(x0, 0))) -> c3(MARK(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_mark(cons_plus(x0, cons_active(z0)))) -> c3(MARK(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_mark(z0)))) -> c3(MARK(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_s(z0)))) -> c3(MARK(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_plus(z0, z1)))) -> c3(MARK(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_plus(tt, x1))) -> c3(MARK(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_mark(cons_plus(0, x1))) -> c3(MARK(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_mark(cons_plus(cons_active(z0), x1))) -> c3(MARK(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_mark(cons_plus(cons_mark(z0), x1))) -> c3(MARK(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_mark(cons_plus(cons_U11(z0, z1, z2), x1))) -> c3(MARK(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_U12(z0, z1, z2), x1))) -> c3(MARK(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_s(z0), x1))) -> c3(MARK(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_mark(cons_plus(cons_plus(z0, z1), x1))) -> c3(MARK(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_U11(x0, x1, cons_active(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_active(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), active(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_active(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_active(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_active(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_active(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_active(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_active(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_active(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_active(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), active(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(tt))) -> c4(U11'(encArg(x0), encArg(x1), active(tt)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, cons_active(0))) -> c4(U11'(encArg(x0), encArg(x1), active(0)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, cons_active(x2))) -> c4(U11'(encArg(x0), tt, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, 0, cons_active(x2))) -> c4(U11'(encArg(x0), 0, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(tt, x1, cons_active(x2))) -> c4(U11'(tt, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(0, x1, cons_active(x2))) -> c4(U11'(0, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_mark(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_mark(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, x1, cons_mark(tt))) -> c4(U11'(encArg(x0), encArg(x1), mark(tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(tt))) ENCARG(cons_U11(x0, x1, cons_mark(0))) -> c4(U11'(encArg(x0), encArg(x1), mark(0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, x1, cons_mark(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), mark(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, tt, cons_mark(x2))) -> c4(U11'(encArg(x0), tt, mark(encArg(x2))), ENCARG(x0), ENCARG(tt), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, 0, cons_mark(x2))) -> c4(U11'(encArg(x0), 0, mark(encArg(x2))), ENCARG(x0), ENCARG(0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_active(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_mark(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(tt, x1, cons_mark(x2))) -> c4(U11'(tt, encArg(x1), mark(encArg(x2))), ENCARG(tt), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(0, x1, cons_mark(x2))) -> c4(U11'(0, encArg(x1), mark(encArg(x2))), ENCARG(0), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_mark(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_mark(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_mark(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_mark(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), mark(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_mark(x2))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c3_2, c8_1 ---------------------------------------- (153) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, x2))) -> c3(MARK(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, tt))) -> c3(MARK(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_mark(cons_U12(x0, x1, 0))) -> c3(MARK(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_mark(cons_U12(x0, x1, cons_active(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_mark(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_s(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U12(x0, tt, x2))) -> c3(MARK(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_mark(cons_U12(x0, 0, x2))) -> c3(MARK(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_mark(cons_U12(x0, cons_active(z0), x2))) -> c3(MARK(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_mark(z0), x2))) -> c3(MARK(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_s(z0), x2))) -> c3(MARK(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U12(tt, x1, x2))) -> c3(MARK(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_mark(cons_U12(0, x1, x2))) -> c3(MARK(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_mark(cons_U12(cons_active(z0), x1, x2))) -> c3(MARK(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_mark(z0), x1, x2))) -> c3(MARK(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_s(z0), x1, x2))) -> c3(MARK(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_s(x0))) -> c3(MARK(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_mark(cons_s(cons_active(z0)))) -> c3(MARK(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_mark(cons_s(cons_mark(z0)))) -> c3(MARK(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_mark(cons_s(cons_U11(z0, z1, z2)))) -> c3(MARK(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_U12(z0, z1, z2)))) -> c3(MARK(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_s(z0)))) -> c3(MARK(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_mark(cons_s(cons_plus(z0, z1)))) -> c3(MARK(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_s(tt))) -> c3(MARK(s(tt))) ENCARG(cons_mark(cons_s(0))) -> c3(MARK(s(0))) ENCARG(cons_mark(cons_plus(x0, x1))) -> c3(MARK(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_mark(cons_plus(x0, tt))) -> c3(MARK(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_mark(cons_plus(x0, 0))) -> c3(MARK(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_mark(cons_plus(x0, cons_active(z0)))) -> c3(MARK(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_mark(z0)))) -> c3(MARK(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_s(z0)))) -> c3(MARK(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_plus(z0, z1)))) -> c3(MARK(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_plus(tt, x1))) -> c3(MARK(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_mark(cons_plus(0, x1))) -> c3(MARK(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_mark(cons_plus(cons_active(z0), x1))) -> c3(MARK(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_mark(cons_plus(cons_mark(z0), x1))) -> c3(MARK(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_mark(cons_plus(cons_U11(z0, z1, z2), x1))) -> c3(MARK(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_U12(z0, z1, z2), x1))) -> c3(MARK(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_s(z0), x1))) -> c3(MARK(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_mark(cons_plus(cons_plus(z0, z1), x1))) -> c3(MARK(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_U11(x0, x1, cons_active(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_active(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), active(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_active(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_active(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_active(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_active(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_active(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_active(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_active(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_active(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), active(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(tt))) -> c4(U11'(encArg(x0), encArg(x1), active(tt)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, cons_active(0))) -> c4(U11'(encArg(x0), encArg(x1), active(0)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, cons_active(x2))) -> c4(U11'(encArg(x0), tt, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, 0, cons_active(x2))) -> c4(U11'(encArg(x0), 0, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(tt, x1, cons_active(x2))) -> c4(U11'(tt, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(0, x1, cons_active(x2))) -> c4(U11'(0, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_mark(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_mark(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, x1, cons_mark(tt))) -> c4(U11'(encArg(x0), encArg(x1), mark(tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(tt))) ENCARG(cons_U11(x0, x1, cons_mark(0))) -> c4(U11'(encArg(x0), encArg(x1), mark(0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, x1, cons_mark(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), mark(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_mark(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_mark(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_mark(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_mark(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_mark(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), mark(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, tt, cons_mark(x2))) -> c4(U11'(encArg(x0), tt, mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, 0, cons_mark(x2))) -> c4(U11'(encArg(x0), 0, mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(tt, x1, cons_mark(x2))) -> c4(U11'(tt, encArg(x1), mark(encArg(x2))), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(0, x1, cons_mark(x2))) -> c4(U11'(0, encArg(x1), mark(encArg(x2))), ENCARG(x1), ENCARG(cons_mark(x2))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c3_2, c8_1 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) by ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), c_U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, tt))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, tt))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, 0))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), 0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, 0))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, tt, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), tt, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, tt, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, 0, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), 0, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, 0, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_active(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), active(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_active(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_mark(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), mark(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_mark(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_U11(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_U11(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_U12(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_U12(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_s(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), s(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_s(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_plus(z0, z1), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), plus(encArg(z0), encArg(z1)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_plus(z0, z1), x4))) ENCARG(cons_U11(x0, x1, cons_U11(tt, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(tt, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(tt, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(0, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(0, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(0, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_active(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(active(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_active(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_mark(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(mark(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_mark(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_U11(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_U11(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_U12(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_U12(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_s(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(s(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_s(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_plus(z0, z1), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(plus(encArg(z0), encArg(z1)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_plus(z0, z1), x3, x4))) ENCARG(cons_U11(x0, tt, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), tt, U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(tt), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, 0, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), 0, U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(0), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_active(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), active(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_mark(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), mark(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_s(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), s(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(tt, x1, cons_U11(x2, x3, x4))) -> c4(U11'(tt, encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(tt), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(0, x1, cons_U11(x2, x3, x4))) -> c4(U11'(0, encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(0), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_active(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(active(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_mark(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(mark(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_U11(x2, x3, x4))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_U11(x2, x3, x4))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_s(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(s(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_U11(x2, x3, x4))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, x2))) -> c3(MARK(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, tt))) -> c3(MARK(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_mark(cons_U12(x0, x1, 0))) -> c3(MARK(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_mark(cons_U12(x0, x1, cons_active(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_mark(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_s(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U12(x0, tt, x2))) -> c3(MARK(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_mark(cons_U12(x0, 0, x2))) -> c3(MARK(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_mark(cons_U12(x0, cons_active(z0), x2))) -> c3(MARK(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_mark(z0), x2))) -> c3(MARK(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_s(z0), x2))) -> c3(MARK(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U12(tt, x1, x2))) -> c3(MARK(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_mark(cons_U12(0, x1, x2))) -> c3(MARK(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_mark(cons_U12(cons_active(z0), x1, x2))) -> c3(MARK(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_mark(z0), x1, x2))) -> c3(MARK(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_s(z0), x1, x2))) -> c3(MARK(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_s(x0))) -> c3(MARK(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_mark(cons_s(cons_active(z0)))) -> c3(MARK(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_mark(cons_s(cons_mark(z0)))) -> c3(MARK(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_mark(cons_s(cons_U11(z0, z1, z2)))) -> c3(MARK(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_U12(z0, z1, z2)))) -> c3(MARK(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_s(z0)))) -> c3(MARK(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_mark(cons_s(cons_plus(z0, z1)))) -> c3(MARK(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_s(tt))) -> c3(MARK(s(tt))) ENCARG(cons_mark(cons_s(0))) -> c3(MARK(s(0))) ENCARG(cons_mark(cons_plus(x0, x1))) -> c3(MARK(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_mark(cons_plus(x0, tt))) -> c3(MARK(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_mark(cons_plus(x0, 0))) -> c3(MARK(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_mark(cons_plus(x0, cons_active(z0)))) -> c3(MARK(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_mark(z0)))) -> c3(MARK(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_s(z0)))) -> c3(MARK(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_plus(z0, z1)))) -> c3(MARK(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_plus(tt, x1))) -> c3(MARK(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_mark(cons_plus(0, x1))) -> c3(MARK(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_mark(cons_plus(cons_active(z0), x1))) -> c3(MARK(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_mark(cons_plus(cons_mark(z0), x1))) -> c3(MARK(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_mark(cons_plus(cons_U11(z0, z1, z2), x1))) -> c3(MARK(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_U12(z0, z1, z2), x1))) -> c3(MARK(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_s(z0), x1))) -> c3(MARK(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_mark(cons_plus(cons_plus(z0, z1), x1))) -> c3(MARK(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_U11(x0, x1, cons_active(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_active(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), active(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_active(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_active(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_active(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_active(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_active(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_active(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_active(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_active(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), active(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(tt))) -> c4(U11'(encArg(x0), encArg(x1), active(tt)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, cons_active(0))) -> c4(U11'(encArg(x0), encArg(x1), active(0)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, cons_active(x2))) -> c4(U11'(encArg(x0), tt, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, 0, cons_active(x2))) -> c4(U11'(encArg(x0), 0, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(tt, x1, cons_active(x2))) -> c4(U11'(tt, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(0, x1, cons_active(x2))) -> c4(U11'(0, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_mark(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_mark(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, x1, cons_mark(tt))) -> c4(U11'(encArg(x0), encArg(x1), mark(tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(tt))) ENCARG(cons_U11(x0, x1, cons_mark(0))) -> c4(U11'(encArg(x0), encArg(x1), mark(0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, x1, cons_mark(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), mark(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_mark(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_mark(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_mark(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_mark(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_mark(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), mark(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, tt, cons_mark(x2))) -> c4(U11'(encArg(x0), tt, mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, 0, cons_mark(x2))) -> c4(U11'(encArg(x0), 0, mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(tt, x1, cons_mark(x2))) -> c4(U11'(tt, encArg(x1), mark(encArg(x2))), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(0, x1, cons_mark(x2))) -> c4(U11'(0, encArg(x1), mark(encArg(x2))), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), c_U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, tt))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, tt))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, 0))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), 0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, 0))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, tt, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), tt, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, tt, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, 0, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), 0, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, 0, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_active(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), active(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_active(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_mark(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), mark(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_mark(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_U11(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_U11(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_U12(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_U12(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_s(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), s(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_s(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_plus(z0, z1), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), plus(encArg(z0), encArg(z1)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_plus(z0, z1), x4))) ENCARG(cons_U11(x0, x1, cons_U11(tt, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(tt, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(tt, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(0, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(0, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(0, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_active(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(active(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_active(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_mark(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(mark(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_mark(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_U11(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_U11(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_U12(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_U12(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_s(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(s(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_s(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_plus(z0, z1), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(plus(encArg(z0), encArg(z1)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_plus(z0, z1), x3, x4))) ENCARG(cons_U11(x0, tt, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), tt, U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(tt), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, 0, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), 0, U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(0), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_active(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), active(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_mark(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), mark(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_s(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), s(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(tt, x1, cons_U11(x2, x3, x4))) -> c4(U11'(tt, encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(tt), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(0, x1, cons_U11(x2, x3, x4))) -> c4(U11'(0, encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(0), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_active(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(active(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_mark(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(mark(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_U11(x2, x3, x4))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_U11(x2, x3, x4))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_s(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(s(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_U11(x2, x3, x4))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c3_2, c8_1 ---------------------------------------- (157) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, x2))) -> c3(MARK(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, tt))) -> c3(MARK(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_mark(cons_U12(x0, x1, 0))) -> c3(MARK(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_mark(cons_U12(x0, x1, cons_active(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_mark(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_s(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U12(x0, tt, x2))) -> c3(MARK(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_mark(cons_U12(x0, 0, x2))) -> c3(MARK(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_mark(cons_U12(x0, cons_active(z0), x2))) -> c3(MARK(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_mark(z0), x2))) -> c3(MARK(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_s(z0), x2))) -> c3(MARK(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U12(tt, x1, x2))) -> c3(MARK(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_mark(cons_U12(0, x1, x2))) -> c3(MARK(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_mark(cons_U12(cons_active(z0), x1, x2))) -> c3(MARK(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_mark(z0), x1, x2))) -> c3(MARK(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_s(z0), x1, x2))) -> c3(MARK(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_s(x0))) -> c3(MARK(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_mark(cons_s(cons_active(z0)))) -> c3(MARK(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_mark(cons_s(cons_mark(z0)))) -> c3(MARK(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_mark(cons_s(cons_U11(z0, z1, z2)))) -> c3(MARK(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_U12(z0, z1, z2)))) -> c3(MARK(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_s(z0)))) -> c3(MARK(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_mark(cons_s(cons_plus(z0, z1)))) -> c3(MARK(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_s(tt))) -> c3(MARK(s(tt))) ENCARG(cons_mark(cons_s(0))) -> c3(MARK(s(0))) ENCARG(cons_mark(cons_plus(x0, x1))) -> c3(MARK(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_mark(cons_plus(x0, tt))) -> c3(MARK(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_mark(cons_plus(x0, 0))) -> c3(MARK(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_mark(cons_plus(x0, cons_active(z0)))) -> c3(MARK(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_mark(z0)))) -> c3(MARK(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_s(z0)))) -> c3(MARK(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_plus(z0, z1)))) -> c3(MARK(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_plus(tt, x1))) -> c3(MARK(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_mark(cons_plus(0, x1))) -> c3(MARK(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_mark(cons_plus(cons_active(z0), x1))) -> c3(MARK(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_mark(cons_plus(cons_mark(z0), x1))) -> c3(MARK(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_mark(cons_plus(cons_U11(z0, z1, z2), x1))) -> c3(MARK(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_U12(z0, z1, z2), x1))) -> c3(MARK(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_s(z0), x1))) -> c3(MARK(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_mark(cons_plus(cons_plus(z0, z1), x1))) -> c3(MARK(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_U11(x0, x1, cons_active(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_active(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), active(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_active(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_active(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_active(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_active(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_active(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_active(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_active(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_active(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), active(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(tt))) -> c4(U11'(encArg(x0), encArg(x1), active(tt)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, cons_active(0))) -> c4(U11'(encArg(x0), encArg(x1), active(0)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, cons_active(x2))) -> c4(U11'(encArg(x0), tt, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, 0, cons_active(x2))) -> c4(U11'(encArg(x0), 0, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(tt, x1, cons_active(x2))) -> c4(U11'(tt, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(0, x1, cons_active(x2))) -> c4(U11'(0, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_mark(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_mark(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, x1, cons_mark(tt))) -> c4(U11'(encArg(x0), encArg(x1), mark(tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(tt))) ENCARG(cons_U11(x0, x1, cons_mark(0))) -> c4(U11'(encArg(x0), encArg(x1), mark(0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, x1, cons_mark(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), mark(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_mark(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_mark(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_mark(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_mark(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_mark(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), mark(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, tt, cons_mark(x2))) -> c4(U11'(encArg(x0), tt, mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, 0, cons_mark(x2))) -> c4(U11'(encArg(x0), 0, mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(tt, x1, cons_mark(x2))) -> c4(U11'(tt, encArg(x1), mark(encArg(x2))), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(0, x1, cons_mark(x2))) -> c4(U11'(0, encArg(x1), mark(encArg(x2))), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), c_U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, tt))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, tt))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, 0))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), 0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, 0))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, tt, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), tt, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, tt, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, 0, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), 0, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, 0, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_active(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), active(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_active(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_mark(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), mark(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_mark(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_U11(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_U11(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_U12(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_U12(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_s(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), s(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_s(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_plus(z0, z1), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), plus(encArg(z0), encArg(z1)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_plus(z0, z1), x4))) ENCARG(cons_U11(x0, x1, cons_U11(tt, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(tt, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(tt, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(0, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(0, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(0, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_active(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(active(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_active(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_mark(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(mark(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_mark(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_U11(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_U11(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_U12(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_U12(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_s(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(s(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_s(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_plus(z0, z1), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(plus(encArg(z0), encArg(z1)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_plus(z0, z1), x3, x4))) ENCARG(cons_U11(x0, cons_active(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), active(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_mark(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), mark(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_s(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), s(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_active(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(active(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_mark(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(mark(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_U11(x2, x3, x4))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_U11(x2, x3, x4))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_s(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(s(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_U11(x2, x3, x4))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, tt, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), tt, U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, 0, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), 0, U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(tt, x1, cons_U11(x2, x3, x4))) -> c4(U11'(tt, encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(0, x1, cons_U11(x2, x3, x4))) -> c4(U11'(0, encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c3_2, c8_1 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) by ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), c_U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, tt))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, tt))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, 0))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), 0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, 0))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, tt, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), tt, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, tt, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, 0, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), 0, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, 0, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_active(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), active(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_active(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_mark(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), mark(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_mark(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_U11(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_U11(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_U12(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_U12(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_s(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), s(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_s(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_plus(z0, z1), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), plus(encArg(z0), encArg(z1)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_plus(z0, z1), x4))) ENCARG(cons_U11(x0, x1, cons_U12(tt, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(tt, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(tt, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(0, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(0, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(0, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_active(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(active(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_active(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_mark(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(mark(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_mark(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_U11(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_U11(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_U12(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_U12(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_s(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(s(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_s(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_plus(z0, z1), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(plus(encArg(z0), encArg(z1)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_plus(z0, z1), x3, x4))) ENCARG(cons_U11(x0, tt, cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), tt, U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(tt), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, 0, cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), 0, U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(0), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_active(z0), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), active(encArg(z0)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_mark(z0), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), mark(encArg(z0)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_s(z0), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), s(encArg(z0)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(tt, x1, cons_U12(x2, x3, x4))) -> c4(U11'(tt, encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(tt), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(0, x1, cons_U12(x2, x3, x4))) -> c4(U11'(0, encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(0), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_active(z0), x1, cons_U12(x2, x3, x4))) -> c4(U11'(active(encArg(z0)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_mark(z0), x1, cons_U12(x2, x3, x4))) -> c4(U11'(mark(encArg(z0)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_U12(x2, x3, x4))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_U12(x2, x3, x4))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_s(z0), x1, cons_U12(x2, x3, x4))) -> c4(U11'(s(encArg(z0)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_U12(x2, x3, x4))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, x2))) -> c3(MARK(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, tt))) -> c3(MARK(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_mark(cons_U12(x0, x1, 0))) -> c3(MARK(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_mark(cons_U12(x0, x1, cons_active(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_mark(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_s(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U12(x0, tt, x2))) -> c3(MARK(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_mark(cons_U12(x0, 0, x2))) -> c3(MARK(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_mark(cons_U12(x0, cons_active(z0), x2))) -> c3(MARK(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_mark(z0), x2))) -> c3(MARK(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_s(z0), x2))) -> c3(MARK(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U12(tt, x1, x2))) -> c3(MARK(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_mark(cons_U12(0, x1, x2))) -> c3(MARK(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_mark(cons_U12(cons_active(z0), x1, x2))) -> c3(MARK(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_mark(z0), x1, x2))) -> c3(MARK(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_s(z0), x1, x2))) -> c3(MARK(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_s(x0))) -> c3(MARK(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_mark(cons_s(cons_active(z0)))) -> c3(MARK(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_mark(cons_s(cons_mark(z0)))) -> c3(MARK(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_mark(cons_s(cons_U11(z0, z1, z2)))) -> c3(MARK(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_U12(z0, z1, z2)))) -> c3(MARK(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_s(z0)))) -> c3(MARK(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_mark(cons_s(cons_plus(z0, z1)))) -> c3(MARK(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_s(tt))) -> c3(MARK(s(tt))) ENCARG(cons_mark(cons_s(0))) -> c3(MARK(s(0))) ENCARG(cons_mark(cons_plus(x0, x1))) -> c3(MARK(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_mark(cons_plus(x0, tt))) -> c3(MARK(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_mark(cons_plus(x0, 0))) -> c3(MARK(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_mark(cons_plus(x0, cons_active(z0)))) -> c3(MARK(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_mark(z0)))) -> c3(MARK(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_s(z0)))) -> c3(MARK(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_plus(z0, z1)))) -> c3(MARK(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_plus(tt, x1))) -> c3(MARK(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_mark(cons_plus(0, x1))) -> c3(MARK(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_mark(cons_plus(cons_active(z0), x1))) -> c3(MARK(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_mark(cons_plus(cons_mark(z0), x1))) -> c3(MARK(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_mark(cons_plus(cons_U11(z0, z1, z2), x1))) -> c3(MARK(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_U12(z0, z1, z2), x1))) -> c3(MARK(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_s(z0), x1))) -> c3(MARK(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_mark(cons_plus(cons_plus(z0, z1), x1))) -> c3(MARK(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_U11(x0, x1, cons_active(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_active(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), active(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_active(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_active(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_active(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_active(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_active(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_active(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_active(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_active(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), active(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(tt))) -> c4(U11'(encArg(x0), encArg(x1), active(tt)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, cons_active(0))) -> c4(U11'(encArg(x0), encArg(x1), active(0)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, cons_active(x2))) -> c4(U11'(encArg(x0), tt, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, 0, cons_active(x2))) -> c4(U11'(encArg(x0), 0, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(tt, x1, cons_active(x2))) -> c4(U11'(tt, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(0, x1, cons_active(x2))) -> c4(U11'(0, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_mark(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_mark(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, x1, cons_mark(tt))) -> c4(U11'(encArg(x0), encArg(x1), mark(tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(tt))) ENCARG(cons_U11(x0, x1, cons_mark(0))) -> c4(U11'(encArg(x0), encArg(x1), mark(0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, x1, cons_mark(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), mark(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_mark(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_mark(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_mark(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_mark(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_mark(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), mark(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, tt, cons_mark(x2))) -> c4(U11'(encArg(x0), tt, mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, 0, cons_mark(x2))) -> c4(U11'(encArg(x0), 0, mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(tt, x1, cons_mark(x2))) -> c4(U11'(tt, encArg(x1), mark(encArg(x2))), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(0, x1, cons_mark(x2))) -> c4(U11'(0, encArg(x1), mark(encArg(x2))), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), c_U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, tt))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, tt))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, 0))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), 0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, 0))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, tt, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), tt, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, tt, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, 0, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), 0, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, 0, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_active(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), active(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_active(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_mark(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), mark(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_mark(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_U11(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_U11(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_U12(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_U12(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_s(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), s(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_s(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_plus(z0, z1), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), plus(encArg(z0), encArg(z1)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_plus(z0, z1), x4))) ENCARG(cons_U11(x0, x1, cons_U11(tt, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(tt, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(tt, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(0, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(0, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(0, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_active(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(active(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_active(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_mark(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(mark(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_mark(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_U11(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_U11(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_U12(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_U12(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_s(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(s(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_s(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_plus(z0, z1), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(plus(encArg(z0), encArg(z1)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_plus(z0, z1), x3, x4))) ENCARG(cons_U11(x0, cons_active(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), active(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_mark(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), mark(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_s(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), s(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_active(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(active(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_mark(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(mark(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_U11(x2, x3, x4))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_U11(x2, x3, x4))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_s(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(s(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_U11(x2, x3, x4))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, tt, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), tt, U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, 0, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), 0, U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(tt, x1, cons_U11(x2, x3, x4))) -> c4(U11'(tt, encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(0, x1, cons_U11(x2, x3, x4))) -> c4(U11'(0, encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), c_U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, tt))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, tt))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, 0))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), 0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, 0))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, tt, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), tt, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, tt, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, 0, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), 0, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, 0, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_active(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), active(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_active(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_mark(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), mark(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_mark(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_U11(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_U11(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_U12(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_U12(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_s(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), s(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_s(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_plus(z0, z1), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), plus(encArg(z0), encArg(z1)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_plus(z0, z1), x4))) ENCARG(cons_U11(x0, x1, cons_U12(tt, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(tt, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(tt, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(0, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(0, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(0, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_active(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(active(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_active(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_mark(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(mark(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_mark(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_U11(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_U11(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_U12(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_U12(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_s(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(s(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_s(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_plus(z0, z1), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(plus(encArg(z0), encArg(z1)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_plus(z0, z1), x3, x4))) ENCARG(cons_U11(x0, tt, cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), tt, U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(tt), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, 0, cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), 0, U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(0), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_active(z0), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), active(encArg(z0)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_mark(z0), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), mark(encArg(z0)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_s(z0), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), s(encArg(z0)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(tt, x1, cons_U12(x2, x3, x4))) -> c4(U11'(tt, encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(tt), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(0, x1, cons_U12(x2, x3, x4))) -> c4(U11'(0, encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(0), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_active(z0), x1, cons_U12(x2, x3, x4))) -> c4(U11'(active(encArg(z0)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_mark(z0), x1, cons_U12(x2, x3, x4))) -> c4(U11'(mark(encArg(z0)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_U12(x2, x3, x4))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_U12(x2, x3, x4))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_s(z0), x1, cons_U12(x2, x3, x4))) -> c4(U11'(s(encArg(z0)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_U12(x2, x3, x4))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c3_2, c8_1 ---------------------------------------- (161) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, x2))) -> c3(MARK(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, tt))) -> c3(MARK(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_mark(cons_U12(x0, x1, 0))) -> c3(MARK(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_mark(cons_U12(x0, x1, cons_active(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_mark(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_s(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U12(x0, tt, x2))) -> c3(MARK(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_mark(cons_U12(x0, 0, x2))) -> c3(MARK(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_mark(cons_U12(x0, cons_active(z0), x2))) -> c3(MARK(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_mark(z0), x2))) -> c3(MARK(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_s(z0), x2))) -> c3(MARK(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U12(tt, x1, x2))) -> c3(MARK(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_mark(cons_U12(0, x1, x2))) -> c3(MARK(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_mark(cons_U12(cons_active(z0), x1, x2))) -> c3(MARK(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_mark(z0), x1, x2))) -> c3(MARK(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_s(z0), x1, x2))) -> c3(MARK(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_s(x0))) -> c3(MARK(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_mark(cons_s(cons_active(z0)))) -> c3(MARK(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_mark(cons_s(cons_mark(z0)))) -> c3(MARK(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_mark(cons_s(cons_U11(z0, z1, z2)))) -> c3(MARK(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_U12(z0, z1, z2)))) -> c3(MARK(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_s(z0)))) -> c3(MARK(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_mark(cons_s(cons_plus(z0, z1)))) -> c3(MARK(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_s(tt))) -> c3(MARK(s(tt))) ENCARG(cons_mark(cons_s(0))) -> c3(MARK(s(0))) ENCARG(cons_mark(cons_plus(x0, x1))) -> c3(MARK(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_mark(cons_plus(x0, tt))) -> c3(MARK(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_mark(cons_plus(x0, 0))) -> c3(MARK(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_mark(cons_plus(x0, cons_active(z0)))) -> c3(MARK(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_mark(z0)))) -> c3(MARK(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_s(z0)))) -> c3(MARK(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_plus(z0, z1)))) -> c3(MARK(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_plus(tt, x1))) -> c3(MARK(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_mark(cons_plus(0, x1))) -> c3(MARK(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_mark(cons_plus(cons_active(z0), x1))) -> c3(MARK(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_mark(cons_plus(cons_mark(z0), x1))) -> c3(MARK(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_mark(cons_plus(cons_U11(z0, z1, z2), x1))) -> c3(MARK(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_U12(z0, z1, z2), x1))) -> c3(MARK(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_s(z0), x1))) -> c3(MARK(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_mark(cons_plus(cons_plus(z0, z1), x1))) -> c3(MARK(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_U11(x0, x1, cons_active(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_active(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), active(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_active(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_active(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_active(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_active(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_active(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_active(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_active(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_active(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), active(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(tt))) -> c4(U11'(encArg(x0), encArg(x1), active(tt)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, cons_active(0))) -> c4(U11'(encArg(x0), encArg(x1), active(0)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, cons_active(x2))) -> c4(U11'(encArg(x0), tt, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, 0, cons_active(x2))) -> c4(U11'(encArg(x0), 0, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(tt, x1, cons_active(x2))) -> c4(U11'(tt, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(0, x1, cons_active(x2))) -> c4(U11'(0, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_mark(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_mark(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, x1, cons_mark(tt))) -> c4(U11'(encArg(x0), encArg(x1), mark(tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(tt))) ENCARG(cons_U11(x0, x1, cons_mark(0))) -> c4(U11'(encArg(x0), encArg(x1), mark(0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, x1, cons_mark(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), mark(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_mark(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_mark(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_mark(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_mark(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_mark(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), mark(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, tt, cons_mark(x2))) -> c4(U11'(encArg(x0), tt, mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, 0, cons_mark(x2))) -> c4(U11'(encArg(x0), 0, mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(tt, x1, cons_mark(x2))) -> c4(U11'(tt, encArg(x1), mark(encArg(x2))), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(0, x1, cons_mark(x2))) -> c4(U11'(0, encArg(x1), mark(encArg(x2))), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), c_U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, tt))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, tt))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, 0))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), 0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, 0))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, tt, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), tt, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, tt, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, 0, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), 0, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, 0, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_active(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), active(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_active(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_mark(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), mark(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_mark(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_U11(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_U11(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_U12(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_U12(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_s(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), s(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_s(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_plus(z0, z1), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), plus(encArg(z0), encArg(z1)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_plus(z0, z1), x4))) ENCARG(cons_U11(x0, x1, cons_U11(tt, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(tt, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(tt, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(0, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(0, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(0, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_active(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(active(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_active(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_mark(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(mark(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_mark(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_U11(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_U11(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_U12(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_U12(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_s(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(s(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_s(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_plus(z0, z1), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(plus(encArg(z0), encArg(z1)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_plus(z0, z1), x3, x4))) ENCARG(cons_U11(x0, cons_active(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), active(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_mark(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), mark(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_s(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), s(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_active(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(active(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_mark(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(mark(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_U11(x2, x3, x4))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_U11(x2, x3, x4))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_s(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(s(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_U11(x2, x3, x4))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, tt, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), tt, U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, 0, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), 0, U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(tt, x1, cons_U11(x2, x3, x4))) -> c4(U11'(tt, encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(0, x1, cons_U11(x2, x3, x4))) -> c4(U11'(0, encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), c_U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, tt))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, tt))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, 0))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), 0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, 0))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, tt, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), tt, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, tt, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, 0, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), 0, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, 0, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_active(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), active(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_active(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_mark(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), mark(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_mark(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_U11(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_U11(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_U12(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_U12(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_s(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), s(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_s(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_plus(z0, z1), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), plus(encArg(z0), encArg(z1)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_plus(z0, z1), x4))) ENCARG(cons_U11(x0, x1, cons_U12(tt, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(tt, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(tt, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(0, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(0, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(0, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_active(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(active(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_active(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_mark(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(mark(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_mark(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_U11(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_U11(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_U12(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_U12(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_s(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(s(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_s(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_plus(z0, z1), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(plus(encArg(z0), encArg(z1)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_plus(z0, z1), x3, x4))) ENCARG(cons_U11(x0, cons_active(z0), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), active(encArg(z0)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_mark(z0), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), mark(encArg(z0)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_s(z0), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), s(encArg(z0)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_active(z0), x1, cons_U12(x2, x3, x4))) -> c4(U11'(active(encArg(z0)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_mark(z0), x1, cons_U12(x2, x3, x4))) -> c4(U11'(mark(encArg(z0)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_U12(x2, x3, x4))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_U12(x2, x3, x4))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_s(z0), x1, cons_U12(x2, x3, x4))) -> c4(U11'(s(encArg(z0)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_U12(x2, x3, x4))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, tt, cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), tt, U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, 0, cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), 0, U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(tt, x1, cons_U12(x2, x3, x4))) -> c4(U11'(tt, encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(0, x1, cons_U12(x2, x3, x4))) -> c4(U11'(0, encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c3_2, c8_1 ---------------------------------------- (163) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U11(x0, x1, cons_s(z0))) -> c4(U11'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) by ENCARG(cons_U11(x0, x1, cons_s(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_s(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, x1, cons_s(tt))) -> c4(U11'(encArg(x0), encArg(x1), s(tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(tt))) ENCARG(cons_U11(x0, x1, cons_s(0))) -> c4(U11'(encArg(x0), encArg(x1), s(0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(0))) ENCARG(cons_U11(x0, x1, cons_s(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), s(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_s(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_s(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_s(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_s(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), s(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_s(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, tt, cons_s(x2))) -> c4(U11'(encArg(x0), tt, s(encArg(x2))), ENCARG(x0), ENCARG(tt), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, 0, cons_s(x2))) -> c4(U11'(encArg(x0), 0, s(encArg(x2))), ENCARG(x0), ENCARG(0), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_active(z0), cons_s(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_s(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_s(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_s(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_s(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_s(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x2))) ENCARG(cons_U11(tt, x1, cons_s(x2))) -> c4(U11'(tt, encArg(x1), s(encArg(x2))), ENCARG(tt), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(0, x1, cons_s(x2))) -> c4(U11'(0, encArg(x1), s(encArg(x2))), ENCARG(0), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_s(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), s(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_s(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), s(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_s(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), s(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_s(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), s(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_s(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), s(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_s(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), s(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_s(x2))) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, x2))) -> c3(MARK(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, tt))) -> c3(MARK(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_mark(cons_U12(x0, x1, 0))) -> c3(MARK(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_mark(cons_U12(x0, x1, cons_active(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_mark(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_s(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U12(x0, tt, x2))) -> c3(MARK(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_mark(cons_U12(x0, 0, x2))) -> c3(MARK(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_mark(cons_U12(x0, cons_active(z0), x2))) -> c3(MARK(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_mark(z0), x2))) -> c3(MARK(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_s(z0), x2))) -> c3(MARK(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U12(tt, x1, x2))) -> c3(MARK(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_mark(cons_U12(0, x1, x2))) -> c3(MARK(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_mark(cons_U12(cons_active(z0), x1, x2))) -> c3(MARK(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_mark(z0), x1, x2))) -> c3(MARK(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_s(z0), x1, x2))) -> c3(MARK(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_s(x0))) -> c3(MARK(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_mark(cons_s(cons_active(z0)))) -> c3(MARK(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_mark(cons_s(cons_mark(z0)))) -> c3(MARK(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_mark(cons_s(cons_U11(z0, z1, z2)))) -> c3(MARK(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_U12(z0, z1, z2)))) -> c3(MARK(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_s(z0)))) -> c3(MARK(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_mark(cons_s(cons_plus(z0, z1)))) -> c3(MARK(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_s(tt))) -> c3(MARK(s(tt))) ENCARG(cons_mark(cons_s(0))) -> c3(MARK(s(0))) ENCARG(cons_mark(cons_plus(x0, x1))) -> c3(MARK(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_mark(cons_plus(x0, tt))) -> c3(MARK(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_mark(cons_plus(x0, 0))) -> c3(MARK(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_mark(cons_plus(x0, cons_active(z0)))) -> c3(MARK(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_mark(z0)))) -> c3(MARK(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_s(z0)))) -> c3(MARK(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_plus(z0, z1)))) -> c3(MARK(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_plus(tt, x1))) -> c3(MARK(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_mark(cons_plus(0, x1))) -> c3(MARK(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_mark(cons_plus(cons_active(z0), x1))) -> c3(MARK(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_mark(cons_plus(cons_mark(z0), x1))) -> c3(MARK(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_mark(cons_plus(cons_U11(z0, z1, z2), x1))) -> c3(MARK(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_U12(z0, z1, z2), x1))) -> c3(MARK(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_s(z0), x1))) -> c3(MARK(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_mark(cons_plus(cons_plus(z0, z1), x1))) -> c3(MARK(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_U11(x0, x1, cons_active(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_active(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), active(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_active(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_active(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_active(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_active(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_active(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_active(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_active(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_active(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), active(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(tt))) -> c4(U11'(encArg(x0), encArg(x1), active(tt)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, cons_active(0))) -> c4(U11'(encArg(x0), encArg(x1), active(0)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, cons_active(x2))) -> c4(U11'(encArg(x0), tt, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, 0, cons_active(x2))) -> c4(U11'(encArg(x0), 0, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(tt, x1, cons_active(x2))) -> c4(U11'(tt, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(0, x1, cons_active(x2))) -> c4(U11'(0, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_mark(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_mark(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, x1, cons_mark(tt))) -> c4(U11'(encArg(x0), encArg(x1), mark(tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(tt))) ENCARG(cons_U11(x0, x1, cons_mark(0))) -> c4(U11'(encArg(x0), encArg(x1), mark(0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, x1, cons_mark(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), mark(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_mark(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_mark(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_mark(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_mark(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_mark(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), mark(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, tt, cons_mark(x2))) -> c4(U11'(encArg(x0), tt, mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, 0, cons_mark(x2))) -> c4(U11'(encArg(x0), 0, mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(tt, x1, cons_mark(x2))) -> c4(U11'(tt, encArg(x1), mark(encArg(x2))), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(0, x1, cons_mark(x2))) -> c4(U11'(0, encArg(x1), mark(encArg(x2))), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), c_U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, tt))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, tt))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, 0))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), 0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, 0))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, tt, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), tt, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, tt, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, 0, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), 0, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, 0, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_active(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), active(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_active(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_mark(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), mark(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_mark(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_U11(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_U11(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_U12(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_U12(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_s(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), s(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_s(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_plus(z0, z1), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), plus(encArg(z0), encArg(z1)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_plus(z0, z1), x4))) ENCARG(cons_U11(x0, x1, cons_U11(tt, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(tt, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(tt, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(0, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(0, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(0, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_active(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(active(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_active(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_mark(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(mark(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_mark(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_U11(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_U11(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_U12(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_U12(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_s(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(s(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_s(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_plus(z0, z1), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(plus(encArg(z0), encArg(z1)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_plus(z0, z1), x3, x4))) ENCARG(cons_U11(x0, cons_active(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), active(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_mark(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), mark(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_s(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), s(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_active(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(active(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_mark(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(mark(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_U11(x2, x3, x4))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_U11(x2, x3, x4))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_s(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(s(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_U11(x2, x3, x4))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, tt, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), tt, U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, 0, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), 0, U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(tt, x1, cons_U11(x2, x3, x4))) -> c4(U11'(tt, encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(0, x1, cons_U11(x2, x3, x4))) -> c4(U11'(0, encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), c_U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, tt))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, tt))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, 0))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), 0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, 0))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, tt, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), tt, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, tt, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, 0, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), 0, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, 0, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_active(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), active(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_active(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_mark(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), mark(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_mark(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_U11(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_U11(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_U12(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_U12(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_s(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), s(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_s(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_plus(z0, z1), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), plus(encArg(z0), encArg(z1)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_plus(z0, z1), x4))) ENCARG(cons_U11(x0, x1, cons_U12(tt, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(tt, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(tt, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(0, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(0, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(0, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_active(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(active(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_active(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_mark(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(mark(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_mark(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_U11(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_U11(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_U12(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_U12(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_s(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(s(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_s(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_plus(z0, z1), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(plus(encArg(z0), encArg(z1)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_plus(z0, z1), x3, x4))) ENCARG(cons_U11(x0, cons_active(z0), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), active(encArg(z0)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_mark(z0), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), mark(encArg(z0)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_s(z0), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), s(encArg(z0)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_active(z0), x1, cons_U12(x2, x3, x4))) -> c4(U11'(active(encArg(z0)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_mark(z0), x1, cons_U12(x2, x3, x4))) -> c4(U11'(mark(encArg(z0)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_U12(x2, x3, x4))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_U12(x2, x3, x4))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_s(z0), x1, cons_U12(x2, x3, x4))) -> c4(U11'(s(encArg(z0)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_U12(x2, x3, x4))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, tt, cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), tt, U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, 0, cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), 0, U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(tt, x1, cons_U12(x2, x3, x4))) -> c4(U11'(tt, encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(0, x1, cons_U12(x2, x3, x4))) -> c4(U11'(0, encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_s(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_s(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, x1, cons_s(tt))) -> c4(U11'(encArg(x0), encArg(x1), s(tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(tt))) ENCARG(cons_U11(x0, x1, cons_s(0))) -> c4(U11'(encArg(x0), encArg(x1), s(0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(0))) ENCARG(cons_U11(x0, x1, cons_s(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), s(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_s(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_s(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_s(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_s(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), s(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_s(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, tt, cons_s(x2))) -> c4(U11'(encArg(x0), tt, s(encArg(x2))), ENCARG(x0), ENCARG(tt), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, 0, cons_s(x2))) -> c4(U11'(encArg(x0), 0, s(encArg(x2))), ENCARG(x0), ENCARG(0), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_active(z0), cons_s(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_s(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_s(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_s(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_s(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_s(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x2))) ENCARG(cons_U11(tt, x1, cons_s(x2))) -> c4(U11'(tt, encArg(x1), s(encArg(x2))), ENCARG(tt), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(0, x1, cons_s(x2))) -> c4(U11'(0, encArg(x1), s(encArg(x2))), ENCARG(0), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_s(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), s(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_s(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), s(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_s(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), s(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_s(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), s(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_s(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), s(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_s(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), s(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_s(x2))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c3_2, c8_1 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1, z2)) -> U11(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U12(z0, z1, z2)) -> U12(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(z0) -> c_active(z0) active(c_U12(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(c_plus(z0, c_s(z1))) -> mark(U11(tt, z1, z0)) active(c_U11(tt, z0, z1)) -> mark(U12(tt, z0, z1)) active(c_plus(z0, 0)) -> mark(z0) mark(z0) -> c_mark(z0) mark(tt) -> active(tt) mark(0) -> active(0) mark(c_U12(z0, z1, z2)) -> active(U12(mark(z0), z1, z2)) mark(c_s(z0)) -> active(s(mark(z0))) mark(c_U11(z0, z1, z2)) -> active(U11(mark(z0), z1, z2)) mark(c_plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) U11(z0, z1, z2) -> c_U11(z0, z1, z2) U11(z0, c_mark(z1), z2) -> U11(z0, z1, z2) U11(c_active(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, c_active(z1), z2) -> U11(z0, z1, z2) U11(c_mark(z0), z1, z2) -> U11(z0, z1, z2) U11(z0, z1, c_mark(z2)) -> U11(z0, z1, z2) U11(z0, z1, c_active(z2)) -> U11(z0, z1, z2) U12(z0, z1, z2) -> c_U12(z0, z1, z2) U12(z0, c_active(z1), z2) -> U12(z0, z1, z2) U12(c_mark(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_mark(z2)) -> U12(z0, z1, z2) U12(c_active(z0), z1, z2) -> U12(z0, z1, z2) U12(z0, z1, c_active(z2)) -> U12(z0, z1, z2) U12(z0, c_mark(z1), z2) -> U12(z0, z1, z2) s(z0) -> c_s(z0) s(c_active(z0)) -> s(z0) s(c_mark(z0)) -> s(z0) plus(z0, z1) -> c_plus(z0, z1) plus(z0, c_mark(z1)) -> plus(z0, z1) plus(c_active(z0), z1) -> plus(z0, z1) plus(c_mark(z0), z1) -> plus(z0, z1) plus(z0, c_active(z1)) -> plus(z0, z1) Tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, x1, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_active(z0), x2)) -> c4(U11'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_mark(z0), x2)) -> c4(U11'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2)) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_s(z0), x2)) -> c4(U11'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U11(x0, cons_plus(z0, z1), x2)) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U11(cons_active(z0), x1, x2)) -> c4(U11'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_mark(z0), x1, x2)) -> c4(U11'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2)) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2)) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_s(z0), x1, x2)) -> c4(U11'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(cons_plus(z0, z1), x1, x2)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(x0, x1, tt)) -> c4(U11'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, 0)) -> c4(U11'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, x2)) -> c4(U11'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(x0, 0, x2)) -> c4(U11'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U11(tt, x1, x2)) -> c4(U11'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U11(0, x1, x2)) -> c4(U11'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, cons_active(z0))) -> c5(U12'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U12(x0, x1, cons_mark(z0))) -> c5(U12'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2))) -> c5(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_U12(x0, x1, cons_s(z0))) -> c5(U12'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U12(x0, x1, cons_plus(z0, z1))) -> c5(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U12(x0, cons_active(z0), x2)) -> c5(U12'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_mark(z0), x2)) -> c5(U12'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2)) -> c5(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_s(z0), x2)) -> c5(U12'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U12(x0, cons_plus(z0, z1), x2)) -> c5(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U12(cons_active(z0), x1, x2)) -> c5(U12'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_mark(z0), x1, x2)) -> c5(U12'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2)) -> c5(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2)) -> c5(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_s(z0), x1, x2)) -> c5(U12'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(cons_plus(z0, z1), x1, x2)) -> c5(U12'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(x0, x1, tt)) -> c5(U12'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, x1, 0)) -> c5(U12'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U12(x0, tt, x2)) -> c5(U12'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(x0, 0, x2)) -> c5(U12'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U12(tt, x1, x2)) -> c5(U12'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U12(0, x1, x2)) -> c5(U12'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1, z2))) -> c6(S(U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_s(cons_U12(z0, z1, z2))) -> c6(S(U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1, z2))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U12(z0, z1, z2))) -> c7(PLUS(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1, z2), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0, z1, z2), x1)) -> c7(PLUS(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1, z2)) -> c(ACTIVE(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U12(z0, z1, z2)) -> c(ACTIVE(U12(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, x1, tt) -> c(U11'(encArg(x0), encArg(x1), tt)) ENCODE_U11(x0, x1, 0) -> c(U11'(encArg(x0), encArg(x1), 0)) ENCODE_U11(x0, x1, cons_active(z0)) -> c(U11'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U11(x0, x1, cons_mark(z0)) -> c(U11'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U11(x0, x1, cons_U11(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_U12(z0, z1, z2)) -> c(U11'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, x1, cons_s(z0)) -> c(U11'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U11(x0, x1, cons_plus(z0, z1)) -> c(U11'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, tt, x2) -> c(U11'(encArg(x0), tt, encArg(x2))) ENCODE_U11(x0, 0, x2) -> c(U11'(encArg(x0), 0, encArg(x2))) ENCODE_U11(x0, cons_active(z0), x2) -> c(U11'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_mark(z0), x2) -> c(U11'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_U11(z0, z1, z2), x2) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_U12(z0, z1, z2), x2) -> c(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U11(x0, cons_s(z0), x2) -> c(U11'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U11(x0, cons_plus(z0, z1), x2) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U11(tt, x1, x2) -> c(U11'(tt, encArg(x1), encArg(x2))) ENCODE_U11(0, x1, x2) -> c(U11'(0, encArg(x1), encArg(x2))) ENCODE_U11(cons_active(z0), x1, x2) -> c(U11'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_mark(z0), x1, x2) -> c(U11'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U11(z0, z1, z2), x1, x2) -> c(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_U12(z0, z1, z2), x1, x2) -> c(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U11(cons_s(z0), x1, x2) -> c(U11'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U11(cons_plus(z0, z1), x1, x2) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) 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, z2)) -> c(MARK(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U12(z0, z1, z2)) -> c(MARK(U12(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(x0, x1, tt) -> c(U12'(encArg(x0), encArg(x1), tt)) ENCODE_U12(x0, x1, 0) -> c(U12'(encArg(x0), encArg(x1), 0)) ENCODE_U12(x0, x1, cons_active(z0)) -> c(U12'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U12(x0, x1, cons_mark(z0)) -> c(U12'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U12(x0, x1, cons_U11(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_U12(z0, z1, z2)) -> c(U12'(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(x0, x1, cons_s(z0)) -> c(U12'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U12(x0, x1, cons_plus(z0, z1)) -> c(U12'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U12(x0, tt, x2) -> c(U12'(encArg(x0), tt, encArg(x2))) ENCODE_U12(x0, 0, x2) -> c(U12'(encArg(x0), 0, encArg(x2))) ENCODE_U12(x0, cons_active(z0), x2) -> c(U12'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_mark(z0), x2) -> c(U12'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_U11(z0, z1, z2), x2) -> c(U12'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_U12(z0, z1, z2), x2) -> c(U12'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U12(x0, cons_s(z0), x2) -> c(U12'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U12(x0, cons_plus(z0, z1), x2) -> c(U12'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U12(tt, x1, x2) -> c(U12'(tt, encArg(x1), encArg(x2))) ENCODE_U12(0, x1, x2) -> c(U12'(0, encArg(x1), encArg(x2))) ENCODE_U12(cons_active(z0), x1, x2) -> c(U12'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_mark(z0), x1, x2) -> c(U12'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U11(z0, z1, z2), x1, x2) -> c(U12'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_U12(z0, z1, z2), x1, x2) -> c(U12'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U12(cons_s(z0), x1, x2) -> c(U12'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U12(cons_plus(z0, z1), x1, x2) -> c(U12'(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, z2)) -> c(S(U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U12(z0, z1, z2)) -> c(S(U12(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, z2)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U12(z0, z1, z2)) -> c(PLUS(encArg(x0), U12(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, z2), x1) -> c(PLUS(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U12(z0, z1, z2), x1) -> c(PLUS(U12(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, z2)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_s(z0)))) -> c2(ACTIVE(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_active(cons_active(x0))) -> c2(ENCARG(cons_active(x0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(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, z2)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(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(x0))) -> c2(ENCARG(cons_mark(x0))) 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, x1, x2))) -> c2(ACTIVE(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_active(cons_U11(x0, x1, tt))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_active(cons_U11(x0, x1, 0))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_active(cons_U11(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, tt, x2))) -> c2(ACTIVE(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_active(cons_U11(x0, 0, x2))) -> c2(ACTIVE(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_active(cons_U11(x0, cons_active(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U11(x0, cons_s(z0), x2))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U11(tt, x1, x2))) -> c2(ACTIVE(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_active(cons_U11(0, x1, x2))) -> c2(ACTIVE(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_active(cons_U11(cons_active(z0), x1, x2))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U11(cons_s(z0), x1, x2))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, x2))) -> c2(ACTIVE(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_active(cons_U12(x0, x1, tt))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_active(cons_U12(x0, x1, 0))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_active(cons_U12(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_U12(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U12(x0, tt, x2))) -> c2(ACTIVE(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_active(cons_U12(x0, 0, x2))) -> c2(ACTIVE(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_active(cons_U12(x0, cons_active(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c2(ACTIVE(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_active(cons_U12(x0, cons_s(z0), x2))) -> c2(ACTIVE(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U12(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U12(tt, x1, x2))) -> c2(ACTIVE(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_active(cons_U12(0, x1, x2))) -> c2(ACTIVE(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_active(cons_U12(cons_active(z0), x1, x2))) -> c2(ACTIVE(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U12(cons_s(z0), x1, x2))) -> c2(ACTIVE(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U12(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_s(cons_active(z0)))) -> c2(ACTIVE(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_active(cons_s(cons_mark(z0)))) -> c2(ACTIVE(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_active(cons_s(cons_U11(z0, z1, z2)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_U12(z0, z1, z2)))) -> c2(ACTIVE(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_s(cons_s(z0)))) -> c2(ACTIVE(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_active(cons_s(x0))) -> c2(ENCARG(cons_s(x0))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0))) ENCARG(cons_active(cons_plus(x0, x1))) -> c2(ACTIVE(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_U11(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_U12(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_mark(cons_active(cons_active(z0)))) -> c3(MARK(active(active(encArg(z0)))), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_mark(cons_active(cons_mark(z0)))) -> c3(MARK(active(mark(encArg(z0)))), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_mark(cons_active(cons_U11(z0, z1, z2)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_U12(z0, z1, z2)))) -> c3(MARK(active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_active(cons_s(z0)))) -> c3(MARK(active(s(encArg(z0)))), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_active(x0))) -> c3(ENCARG(cons_active(x0))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0))) ENCARG(cons_mark(cons_mark(cons_active(z0)))) -> c3(MARK(mark(active(encArg(z0)))), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_mark(cons_mark(cons_mark(z0)))) -> c3(MARK(mark(mark(encArg(z0)))), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_mark(cons_mark(cons_U11(z0, z1, z2)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_U12(z0, z1, z2)))) -> c3(MARK(mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_mark(cons_s(z0)))) -> c3(MARK(mark(s(encArg(z0)))), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_mark(x0))) -> c3(ENCARG(cons_mark(x0))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_mark(cons_U11(x0, x1, x2))) -> c3(MARK(c_U11(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U11(x0, x1, x2))) ENCARG(cons_mark(cons_U11(x0, x1, tt))) -> c3(MARK(U11(encArg(x0), encArg(x1), tt)), ENCARG(cons_U11(x0, x1, tt))) ENCARG(cons_mark(cons_U11(x0, x1, 0))) -> c3(MARK(U11(encArg(x0), encArg(x1), 0)), ENCARG(cons_U11(x0, x1, 0))) ENCARG(cons_mark(cons_U11(x0, x1, cons_active(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_mark(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U11(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_s(z0)))) -> c3(MARK(U11(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U11(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U11(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U11(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U11(x0, tt, x2))) -> c3(MARK(U11(encArg(x0), tt, encArg(x2))), ENCARG(cons_U11(x0, tt, x2))) ENCARG(cons_mark(cons_U11(x0, 0, x2))) -> c3(MARK(U11(encArg(x0), 0, encArg(x2))), ENCARG(cons_U11(x0, 0, x2))) ENCARG(cons_mark(cons_U11(x0, cons_active(z0), x2))) -> c3(MARK(U11(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_mark(z0), x2))) -> c3(MARK(U11(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U11(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U11(x0, cons_s(z0), x2))) -> c3(MARK(U11(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U11(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U11(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U11(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U11(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U11(tt, x1, x2))) -> c3(MARK(U11(tt, encArg(x1), encArg(x2))), ENCARG(cons_U11(tt, x1, x2))) ENCARG(cons_mark(cons_U11(0, x1, x2))) -> c3(MARK(U11(0, encArg(x1), encArg(x2))), ENCARG(cons_U11(0, x1, x2))) ENCARG(cons_mark(cons_U11(cons_active(z0), x1, x2))) -> c3(MARK(U11(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_mark(z0), x1, x2))) -> c3(MARK(U11(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U11(cons_s(z0), x1, x2))) -> c3(MARK(U11(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U11(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U11(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U11(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, x2))) -> c3(MARK(c_U12(encArg(x0), encArg(x1), encArg(x2))), ENCARG(cons_U12(x0, x1, x2))) ENCARG(cons_mark(cons_U12(x0, x1, tt))) -> c3(MARK(U12(encArg(x0), encArg(x1), tt)), ENCARG(cons_U12(x0, x1, tt))) ENCARG(cons_mark(cons_U12(x0, x1, 0))) -> c3(MARK(U12(encArg(x0), encArg(x1), 0)), ENCARG(cons_U12(x0, x1, 0))) ENCARG(cons_mark(cons_U12(x0, x1, cons_active(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_active(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_mark(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_mark(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) -> c3(MARK(U12(encArg(x0), encArg(x1), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U12(x0, x1, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_s(z0)))) -> c3(MARK(U12(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U12(x0, x1, cons_s(z0)))) ENCARG(cons_mark(cons_U12(x0, x1, cons_plus(z0, z1)))) -> c3(MARK(U12(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U12(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_U12(x0, tt, x2))) -> c3(MARK(U12(encArg(x0), tt, encArg(x2))), ENCARG(cons_U12(x0, tt, x2))) ENCARG(cons_mark(cons_U12(x0, 0, x2))) -> c3(MARK(U12(encArg(x0), 0, encArg(x2))), ENCARG(cons_U12(x0, 0, x2))) ENCARG(cons_mark(cons_U12(x0, cons_active(z0), x2))) -> c3(MARK(U12(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_active(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_mark(z0), x2))) -> c3(MARK(U12(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_mark(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U11(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U11(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_U12(z0, z1, z2), x2))) -> c3(MARK(U12(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U12(x0, cons_U12(z0, z1, z2), x2))) ENCARG(cons_mark(cons_U12(x0, cons_s(z0), x2))) -> c3(MARK(U12(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U12(x0, cons_s(z0), x2))) ENCARG(cons_mark(cons_U12(x0, cons_plus(z0, z1), x2))) -> c3(MARK(U12(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U12(x0, cons_plus(z0, z1), x2))) ENCARG(cons_mark(cons_U12(tt, x1, x2))) -> c3(MARK(U12(tt, encArg(x1), encArg(x2))), ENCARG(cons_U12(tt, x1, x2))) ENCARG(cons_mark(cons_U12(0, x1, x2))) -> c3(MARK(U12(0, encArg(x1), encArg(x2))), ENCARG(cons_U12(0, x1, x2))) ENCARG(cons_mark(cons_U12(cons_active(z0), x1, x2))) -> c3(MARK(U12(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_active(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_mark(z0), x1, x2))) -> c3(MARK(U12(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_mark(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U11(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U11(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_U12(z0, z1, z2), x1, x2))) -> c3(MARK(U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_U12(z0, z1, z2), x1, x2))) ENCARG(cons_mark(cons_U12(cons_s(z0), x1, x2))) -> c3(MARK(U12(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_s(z0), x1, x2))) ENCARG(cons_mark(cons_U12(cons_plus(z0, z1), x1, x2))) -> c3(MARK(U12(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U12(cons_plus(z0, z1), x1, x2))) ENCARG(cons_mark(cons_s(x0))) -> c3(MARK(c_s(encArg(x0))), ENCARG(cons_s(x0))) ENCARG(cons_mark(cons_s(cons_active(z0)))) -> c3(MARK(s(active(encArg(z0)))), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_mark(cons_s(cons_mark(z0)))) -> c3(MARK(s(mark(encArg(z0)))), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_mark(cons_s(cons_U11(z0, z1, z2)))) -> c3(MARK(s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_U12(z0, z1, z2)))) -> c3(MARK(s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_s(cons_s(z0)))) -> c3(MARK(s(s(encArg(z0)))), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_mark(cons_s(cons_plus(z0, z1)))) -> c3(MARK(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_mark(cons_s(tt))) -> c3(MARK(s(tt))) ENCARG(cons_mark(cons_s(0))) -> c3(MARK(s(0))) ENCARG(cons_mark(cons_plus(x0, x1))) -> c3(MARK(c_plus(encArg(x0), encArg(x1))), ENCARG(cons_plus(x0, x1))) ENCARG(cons_mark(cons_plus(x0, tt))) -> c3(MARK(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_mark(cons_plus(x0, 0))) -> c3(MARK(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_mark(cons_plus(x0, cons_active(z0)))) -> c3(MARK(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_mark(z0)))) -> c3(MARK(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_U11(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U11(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_U12(z0, z1, z2)))) -> c3(MARK(plus(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U12(z0, z1, z2)))) ENCARG(cons_mark(cons_plus(x0, cons_s(z0)))) -> c3(MARK(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_mark(cons_plus(x0, cons_plus(z0, z1)))) -> c3(MARK(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_mark(cons_plus(tt, x1))) -> c3(MARK(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_mark(cons_plus(0, x1))) -> c3(MARK(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_mark(cons_plus(cons_active(z0), x1))) -> c3(MARK(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_mark(cons_plus(cons_mark(z0), x1))) -> c3(MARK(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_mark(cons_plus(cons_U11(z0, z1, z2), x1))) -> c3(MARK(plus(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_U12(z0, z1, z2), x1))) -> c3(MARK(plus(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U12(z0, z1, z2), x1))) ENCARG(cons_mark(cons_plus(cons_s(z0), x1))) -> c3(MARK(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_mark(cons_plus(cons_plus(z0, z1), x1))) -> c3(MARK(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_U11(x0, x1, cons_active(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_active(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), active(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_active(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), active(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_active(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), active(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_active(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_active(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_active(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_active(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_active(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), active(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_active(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_active(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_active(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), active(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_active(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), active(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_active(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), active(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_active(tt))) -> c4(U11'(encArg(x0), encArg(x1), active(tt)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, cons_active(0))) -> c4(U11'(encArg(x0), encArg(x1), active(0)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, cons_active(x2))) -> c4(U11'(encArg(x0), tt, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, 0, cons_active(x2))) -> c4(U11'(encArg(x0), 0, active(encArg(x2))), ENCARG(x0), ENCARG(cons_active(x2))) ENCARG(cons_U11(tt, x1, cons_active(x2))) -> c4(U11'(tt, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(0, x1, cons_active(x2))) -> c4(U11'(0, encArg(x1), active(encArg(x2))), ENCARG(x1), ENCARG(cons_active(x2))) ENCARG(cons_U11(x0, x1, cons_mark(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_mark(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, x1, cons_mark(tt))) -> c4(U11'(encArg(x0), encArg(x1), mark(tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(tt))) ENCARG(cons_U11(x0, x1, cons_mark(0))) -> c4(U11'(encArg(x0), encArg(x1), mark(0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, x1, cons_mark(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), mark(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), mark(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_mark(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), mark(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_mark(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_mark(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_mark(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), mark(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_mark(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_mark(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_mark(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), mark(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_mark(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), mark(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_mark(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), mark(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, tt, cons_mark(x2))) -> c4(U11'(encArg(x0), tt, mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, 0, cons_mark(x2))) -> c4(U11'(encArg(x0), 0, mark(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(x2))) ENCARG(cons_U11(tt, x1, cons_mark(x2))) -> c4(U11'(tt, encArg(x1), mark(encArg(x2))), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(0, x1, cons_mark(x2))) -> c4(U11'(0, encArg(x1), mark(encArg(x2))), ENCARG(x1), ENCARG(cons_mark(x2))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), c_U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, tt))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, tt))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, 0))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), 0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, 0))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, x3, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), encArg(x3), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, x3, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, x1, cons_U11(x2, tt, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), tt, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, tt, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, 0, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), 0, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, 0, x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_active(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), active(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_active(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_mark(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), mark(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_mark(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_U11(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_U11(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_U12(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_U12(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_s(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), s(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_s(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U11(x2, cons_plus(z0, z1), x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(encArg(x2), plus(encArg(z0), encArg(z1)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(x2, cons_plus(z0, z1), x4))) ENCARG(cons_U11(x0, x1, cons_U11(tt, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(tt, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(tt, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(0, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(0, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(0, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_active(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(active(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_active(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_mark(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(mark(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_mark(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_U11(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_U11(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_U12(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_U12(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_s(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(s(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_s(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U11(cons_plus(z0, z1), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U11(plus(encArg(z0), encArg(z1)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(cons_plus(z0, z1), x3, x4))) ENCARG(cons_U11(x0, cons_active(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), active(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_mark(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), mark(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_s(z0), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), s(encArg(z0)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_active(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(active(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_mark(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(mark(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_U11(x2, x3, x4))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_U11(x2, x3, x4))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_s(z0), x1, cons_U11(x2, x3, x4))) -> c4(U11'(s(encArg(z0)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_U11(x2, x3, x4))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, tt, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), tt, U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, 0, cons_U11(x2, x3, x4))) -> c4(U11'(encArg(x0), 0, U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(tt, x1, cons_U11(x2, x3, x4))) -> c4(U11'(tt, encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(0, x1, cons_U11(x2, x3, x4))) -> c4(U11'(0, encArg(x1), U11(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U11(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), c_U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, tt))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), tt)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, tt))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, 0))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), 0)), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, 0))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, x3, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), encArg(x3), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, x3, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, x1, cons_U12(x2, tt, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), tt, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, tt, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, 0, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), 0, encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, 0, x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_active(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), active(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_active(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_mark(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), mark(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_mark(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_U11(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_U11(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_U12(z0, z1, z2), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_U12(z0, z1, z2), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_s(z0), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), s(encArg(z0)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_s(z0), x4))) ENCARG(cons_U11(x0, x1, cons_U12(x2, cons_plus(z0, z1), x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(encArg(x2), plus(encArg(z0), encArg(z1)), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(x2, cons_plus(z0, z1), x4))) ENCARG(cons_U11(x0, x1, cons_U12(tt, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(tt, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(tt, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(0, x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(0, encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(0, x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_active(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(active(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_active(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_mark(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(mark(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_mark(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_U11(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_U11(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_U12(z0, z1, z2), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_U12(z0, z1, z2), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_s(z0), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(s(encArg(z0)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_s(z0), x3, x4))) ENCARG(cons_U11(x0, x1, cons_U12(cons_plus(z0, z1), x3, x4))) -> c4(U11'(encArg(x0), encArg(x1), U12(plus(encArg(z0), encArg(z1)), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(cons_plus(z0, z1), x3, x4))) ENCARG(cons_U11(x0, cons_active(z0), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), active(encArg(z0)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_mark(z0), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), mark(encArg(z0)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_s(z0), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), s(encArg(z0)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_active(z0), x1, cons_U12(x2, x3, x4))) -> c4(U11'(active(encArg(z0)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_mark(z0), x1, cons_U12(x2, x3, x4))) -> c4(U11'(mark(encArg(z0)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_U12(x2, x3, x4))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_U12(x2, x3, x4))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_s(z0), x1, cons_U12(x2, x3, x4))) -> c4(U11'(s(encArg(z0)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_U12(x2, x3, x4))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, tt, cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), tt, U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, 0, cons_U12(x2, x3, x4))) -> c4(U11'(encArg(x0), 0, U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x0), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(tt, x1, cons_U12(x2, x3, x4))) -> c4(U11'(tt, encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(0, x1, cons_U12(x2, x3, x4))) -> c4(U11'(0, encArg(x1), U12(encArg(x2), encArg(x3), encArg(x4))), ENCARG(x1), ENCARG(cons_U12(x2, x3, x4))) ENCARG(cons_U11(x0, x1, cons_s(x2))) -> c4(U11'(encArg(x0), encArg(x1), c_s(encArg(x2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, x1, cons_s(cons_active(z0)))) -> c4(U11'(encArg(x0), encArg(x1), s(active(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_U11(x0, x1, cons_s(cons_mark(z0)))) -> c4(U11'(encArg(x0), encArg(x1), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_U11(x0, x1, cons_s(cons_U11(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), s(U11(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_U11(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_s(cons_U12(z0, z1, z2)))) -> c4(U11'(encArg(x0), encArg(x1), s(U12(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_U12(z0, z1, z2)))) ENCARG(cons_U11(x0, x1, cons_s(cons_s(z0)))) -> c4(U11'(encArg(x0), encArg(x1), s(s(encArg(z0)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_U11(x0, x1, cons_s(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), encArg(x1), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_active(z0), cons_s(x2))) -> c4(U11'(encArg(x0), active(encArg(z0)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_mark(z0), cons_s(x2))) -> c4(U11'(encArg(x0), mark(encArg(z0)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_U11(z0, z1, z2), cons_s(x2))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1), encArg(z2)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_U11(z0, z1, z2)), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_U12(z0, z1, z2), cons_s(x2))) -> c4(U11'(encArg(x0), U12(encArg(z0), encArg(z1), encArg(z2)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_U12(z0, z1, z2)), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_s(z0), cons_s(x2))) -> c4(U11'(encArg(x0), s(encArg(z0)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, cons_plus(z0, z1), cons_s(x2))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1)), s(encArg(x2))), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_active(z0), x1, cons_s(x2))) -> c4(U11'(active(encArg(z0)), encArg(x1), s(encArg(x2))), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_mark(z0), x1, cons_s(x2))) -> c4(U11'(mark(encArg(z0)), encArg(x1), s(encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_U11(z0, z1, z2), x1, cons_s(x2))) -> c4(U11'(U11(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), s(encArg(x2))), ENCARG(cons_U11(z0, z1, z2)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_U12(z0, z1, z2), x1, cons_s(x2))) -> c4(U11'(U12(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), s(encArg(x2))), ENCARG(cons_U12(z0, z1, z2)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_s(z0), x1, cons_s(x2))) -> c4(U11'(s(encArg(z0)), encArg(x1), s(encArg(x2))), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(cons_plus(z0, z1), x1, cons_s(x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1), s(encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, x1, cons_s(tt))) -> c4(U11'(encArg(x0), encArg(x1), s(tt)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, x1, cons_s(0))) -> c4(U11'(encArg(x0), encArg(x1), s(0)), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U11(x0, tt, cons_s(x2))) -> c4(U11'(encArg(x0), tt, s(encArg(x2))), ENCARG(x0), ENCARG(cons_s(x2))) ENCARG(cons_U11(x0, 0, cons_s(x2))) -> c4(U11'(encArg(x0), 0, s(encArg(x2))), ENCARG(x0), ENCARG(cons_s(x2))) ENCARG(cons_U11(tt, x1, cons_s(x2))) -> c4(U11'(tt, encArg(x1), s(encArg(x2))), ENCARG(x1), ENCARG(cons_s(x2))) ENCARG(cons_U11(0, x1, cons_s(x2))) -> c4(U11'(0, encArg(x1), s(encArg(x2))), ENCARG(x1), ENCARG(cons_s(x2))) S tuples: S(c_active(z0)) -> c17(S(z0)) S(c_mark(z0)) -> c18(S(z0)) ACTIVE(c_plus(z0, 0)) -> c23(MARK(z0)) PLUS(z0, c_mark(z1)) -> c25(PLUS(z0, z1)) PLUS(c_active(z0), z1) -> c26(PLUS(z0, z1)) PLUS(c_mark(z0), z1) -> c27(PLUS(z0, z1)) PLUS(z0, c_active(z1)) -> c28(PLUS(z0, z1)) U12'(z0, c_active(z1), z2) -> c30(U12'(z0, z1, z2)) U12'(c_mark(z0), z1, z2) -> c31(U12'(z0, z1, z2)) U12'(z0, z1, c_mark(z2)) -> c32(U12'(z0, z1, z2)) U12'(c_active(z0), z1, z2) -> c33(U12'(z0, z1, z2)) U12'(z0, z1, c_active(z2)) -> c34(U12'(z0, z1, z2)) U12'(z0, c_mark(z1), z2) -> c35(U12'(z0, z1, z2)) U11'(z0, c_mark(z1), z2) -> c37(U11'(z0, z1, z2)) U11'(c_active(z0), z1, z2) -> c38(U11'(z0, z1, z2)) U11'(z0, c_active(z1), z2) -> c39(U11'(z0, z1, z2)) U11'(c_mark(z0), z1, z2) -> c40(U11'(z0, z1, z2)) U11'(z0, z1, c_mark(z2)) -> c41(U11'(z0, z1, z2)) U11'(z0, z1, c_active(z2)) -> c42(U11'(z0, z1, z2)) MARK(tt) -> c44 MARK(0) -> c45 ACTIVE(c_U12(tt, x0, x1)) -> c20(MARK(c_s(plus(x1, x0))), S(plus(x1, x0)), PLUS(x1, x0)) ACTIVE(c_U12(tt, z1, z0)) -> c20(MARK(s(c_plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(c_U12(tt, c_mark(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_mark(z1))), PLUS(z0, c_mark(z1))) ACTIVE(c_U12(tt, z1, c_active(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_active(z0), z1)), PLUS(c_active(z0), z1)) ACTIVE(c_U12(tt, z1, c_mark(z0))) -> c20(MARK(s(plus(z0, z1))), S(plus(c_mark(z0), z1)), PLUS(c_mark(z0), z1)) ACTIVE(c_U12(tt, c_active(z1), z0)) -> c20(MARK(s(plus(z0, z1))), S(plus(z0, c_active(z1))), PLUS(z0, c_active(z1))) ACTIVE(c_plus(z2, c_s(z1))) -> c21(MARK(c_U11(tt, z1, z2)), U11'(tt, z1, z2)) ACTIVE(c_plus(z2, c_s(c_mark(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_mark(z1), z2)) ACTIVE(c_plus(z2, c_s(c_active(z1)))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, c_active(z1), z2)) ACTIVE(c_plus(c_mark(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_mark(z2))) ACTIVE(c_plus(c_active(z2), c_s(z1))) -> c21(MARK(U11(tt, z1, z2)), U11'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, z1, z2)) -> c22(MARK(c_U12(tt, z1, z2)), U12'(tt, z1, z2)) ACTIVE(c_U11(tt, c_active(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_active(z1), z2)) ACTIVE(c_U11(tt, z1, c_mark(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_mark(z2))) ACTIVE(c_U11(tt, z1, c_active(z2))) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, z1, c_active(z2))) ACTIVE(c_U11(tt, c_mark(z1), z2)) -> c22(MARK(U12(tt, z1, z2)), U12'(tt, c_mark(z1), z2)) MARK(c_U12(x0, z1, z2)) -> c46(ACTIVE(c_U12(mark(x0), z1, z2)), U12'(mark(x0), z1, z2), MARK(x0)) MARK(c_U12(x0, c_active(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U12(x0, z1, c_mark(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U12(x0, z1, c_active(z2))) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U12(x0, c_mark(z1), z2)) -> c46(ACTIVE(U12(mark(x0), z1, z2)), U12'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U12(z0, x1, x2)) -> c46(ACTIVE(U12(c_mark(z0), x1, x2)), U12'(mark(z0), x1, x2), MARK(z0)) MARK(c_U12(tt, x1, x2)) -> c46(ACTIVE(U12(active(tt), x1, x2)), U12'(mark(tt), x1, x2), MARK(tt)) MARK(c_U12(0, x1, x2)) -> c46(ACTIVE(U12(active(0), x1, x2)), U12'(mark(0), x1, x2), MARK(0)) MARK(c_U12(c_U12(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U12(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U12(c_s(z0), x1, x2)) -> c46(ACTIVE(U12(active(s(mark(z0))), x1, x2)), U12'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U12(c_U11(z0, z1, z2), x1, x2)) -> c46(ACTIVE(U12(active(U11(mark(z0), z1, z2)), x1, x2)), U12'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U12(c_plus(z0, z1), x1, x2)) -> c46(ACTIVE(U12(active(plus(mark(z0), mark(z1))), x1, x2)), U12'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_s(z0)) -> c47(ACTIVE(s(c_mark(z0))), S(mark(z0)), MARK(z0)) MARK(c_s(tt)) -> c47(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(c_s(0)) -> c47(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(c_s(c_U12(z0, z1, z2))) -> c47(ACTIVE(s(active(U12(mark(z0), z1, z2)))), S(mark(c_U12(z0, z1, z2))), MARK(c_U12(z0, z1, z2))) MARK(c_s(c_s(z0))) -> c47(ACTIVE(s(active(s(mark(z0))))), S(mark(c_s(z0))), MARK(c_s(z0))) MARK(c_s(c_U11(z0, z1, z2))) -> c47(ACTIVE(s(active(U11(mark(z0), z1, z2)))), S(mark(c_U11(z0, z1, z2))), MARK(c_U11(z0, z1, z2))) MARK(c_s(c_plus(z0, z1))) -> c47(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(c_plus(z0, z1))), MARK(c_plus(z0, z1))) MARK(c_s(x0)) -> c47(S(mark(x0)), MARK(x0)) MARK(c_U11(x0, z1, z2)) -> c48(ACTIVE(c_U11(mark(x0), z1, z2)), U11'(mark(x0), z1, z2), MARK(x0)) MARK(c_U11(x0, c_mark(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_mark(z1), z2), MARK(x0)) MARK(c_U11(x0, c_active(z1), z2)) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), c_active(z1), z2), MARK(x0)) MARK(c_U11(x0, z1, c_mark(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_mark(z2)), MARK(x0)) MARK(c_U11(x0, z1, c_active(z2))) -> c48(ACTIVE(U11(mark(x0), z1, z2)), U11'(mark(x0), z1, c_active(z2)), MARK(x0)) MARK(c_U11(z0, x1, x2)) -> c48(ACTIVE(U11(c_mark(z0), x1, x2)), U11'(mark(z0), x1, x2), MARK(z0)) MARK(c_U11(tt, x1, x2)) -> c48(ACTIVE(U11(active(tt), x1, x2)), U11'(mark(tt), x1, x2), MARK(tt)) MARK(c_U11(0, x1, x2)) -> c48(ACTIVE(U11(active(0), x1, x2)), U11'(mark(0), x1, x2), MARK(0)) MARK(c_U11(c_U12(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U12(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U12(z0, z1, z2)), x1, x2), MARK(c_U12(z0, z1, z2))) MARK(c_U11(c_s(z0), x1, x2)) -> c48(ACTIVE(U11(active(s(mark(z0))), x1, x2)), U11'(mark(c_s(z0)), x1, x2), MARK(c_s(z0))) MARK(c_U11(c_U11(z0, z1, z2), x1, x2)) -> c48(ACTIVE(U11(active(U11(mark(z0), z1, z2)), x1, x2)), U11'(mark(c_U11(z0, z1, z2)), x1, x2), MARK(c_U11(z0, z1, z2))) MARK(c_U11(c_plus(z0, z1), x1, x2)) -> c48(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1, x2)), U11'(mark(c_plus(z0, z1)), x1, x2), MARK(c_plus(z0, z1))) MARK(c_plus(x0, x1)) -> c49(ACTIVE(c_plus(mark(x0), mark(x1))), PLUS(mark(x0), mark(x1)), MARK(x0), MARK(x1)) MARK(c_plus(x0, z0)) -> c49(ACTIVE(plus(mark(x0), c_mark(z0))), PLUS(mark(x0), mark(z0)), MARK(x0), MARK(z0)) MARK(c_plus(x0, tt)) -> c49(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(c_plus(x0, 0)) -> c49(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(c_plus(x0, c_U12(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U12(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U12(z0, z1, z2))), MARK(x0), MARK(c_U12(z0, z1, z2))) MARK(c_plus(x0, c_s(z0))) -> c49(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(c_s(z0))), MARK(x0), MARK(c_s(z0))) MARK(c_plus(x0, c_U11(z0, z1, z2))) -> c49(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1, z2)))), PLUS(mark(x0), mark(c_U11(z0, z1, z2))), MARK(x0), MARK(c_U11(z0, z1, z2))) MARK(c_plus(x0, c_plus(z0, z1))) -> c49(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(c_plus(z0, z1))), MARK(x0), MARK(c_plus(z0, z1))) MARK(c_plus(z0, x1)) -> c49(ACTIVE(plus(c_mark(z0), mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(c_plus(tt, x1)) -> c49(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(c_plus(0, x1)) -> c49(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(c_plus(c_U12(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U12(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U12(z0, z1, z2)), mark(x1)), MARK(c_U12(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_s(z0), x1)) -> c49(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(c_s(z0)), mark(x1)), MARK(c_s(z0)), MARK(x1)) MARK(c_plus(c_U11(z0, z1, z2), x1)) -> c49(ACTIVE(plus(active(U11(mark(z0), z1, z2)), mark(x1))), PLUS(mark(c_U11(z0, z1, z2)), mark(x1)), MARK(c_U11(z0, z1, z2)), MARK(x1)) MARK(c_plus(c_plus(z0, z1), x1)) -> c49(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(c_plus(z0, z1)), mark(x1)), MARK(c_plus(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_3, U12_3, s_1, plus_2 Defined Pair Symbols: S_1, ACTIVE_1, PLUS_2, U12'_3, U11'_3, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_3, ENCODE_MARK_1, ENCODE_U12_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c17_1, c18_1, c23_1, c25_1, c26_1, c27_1, c28_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c44, c45, c3_1, c4_4, c4_3, c5_4, c5_3, c6_2, c7_3, c7_2, c20_3, c21_2, c22_2, c46_3, c47_3, c47_2, c48_3, c49_4, c_1, c2_2, c2_1, c1_1, c3_2, c8_1