KILLED proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF).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), 166 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 200 ms] (12) BOUNDS(1, INF) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (16) CpxTRS (17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (18) CpxRelTRS (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 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), 0 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), 0 ms] (36) CpxRNTS (37) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (38) CdtProblem (39) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 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), 0 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 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) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 2 ms] (86) CdtProblem (87) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtRewritingProof [BOTH BOUNDS(ID, ID), 17 ms] (94) CdtProblem (95) CdtRewritingProof [BOTH BOUNDS(ID, ID), 13 ms] (96) CdtProblem (97) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtRewritingProof [BOTH BOUNDS(ID, ID), 7 ms] (100) CdtProblem (101) CdtRewritingProof [BOTH BOUNDS(ID, ID), 33 ms] (102) CdtProblem (103) CdtRewritingProof [BOTH BOUNDS(ID, ID), 45 ms] (104) CdtProblem (105) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 30 ms] (106) CdtProblem (107) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 37 ms] (108) CdtProblem (109) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtRewritingProof [BOTH BOUNDS(ID, ID), 28 ms] (112) CdtProblem (113) CdtRewritingProof [BOTH BOUNDS(ID, ID), 9 ms] (114) CdtProblem (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 5 ms] (116) CdtProblem (117) CdtRewritingProof [BOTH BOUNDS(ID, ID), 75 ms] (118) CdtProblem (119) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 27 ms] (120) CdtProblem (121) CdtRewritingProof [BOTH BOUNDS(ID, ID), 5 ms] (122) CdtProblem (123) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 35 ms] (124) 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: c(c(c(a(x, y)))) -> b(c(c(c(c(y)))), x) c(c(b(c(y), 0))) -> a(0, c(c(a(y, 0)))) c(c(a(a(y, 0), x))) -> c(y) 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(a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encArg(b(x_1, x_2)) -> b(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(cons_c(x_1)) -> c(encArg(x_1)) encode_c(x_1) -> c(encArg(x_1)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_b(x_1, x_2) -> b(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: c(c(c(a(x, y)))) -> b(c(c(c(c(y)))), x) c(c(b(c(y), 0))) -> a(0, c(c(a(y, 0)))) c(c(a(a(y, 0), x))) -> c(y) The (relative) TRS S consists of the following rules: encArg(a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encArg(b(x_1, x_2)) -> b(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(cons_c(x_1)) -> c(encArg(x_1)) encode_c(x_1) -> c(encArg(x_1)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_b(x_1, x_2) -> b(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: c(c(c(a(x, y)))) -> b(c(c(c(c(y)))), x) c(c(b(c(y), 0))) -> a(0, c(c(a(y, 0)))) c(c(a(a(y, 0), x))) -> c(y) The (relative) TRS S consists of the following rules: encArg(a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encArg(b(x_1, x_2)) -> b(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(cons_c(x_1)) -> c(encArg(x_1)) encode_c(x_1) -> c(encArg(x_1)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_b(x_1, x_2) -> b(encArg(x_1), encArg(x_2)) encode_0 -> 0 Rewrite Strategy: FULL ---------------------------------------- (5) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (6) 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: c(c(c(a(x, y)))) -> b(c(c(c(c(y)))), x) c(c(b(c(y), 0'))) -> a(0', c(c(a(y, 0')))) c(c(a(a(y, 0'), x))) -> c(y) The (relative) TRS S consists of the following rules: encArg(a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encArg(b(x_1, x_2)) -> b(encArg(x_1), encArg(x_2)) encArg(0') -> 0' encArg(cons_c(x_1)) -> c(encArg(x_1)) encode_c(x_1) -> c(encArg(x_1)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_b(x_1, x_2) -> b(encArg(x_1), encArg(x_2)) encode_0 -> 0' Rewrite Strategy: FULL ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: TRS: Rules: c(c(c(a(x, y)))) -> b(c(c(c(c(y)))), x) c(c(b(c(y), 0'))) -> a(0', c(c(a(y, 0')))) c(c(a(a(y, 0'), x))) -> c(y) encArg(a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encArg(b(x_1, x_2)) -> b(encArg(x_1), encArg(x_2)) encArg(0') -> 0' encArg(cons_c(x_1)) -> c(encArg(x_1)) encode_c(x_1) -> c(encArg(x_1)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_b(x_1, x_2) -> b(encArg(x_1), encArg(x_2)) encode_0 -> 0' Types: c :: a:b:0':cons_c -> a:b:0':cons_c a :: a:b:0':cons_c -> a:b:0':cons_c -> a:b:0':cons_c b :: a:b:0':cons_c -> a:b:0':cons_c -> a:b:0':cons_c 0' :: a:b:0':cons_c encArg :: a:b:0':cons_c -> a:b:0':cons_c cons_c :: a:b:0':cons_c -> a:b:0':cons_c encode_c :: a:b:0':cons_c -> a:b:0':cons_c encode_a :: a:b:0':cons_c -> a:b:0':cons_c -> a:b:0':cons_c encode_b :: a:b:0':cons_c -> a:b:0':cons_c -> a:b:0':cons_c encode_0 :: a:b:0':cons_c hole_a:b:0':cons_c1_3 :: a:b:0':cons_c gen_a:b:0':cons_c2_3 :: Nat -> a:b:0':cons_c ---------------------------------------- (9) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: c, encArg They will be analysed ascendingly in the following order: c < encArg ---------------------------------------- (10) Obligation: TRS: Rules: c(c(c(a(x, y)))) -> b(c(c(c(c(y)))), x) c(c(b(c(y), 0'))) -> a(0', c(c(a(y, 0')))) c(c(a(a(y, 0'), x))) -> c(y) encArg(a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encArg(b(x_1, x_2)) -> b(encArg(x_1), encArg(x_2)) encArg(0') -> 0' encArg(cons_c(x_1)) -> c(encArg(x_1)) encode_c(x_1) -> c(encArg(x_1)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_b(x_1, x_2) -> b(encArg(x_1), encArg(x_2)) encode_0 -> 0' Types: c :: a:b:0':cons_c -> a:b:0':cons_c a :: a:b:0':cons_c -> a:b:0':cons_c -> a:b:0':cons_c b :: a:b:0':cons_c -> a:b:0':cons_c -> a:b:0':cons_c 0' :: a:b:0':cons_c encArg :: a:b:0':cons_c -> a:b:0':cons_c cons_c :: a:b:0':cons_c -> a:b:0':cons_c encode_c :: a:b:0':cons_c -> a:b:0':cons_c encode_a :: a:b:0':cons_c -> a:b:0':cons_c -> a:b:0':cons_c encode_b :: a:b:0':cons_c -> a:b:0':cons_c -> a:b:0':cons_c encode_0 :: a:b:0':cons_c hole_a:b:0':cons_c1_3 :: a:b:0':cons_c gen_a:b:0':cons_c2_3 :: Nat -> a:b:0':cons_c Generator Equations: gen_a:b:0':cons_c2_3(0) <=> 0' gen_a:b:0':cons_c2_3(+(x, 1)) <=> a(0', gen_a:b:0':cons_c2_3(x)) The following defined symbols remain to be analysed: c, encArg They will be analysed ascendingly in the following order: c < encArg ---------------------------------------- (11) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_a:b:0':cons_c2_3(n23_3)) -> gen_a:b:0':cons_c2_3(n23_3), rt in Omega(0) Induction Base: encArg(gen_a:b:0':cons_c2_3(0)) ->_R^Omega(0) 0' Induction Step: encArg(gen_a:b:0':cons_c2_3(+(n23_3, 1))) ->_R^Omega(0) a(encArg(0'), encArg(gen_a:b:0':cons_c2_3(n23_3))) ->_R^Omega(0) a(0', encArg(gen_a:b:0':cons_c2_3(n23_3))) ->_IH a(0', gen_a:b:0':cons_c2_3(c24_3)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (12) BOUNDS(1, INF) ---------------------------------------- (13) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (14) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: c(c(c(a(x, y)))) -> b(c(c(c(c(y)))), x) c(c(b(c(y), 0))) -> a(0, c(c(a(y, 0)))) c(c(a(a(y, 0), x))) -> c(y) The (relative) TRS S consists of the following rules: encArg(a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encArg(b(x_1, x_2)) -> b(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(cons_c(x_1)) -> c(encArg(x_1)) encode_c(x_1) -> c(encArg(x_1)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_b(x_1, x_2) -> b(encArg(x_1), encArg(x_2)) encode_0 -> 0 Rewrite Strategy: FULL ---------------------------------------- (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: c(c(c(a(x, y)))) -> b(c(c(c(c(y)))), x) c(c(b(c(y), 0))) -> a(0, c(c(a(y, 0)))) c(c(a(a(y, 0), x))) -> c(y) encArg(a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encArg(b(x_1, x_2)) -> b(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(cons_c(x_1)) -> c(encArg(x_1)) encode_c(x_1) -> c(encArg(x_1)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_b(x_1, x_2) -> b(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: c(c_c(b(c_c(y), 0))) -> a(0, c(c(a(y, 0)))) c(c_c(c_c(a(x, y)))) -> b(c(c(c(c(y)))), x) c(c_c(a(a(y, 0), x))) -> c(y) The (relative) TRS S consists of the following rules: encArg(a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encArg(b(x_1, x_2)) -> b(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(cons_c(x_1)) -> c(encArg(x_1)) encode_c(x_1) -> c(encArg(x_1)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_b(x_1, x_2) -> b(encArg(x_1), encArg(x_2)) encode_0 -> 0 c(x0) -> c_c(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: c(c_c(b(c_c(y), 0))) -> a(0, c(c(a(y, 0)))) c(c_c(c_c(a(x, y)))) -> b(c(c(c(c(y)))), x) c(c_c(a(a(y, 0), x))) -> c(y) The (relative) TRS S consists of the following rules: encArg(a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encArg(b(x_1, x_2)) -> b(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(cons_c(x_1)) -> c(encArg(x_1)) encode_c(x_1) -> c(encArg(x_1)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_b(x_1, x_2) -> b(encArg(x_1), encArg(x_2)) encode_0 -> 0 c(x0) -> c_c(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: c(c_c(b(c_c(y), 0))) -> a(0, c(c(a(y, 0)))) [1] c(c_c(c_c(a(x, y)))) -> b(c(c(c(c(y)))), x) [1] c(c_c(a(a(y, 0), x))) -> c(y) [1] encArg(a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) [0] encArg(b(x_1, x_2)) -> b(encArg(x_1), encArg(x_2)) [0] encArg(0) -> 0 [0] encArg(cons_c(x_1)) -> c(encArg(x_1)) [0] encode_c(x_1) -> c(encArg(x_1)) [0] encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) [0] encode_b(x_1, x_2) -> b(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] c(x0) -> c_c(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: c(c_c(b(c_c(y), 0))) -> a(0, c(c(a(y, 0)))) [1] c(c_c(c_c(a(x, y)))) -> b(c(c(c(c(y)))), x) [1] c(c_c(a(a(y, 0), x))) -> c(y) [1] encArg(a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) [0] encArg(b(x_1, x_2)) -> b(encArg(x_1), encArg(x_2)) [0] encArg(0) -> 0 [0] encArg(cons_c(x_1)) -> c(encArg(x_1)) [0] encode_c(x_1) -> c(encArg(x_1)) [0] encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) [0] encode_b(x_1, x_2) -> b(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] c(x0) -> c_c(x0) [0] The TRS has the following type information: c :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c c_c :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c b :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c 0 :: c_c:0:b:a:cons_c a :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c encArg :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c cons_c :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c encode_c :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c encode_a :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c encode_b :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c encode_0 :: c_c:0:b:a:cons_c 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_c_1 encode_a_2 encode_b_2 encode_0 c_1 Due to the following rules being added: encArg(v0) -> 0 [0] encode_c(v0) -> 0 [0] encode_a(v0, v1) -> 0 [0] encode_b(v0, v1) -> 0 [0] encode_0 -> 0 [0] c(v0) -> 0 [0] And the following fresh constants: none ---------------------------------------- (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: c(c_c(b(c_c(y), 0))) -> a(0, c(c(a(y, 0)))) [1] c(c_c(c_c(a(x, y)))) -> b(c(c(c(c(y)))), x) [1] c(c_c(a(a(y, 0), x))) -> c(y) [1] encArg(a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) [0] encArg(b(x_1, x_2)) -> b(encArg(x_1), encArg(x_2)) [0] encArg(0) -> 0 [0] encArg(cons_c(x_1)) -> c(encArg(x_1)) [0] encode_c(x_1) -> c(encArg(x_1)) [0] encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) [0] encode_b(x_1, x_2) -> b(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] c(x0) -> c_c(x0) [0] encArg(v0) -> 0 [0] encode_c(v0) -> 0 [0] encode_a(v0, v1) -> 0 [0] encode_b(v0, v1) -> 0 [0] encode_0 -> 0 [0] c(v0) -> 0 [0] The TRS has the following type information: c :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c c_c :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c b :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c 0 :: c_c:0:b:a:cons_c a :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c encArg :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c cons_c :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c encode_c :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c encode_a :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c encode_b :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c encode_0 :: c_c:0:b:a:cons_c 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: c(c_c(b(c_c(y), 0))) -> a(0, c(c_c(a(y, 0)))) [1] c(c_c(b(c_c(y), 0))) -> a(0, c(0)) [1] c(c_c(c_c(a(x, c_c(b(c_c(y'), 0)))))) -> b(c(c(c(a(0, c(c(a(y', 0))))))), x) [2] c(c_c(c_c(a(x, c_c(c_c(a(x', y''))))))) -> b(c(c(c(b(c(c(c(c(y'')))), x')))), x) [2] c(c_c(c_c(a(x, c_c(a(a(y1, 0), x'')))))) -> b(c(c(c(c(y1)))), x) [2] c(c_c(c_c(a(x, y)))) -> b(c(c(c(c_c(y)))), x) [1] c(c_c(c_c(a(x, y)))) -> b(c(c(c(0))), x) [1] c(c_c(a(a(y, 0), x))) -> c(y) [1] encArg(a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) [0] encArg(b(x_1, x_2)) -> b(encArg(x_1), encArg(x_2)) [0] encArg(0) -> 0 [0] encArg(cons_c(a(x_1', x_2'))) -> c(a(encArg(x_1'), encArg(x_2'))) [0] encArg(cons_c(b(x_1'', x_2''))) -> c(b(encArg(x_1''), encArg(x_2''))) [0] encArg(cons_c(0)) -> c(0) [0] encArg(cons_c(cons_c(x_11))) -> c(c(encArg(x_11))) [0] encArg(cons_c(x_1)) -> c(0) [0] encode_c(a(x_12, x_21)) -> c(a(encArg(x_12), encArg(x_21))) [0] encode_c(b(x_13, x_22)) -> c(b(encArg(x_13), encArg(x_22))) [0] encode_c(0) -> c(0) [0] encode_c(cons_c(x_14)) -> c(c(encArg(x_14))) [0] encode_c(x_1) -> c(0) [0] encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) [0] encode_b(x_1, x_2) -> b(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] c(x0) -> c_c(x0) [0] encArg(v0) -> 0 [0] encode_c(v0) -> 0 [0] encode_a(v0, v1) -> 0 [0] encode_b(v0, v1) -> 0 [0] encode_0 -> 0 [0] c(v0) -> 0 [0] The TRS has the following type information: c :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c c_c :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c b :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c 0 :: c_c:0:b:a:cons_c a :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c encArg :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c cons_c :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c encode_c :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c encode_a :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c encode_b :: c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c -> c_c:0:b:a:cons_c encode_0 :: c_c:0:b:a:cons_c 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: 0 => 0 ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: c(z) -{ 1 }-> c(y) :|: y >= 0, x >= 0, z = 1 + (1 + (1 + y + 0) + x) c(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 c(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 c(z) -{ 2 }-> 1 + c(c(c(c(y1)))) + x :|: y1 >= 0, x >= 0, z = 1 + (1 + (1 + x + (1 + (1 + (1 + y1 + 0) + x'')))), x'' >= 0 c(z) -{ 1 }-> 1 + c(c(c(0))) + x :|: x >= 0, y >= 0, z = 1 + (1 + (1 + x + y)) c(z) -{ 1 }-> 1 + c(c(c(1 + y))) + x :|: x >= 0, y >= 0, z = 1 + (1 + (1 + x + y)) c(z) -{ 2 }-> 1 + c(c(c(1 + c(c(c(c(y'')))) + x'))) + x :|: z = 1 + (1 + (1 + x + (1 + (1 + (1 + x' + y''))))), x >= 0, x' >= 0, y'' >= 0 c(z) -{ 2 }-> 1 + c(c(c(1 + 0 + c(c(1 + y' + 0))))) + x :|: z = 1 + (1 + (1 + x + (1 + (1 + (1 + y') + 0)))), x >= 0, y' >= 0 c(z) -{ 1 }-> 1 + 0 + c(0) :|: z = 1 + (1 + (1 + y) + 0), y >= 0 c(z) -{ 1 }-> 1 + 0 + c(1 + (1 + y + 0)) :|: z = 1 + (1 + (1 + y) + 0), y >= 0 encArg(z) -{ 0 }-> c(c(encArg(x_11))) :|: x_11 >= 0, z = 1 + (1 + x_11) encArg(z) -{ 0 }-> c(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> c(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> c(1 + encArg(x_1') + encArg(x_2')) :|: z = 1 + (1 + x_1' + x_2'), x_2' >= 0, x_1' >= 0 encArg(z) -{ 0 }-> c(1 + encArg(x_1'') + encArg(x_2'')) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encArg(z) -{ 0 }-> 1 + encArg(x_1) + encArg(x_2) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encode_0 -{ 0 }-> 0 :|: encode_a(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_a(z, z') -{ 0 }-> 1 + encArg(x_1) + encArg(x_2) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_b(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_b(z, z') -{ 0 }-> 1 + encArg(x_1) + encArg(x_2) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_c(z) -{ 0 }-> c(c(encArg(x_14))) :|: x_14 >= 0, z = 1 + x_14 encode_c(z) -{ 0 }-> c(0) :|: z = 0 encode_c(z) -{ 0 }-> c(0) :|: x_1 >= 0, z = x_1 encode_c(z) -{ 0 }-> c(1 + encArg(x_12) + encArg(x_21)) :|: z = 1 + x_12 + x_21, x_12 >= 0, x_21 >= 0 encode_c(z) -{ 0 }-> c(1 + encArg(x_13) + encArg(x_22)) :|: x_13 >= 0, z = 1 + x_13 + x_22, x_22 >= 0 encode_c(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 ---------------------------------------- (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: c(z) -{ 1 }-> c(y) :|: y >= 0, x >= 0, z = 1 + (1 + (1 + y + 0) + x) c(z) -{ 0 }-> 0 :|: z >= 0 c(z) -{ 0 }-> 1 + z :|: z >= 0 c(z) -{ 2 }-> 1 + c(c(c(c(y1)))) + x :|: y1 >= 0, x >= 0, z = 1 + (1 + (1 + x + (1 + (1 + (1 + y1 + 0) + x'')))), x'' >= 0 c(z) -{ 1 }-> 1 + c(c(c(0))) + x :|: x >= 0, y >= 0, z = 1 + (1 + (1 + x + y)) c(z) -{ 1 }-> 1 + c(c(c(1 + y))) + x :|: x >= 0, y >= 0, z = 1 + (1 + (1 + x + y)) c(z) -{ 2 }-> 1 + c(c(c(1 + c(c(c(c(y'')))) + x'))) + x :|: z = 1 + (1 + (1 + x + (1 + (1 + (1 + x' + y''))))), x >= 0, x' >= 0, y'' >= 0 c(z) -{ 2 }-> 1 + c(c(c(1 + 0 + c(c(1 + y' + 0))))) + x :|: z = 1 + (1 + (1 + x + (1 + (1 + (1 + y') + 0)))), x >= 0, y' >= 0 c(z) -{ 1 }-> 1 + 0 + c(0) :|: z - 3 >= 0 c(z) -{ 1 }-> 1 + 0 + c(1 + (1 + (z - 3) + 0)) :|: z - 3 >= 0 encArg(z) -{ 0 }-> c(c(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> c(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> c(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> c(1 + encArg(x_1') + encArg(x_2')) :|: z = 1 + (1 + x_1' + x_2'), x_2' >= 0, x_1' >= 0 encArg(z) -{ 0 }-> c(1 + encArg(x_1'') + encArg(x_2'')) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 0 }-> 1 + encArg(x_1) + encArg(x_2) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encode_0 -{ 0 }-> 0 :|: encode_a(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_a(z, z') -{ 0 }-> 1 + encArg(z) + encArg(z') :|: z >= 0, z' >= 0 encode_b(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_b(z, z') -{ 0 }-> 1 + encArg(z) + encArg(z') :|: z >= 0, z' >= 0 encode_c(z) -{ 0 }-> c(c(encArg(z - 1))) :|: z - 1 >= 0 encode_c(z) -{ 0 }-> c(0) :|: z = 0 encode_c(z) -{ 0 }-> c(0) :|: z >= 0 encode_c(z) -{ 0 }-> c(1 + encArg(x_12) + encArg(x_21)) :|: z = 1 + x_12 + x_21, x_12 >= 0, x_21 >= 0 encode_c(z) -{ 0 }-> c(1 + encArg(x_13) + encArg(x_22)) :|: x_13 >= 0, z = 1 + x_13 + x_22, x_22 >= 0 encode_c(z) -{ 0 }-> 0 :|: 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_c(v0) -> null_encode_c [0] encode_a(v0, v1) -> null_encode_a [0] encode_b(v0, v1) -> null_encode_b [0] encode_0 -> null_encode_0 [0] c(v0) -> null_c [0] And the following fresh constants: null_encArg, null_encode_c, null_encode_a, null_encode_b, null_encode_0, null_c ---------------------------------------- (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: c(c_c(b(c_c(y), 0))) -> a(0, c(c(a(y, 0)))) [1] c(c_c(c_c(a(x, y)))) -> b(c(c(c(c(y)))), x) [1] c(c_c(a(a(y, 0), x))) -> c(y) [1] encArg(a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) [0] encArg(b(x_1, x_2)) -> b(encArg(x_1), encArg(x_2)) [0] encArg(0) -> 0 [0] encArg(cons_c(x_1)) -> c(encArg(x_1)) [0] encode_c(x_1) -> c(encArg(x_1)) [0] encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) [0] encode_b(x_1, x_2) -> b(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] c(x0) -> c_c(x0) [0] encArg(v0) -> null_encArg [0] encode_c(v0) -> null_encode_c [0] encode_a(v0, v1) -> null_encode_a [0] encode_b(v0, v1) -> null_encode_b [0] encode_0 -> null_encode_0 [0] c(v0) -> null_c [0] The TRS has the following type information: c :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c -> c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c c_c :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c -> c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c b :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c -> c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c -> c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c 0 :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c a :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c -> c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c -> c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c encArg :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c -> c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c cons_c :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c -> c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c encode_c :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c -> c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c encode_a :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c -> c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c -> c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c encode_b :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c -> c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c -> c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c encode_0 :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c null_encArg :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c null_encode_c :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c null_encode_a :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c null_encode_b :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c null_encode_0 :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c null_c :: c_c:0:b:a:cons_c:null_encArg:null_encode_c:null_encode_a:null_encode_b:null_encode_0:null_c 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: 0 => 0 null_encArg => 0 null_encode_c => 0 null_encode_a => 0 null_encode_b => 0 null_encode_0 => 0 null_c => 0 ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: c(z) -{ 1 }-> c(y) :|: y >= 0, x >= 0, z = 1 + (1 + (1 + y + 0) + x) c(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 c(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 c(z) -{ 1 }-> 1 + c(c(c(c(y)))) + x :|: x >= 0, y >= 0, z = 1 + (1 + (1 + x + y)) c(z) -{ 1 }-> 1 + 0 + c(c(1 + y + 0)) :|: z = 1 + (1 + (1 + y) + 0), y >= 0 encArg(z) -{ 0 }-> c(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encArg(z) -{ 0 }-> 1 + encArg(x_1) + encArg(x_2) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encode_0 -{ 0 }-> 0 :|: encode_a(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_a(z, z') -{ 0 }-> 1 + encArg(x_1) + encArg(x_2) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_b(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_b(z, z') -{ 0 }-> 1 + encArg(x_1) + encArg(x_2) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_c(z) -{ 0 }-> c(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_c(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 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(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) encode_c(z0) -> c(encArg(z0)) encode_a(z0, z1) -> a(encArg(z0), encArg(z1)) encode_b(z0, z1) -> b(encArg(z0), encArg(z1)) encode_0 -> 0 c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) ENCARG(0) -> c3 ENCARG(cons_c(z0)) -> c4(C(encArg(z0)), ENCARG(z0)) ENCODE_C(z0) -> c5(C(encArg(z0)), ENCARG(z0)) ENCODE_A(z0, z1) -> c6(ENCARG(z0), ENCARG(z1)) ENCODE_B(z0, z1) -> c7(ENCARG(z0), ENCARG(z1)) ENCODE_0 -> c8 C(z0) -> c9 C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0))), C(a(z0, 0))) C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) S tuples: C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0))), C(a(z0, 0))) C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) K tuples:none Defined Rule Symbols: c_1, encArg_1, encode_c_1, encode_a_2, encode_b_2, encode_0 Defined Pair Symbols: ENCARG_1, ENCODE_C_1, ENCODE_A_2, ENCODE_B_2, ENCODE_0, C_1 Compound Symbols: c1_2, c2_2, c3, c4_2, c5_2, c6_2, c7_2, c8, c9, c10_2, c11_4, c12_1 ---------------------------------------- (39) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 2 leading nodes: ENCODE_A(z0, z1) -> c6(ENCARG(z0), ENCARG(z1)) ENCODE_B(z0, z1) -> c7(ENCARG(z0), ENCARG(z1)) Removed 3 trailing nodes: ENCODE_0 -> c8 C(z0) -> c9 ENCARG(0) -> c3 ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) encode_c(z0) -> c(encArg(z0)) encode_a(z0, z1) -> a(encArg(z0), encArg(z1)) encode_b(z0, z1) -> b(encArg(z0), encArg(z1)) encode_0 -> 0 c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) ENCARG(cons_c(z0)) -> c4(C(encArg(z0)), ENCARG(z0)) ENCODE_C(z0) -> c5(C(encArg(z0)), ENCARG(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0))), C(a(z0, 0))) C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) S tuples: C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0))), C(a(z0, 0))) C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) K tuples:none Defined Rule Symbols: c_1, encArg_1, encode_c_1, encode_a_2, encode_b_2, encode_0 Defined Pair Symbols: ENCARG_1, ENCODE_C_1, C_1 Compound Symbols: c1_2, c2_2, c4_2, c5_2, c10_2, c11_4, c12_1 ---------------------------------------- (41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) encode_c(z0) -> c(encArg(z0)) encode_a(z0, z1) -> a(encArg(z0), encArg(z1)) encode_b(z0, z1) -> b(encArg(z0), encArg(z1)) encode_0 -> 0 c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) ENCARG(cons_c(z0)) -> c4(C(encArg(z0)), ENCARG(z0)) ENCODE_C(z0) -> c5(C(encArg(z0)), ENCARG(z0)) C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) S tuples: C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) K tuples:none Defined Rule Symbols: c_1, encArg_1, encode_c_1, encode_a_2, encode_b_2, encode_0 Defined Pair Symbols: ENCARG_1, ENCODE_C_1, C_1 Compound Symbols: c1_2, c2_2, c4_2, c5_2, c11_4, c12_1, c10_1 ---------------------------------------- (43) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) encode_c(z0) -> c(encArg(z0)) encode_a(z0, z1) -> a(encArg(z0), encArg(z1)) encode_b(z0, z1) -> b(encArg(z0), encArg(z1)) encode_0 -> 0 c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) ENCARG(cons_c(z0)) -> c4(C(encArg(z0)), ENCARG(z0)) C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) ENCODE_C(z0) -> c3(C(encArg(z0))) ENCODE_C(z0) -> c3(ENCARG(z0)) S tuples: C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) K tuples:none Defined Rule Symbols: c_1, encArg_1, encode_c_1, encode_a_2, encode_b_2, encode_0 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c4_2, c11_4, c12_1, c10_1, c3_1 ---------------------------------------- (45) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: ENCODE_C(z0) -> c3(ENCARG(z0)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) encode_c(z0) -> c(encArg(z0)) encode_a(z0, z1) -> a(encArg(z0), encArg(z1)) encode_b(z0, z1) -> b(encArg(z0), encArg(z1)) encode_0 -> 0 c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) ENCARG(cons_c(z0)) -> c4(C(encArg(z0)), ENCARG(z0)) C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) ENCODE_C(z0) -> c3(C(encArg(z0))) S tuples: C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) K tuples:none Defined Rule Symbols: c_1, encArg_1, encode_c_1, encode_a_2, encode_b_2, encode_0 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c4_2, c11_4, c12_1, c10_1, c3_1 ---------------------------------------- (47) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_c(z0) -> c(encArg(z0)) encode_a(z0, z1) -> a(encArg(z0), encArg(z1)) encode_b(z0, z1) -> b(encArg(z0), encArg(z1)) encode_0 -> 0 ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) ENCARG(cons_c(z0)) -> c4(C(encArg(z0)), ENCARG(z0)) C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) ENCODE_C(z0) -> c3(C(encArg(z0))) S tuples: C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c4_2, c11_4, c12_1, c10_1, c3_1 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_c(z0)) -> c4(C(encArg(z0)), ENCARG(z0)) by ENCARG(cons_c(a(z0, z1))) -> c4(C(a(encArg(z0), encArg(z1))), ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(C(b(encArg(z0), encArg(z1))), ENCARG(b(z0, z1))) ENCARG(cons_c(0)) -> c4(C(0), ENCARG(0)) ENCARG(cons_c(cons_c(z0))) -> c4(C(c(encArg(z0))), ENCARG(cons_c(z0))) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) ENCODE_C(z0) -> c3(C(encArg(z0))) ENCARG(cons_c(a(z0, z1))) -> c4(C(a(encArg(z0), encArg(z1))), ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(C(b(encArg(z0), encArg(z1))), ENCARG(b(z0, z1))) ENCARG(cons_c(0)) -> c4(C(0), ENCARG(0)) ENCARG(cons_c(cons_c(z0))) -> c4(C(c(encArg(z0))), ENCARG(cons_c(z0))) S tuples: C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c11_4, c12_1, c10_1, c3_1, c4_2 ---------------------------------------- (51) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCARG(cons_c(0)) -> c4(C(0), ENCARG(0)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) ENCODE_C(z0) -> c3(C(encArg(z0))) ENCARG(cons_c(a(z0, z1))) -> c4(C(a(encArg(z0), encArg(z1))), ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(C(b(encArg(z0), encArg(z1))), ENCARG(b(z0, z1))) ENCARG(cons_c(cons_c(z0))) -> c4(C(c(encArg(z0))), ENCARG(cons_c(z0))) S tuples: C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c11_4, c12_1, c10_1, c3_1, c4_2 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) ENCODE_C(z0) -> c3(C(encArg(z0))) ENCARG(cons_c(cons_c(z0))) -> c4(C(c(encArg(z0))), ENCARG(cons_c(z0))) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) S tuples: C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c11_4, c12_1, c10_1, c3_1, c4_2, c4_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace C(c_c(c_c(a(z0, z1)))) -> c11(C(c(c(c(z1)))), C(c(c(z1))), C(c(z1)), C(z1)) by C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) ENCODE_C(z0) -> c3(C(encArg(z0))) ENCARG(cons_c(cons_c(z0))) -> c4(C(c(encArg(z0))), ENCARG(cons_c(z0))) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c10_1, c3_1, c4_2, c4_1, c11_4 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace C(c_c(b(c_c(z0), 0))) -> c10(C(c(a(z0, 0)))) by C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCODE_C(z0) -> c3(C(encArg(z0))) ENCARG(cons_c(cons_c(z0))) -> c4(C(c(encArg(z0))), ENCARG(cons_c(z0))) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c3_1, c4_2, c4_1, c11_4, c10_1 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_C(z0) -> c3(C(encArg(z0))) by ENCODE_C(a(z0, z1)) -> c3(C(a(encArg(z0), encArg(z1)))) ENCODE_C(b(z0, z1)) -> c3(C(b(encArg(z0), encArg(z1)))) ENCODE_C(0) -> c3(C(0)) ENCODE_C(cons_c(z0)) -> c3(C(c(encArg(z0)))) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(cons_c(z0))) -> c4(C(c(encArg(z0))), ENCARG(cons_c(z0))) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCODE_C(a(z0, z1)) -> c3(C(a(encArg(z0), encArg(z1)))) ENCODE_C(b(z0, z1)) -> c3(C(b(encArg(z0), encArg(z1)))) ENCODE_C(0) -> c3(C(0)) ENCODE_C(cons_c(z0)) -> c3(C(c(encArg(z0)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_2, c4_1, c11_4, c10_1, c3_1 ---------------------------------------- (61) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: ENCODE_C(a(z0, z1)) -> c3(C(a(encArg(z0), encArg(z1)))) ENCODE_C(b(z0, z1)) -> c3(C(b(encArg(z0), encArg(z1)))) ENCODE_C(0) -> c3(C(0)) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(cons_c(z0))) -> c4(C(c(encArg(z0))), ENCARG(cons_c(z0))) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCODE_C(cons_c(z0)) -> c3(C(c(encArg(z0)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_2, c4_1, c11_4, c10_1, c3_1 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_c(cons_c(z0))) -> c4(C(c(encArg(z0))), ENCARG(cons_c(z0))) by ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(0))) -> c4(C(c(0)), ENCARG(cons_c(0))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCODE_C(cons_c(z0)) -> c3(C(c(encArg(z0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(0))) -> c4(C(c(0)), ENCARG(cons_c(0))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_1, c11_4, c10_1, c3_1, c4_2 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCODE_C(cons_c(z0)) -> c3(C(c(encArg(z0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) ENCARG(cons_c(cons_c(0))) -> c4(C(c(0))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_1, c11_4, c10_1, c3_1, c4_2 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) by C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCODE_C(cons_c(z0)) -> c3(C(c(encArg(z0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) ENCARG(cons_c(cons_c(0))) -> c4(C(c(0))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_1, c11_4, c10_1, c3_1, c4_2 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) by C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCODE_C(cons_c(z0)) -> c3(C(c(encArg(z0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) ENCARG(cons_c(cons_c(0))) -> c4(C(c(0))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_1, c11_4, c10_1, c3_1, c4_2, c11_1 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) by C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c(c_c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c_c(c_c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0))), C(b(c_c(z0), 0))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1))), C(a(a(z0, 0), z1))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCODE_C(cons_c(z0)) -> c3(C(c(encArg(z0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) ENCARG(cons_c(cons_c(0))) -> c4(C(c(0))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0))), C(b(c_c(z0), 0))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1))), C(a(a(z0, 0), z1))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0))), C(b(c_c(z0), 0))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1))), C(a(a(z0, 0), z1))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_1, c11_4, c10_1, c3_1, c4_2, c11_1, c11_3 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCODE_C(cons_c(z0)) -> c3(C(c(encArg(z0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) ENCARG(cons_c(cons_c(0))) -> c4(C(c(0))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_1, c11_4, c10_1, c3_1, c4_2, c11_1, c11_3 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) by C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCODE_C(cons_c(z0)) -> c3(C(c(encArg(z0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) ENCARG(cons_c(cons_c(0))) -> c4(C(c(0))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_1, c11_4, c10_1, c3_1, c4_2, c11_1, c11_3 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) by C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c_c(c(b(c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c_c(b(c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCODE_C(cons_c(z0)) -> c3(C(c(encArg(z0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) ENCARG(cons_c(cons_c(0))) -> c4(C(c(0))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_1, c11_4, c10_1, c3_1, c4_2, c11_1, c11_3, c11_2 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) by C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c_c(c(c(x1)))), C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2)))), C(c_c(a(a(x1, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c_c(c(x1)))), C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2)))), C(c_c(a(a(x1, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCODE_C(cons_c(z0)) -> c3(C(c(encArg(z0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) ENCARG(cons_c(cons_c(0))) -> c4(C(c(0))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_1, c10_1, c3_1, c4_2, c11_4, c11_1, c11_3, c11_2 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_C(cons_c(z0)) -> c3(C(c(encArg(z0)))) by ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) ENCARG(cons_c(cons_c(0))) -> c4(C(c(0))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1 ---------------------------------------- (83) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace ENCARG(cons_c(cons_c(0))) -> c4(C(c(0))) by ENCARG(cons_c(cons_c(0))) -> c4(C(c_c(0))) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) ENCARG(cons_c(cons_c(0))) -> c4(C(c_c(0))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1 ---------------------------------------- (85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCARG(cons_c(cons_c(0))) -> c4(C(c_c(0))) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1 ---------------------------------------- (87) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) by C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1 ---------------------------------------- (89) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) by C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c1_2, c2_2, c12_1, c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1 ---------------------------------------- (91) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(a(z0, z1)) -> c1(ENCARG(z0), ENCARG(z1)) by ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c2_2, c12_1, c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2 ---------------------------------------- (93) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace C(c_c(c_c(a(x0, b(c_c(z0), 0))))) -> c11(C(c(a(0, c(c(a(z0, 0)))))), C(c(c(b(c_c(z0), 0)))), C(c(b(c_c(z0), 0)))) by C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c2_2, c12_1, c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2 ---------------------------------------- (95) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace C(c_c(c_c(a(x0, a(a(z0, 0), z1))))) -> c11(C(c(c(z0))), C(c(c(a(a(z0, 0), z1)))), C(c(a(a(z0, 0), z1)))) by C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c2_2, c12_1, c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2 ---------------------------------------- (97) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c_c(c(a(0, c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) by C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(b(c_c(z0), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(b(c_c(z0), 0))))), C(c(c_c(b(c_c(z0), 0)))), C(c_c(b(c_c(z0), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c2_2, c12_1, c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2 ---------------------------------------- (99) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c_c(a(0, c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) by C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c2_2, c12_1, c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2 ---------------------------------------- (101) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c_c(c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) by C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c2_2, c12_1, c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2 ---------------------------------------- (103) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c(a(z0, 0))))))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0)))))))), C(c(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))), C(c_c(c_c(a(x1, c_c(b(c_c(z0), 0))))))) by C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c2_2, c12_1, c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2 ---------------------------------------- (105) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(b(z0, z1)) -> c2(ENCARG(z0), ENCARG(z1)) by ENCARG(b(b(y0, y1), z1)) -> c2(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(b(z0, b(y0, y1))) -> c2(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(b(cons_c(a(y0, y1)), z1)) -> c2(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(a(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(b(cons_c(b(y0, y1)), z1)) -> c2(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(b(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(b(cons_c(cons_c(y0)), z1)) -> c2(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(y0)))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(b(cons_c(cons_c(a(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(a(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(b(cons_c(cons_c(b(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(b(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(b(cons_c(cons_c(cons_c(y0))), z1)) -> c2(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(cons_c(y0))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) ENCARG(b(a(a(y0, y1), y2), z1)) -> c2(ENCARG(a(a(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(a(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(a(y0, y1), y2))) ENCARG(b(a(y0, a(y1, y2)), z1)) -> c2(ENCARG(a(y0, a(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, a(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, a(y1, y2)))) ENCARG(b(a(b(y0, y1), y2), z1)) -> c2(ENCARG(a(b(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(b(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(b(y0, y1), y2))) ENCARG(b(a(y0, b(y1, y2)), z1)) -> c2(ENCARG(a(y0, b(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, b(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, b(y1, y2)))) ENCARG(b(a(cons_c(a(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(a(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(a(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(a(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(a(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(a(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(a(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(a(y1, y2))))) ENCARG(b(a(cons_c(b(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(b(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(b(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(b(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(b(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(b(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(b(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(b(y1, y2))))) ENCARG(b(a(cons_c(cons_c(y0)), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(y0)), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(y0)), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(y0)), y1))) ENCARG(b(a(y0, cons_c(cons_c(y1))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(y1)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(y1))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(y1))))) ENCARG(b(a(cons_c(cons_c(a(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(a(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(a(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(a(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(a(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(a(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(a(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(b(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(b(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(b(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(b(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(b(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(b(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(b(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(cons_c(y0))), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(cons_c(y0))), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(cons_c(y0))), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(cons_c(y0))), y1))) ENCARG(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(cons_c(y1))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(cons_c(y1)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(cons_c(y1)))))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) ENCARG(b(b(y0, y1), z1)) -> c2(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(b(z0, b(y0, y1))) -> c2(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(b(cons_c(a(y0, y1)), z1)) -> c2(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(a(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(b(cons_c(b(y0, y1)), z1)) -> c2(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(b(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(b(cons_c(cons_c(y0)), z1)) -> c2(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(y0)))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(b(cons_c(cons_c(a(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(a(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(b(cons_c(cons_c(b(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(b(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(b(cons_c(cons_c(cons_c(y0))), z1)) -> c2(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(cons_c(y0))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) ENCARG(b(a(a(y0, y1), y2), z1)) -> c2(ENCARG(a(a(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(a(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(a(y0, y1), y2))) ENCARG(b(a(y0, a(y1, y2)), z1)) -> c2(ENCARG(a(y0, a(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, a(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, a(y1, y2)))) ENCARG(b(a(b(y0, y1), y2), z1)) -> c2(ENCARG(a(b(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(b(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(b(y0, y1), y2))) ENCARG(b(a(y0, b(y1, y2)), z1)) -> c2(ENCARG(a(y0, b(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, b(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, b(y1, y2)))) ENCARG(b(a(cons_c(a(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(a(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(a(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(a(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(a(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(a(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(a(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(a(y1, y2))))) ENCARG(b(a(cons_c(b(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(b(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(b(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(b(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(b(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(b(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(b(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(b(y1, y2))))) ENCARG(b(a(cons_c(cons_c(y0)), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(y0)), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(y0)), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(y0)), y1))) ENCARG(b(a(y0, cons_c(cons_c(y1))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(y1)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(y1))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(y1))))) ENCARG(b(a(cons_c(cons_c(a(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(a(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(a(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(a(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(a(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(a(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(a(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(b(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(b(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(b(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(b(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(b(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(b(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(b(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(cons_c(y0))), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(cons_c(y0))), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(cons_c(y0))), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(cons_c(y0))), y1))) ENCARG(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(cons_c(y1))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(cons_c(y1)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(cons_c(y1)))))) S tuples: C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: C_1, ENCARG_1, ENCODE_C_1 Compound Symbols: c12_1, c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2, c2_2 ---------------------------------------- (107) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace C(c_c(a(a(z0, 0), z1))) -> c12(C(z0)) by C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) ENCARG(b(b(y0, y1), z1)) -> c2(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(b(z0, b(y0, y1))) -> c2(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(b(cons_c(a(y0, y1)), z1)) -> c2(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(a(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(b(cons_c(b(y0, y1)), z1)) -> c2(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(b(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(b(cons_c(cons_c(y0)), z1)) -> c2(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(y0)))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(b(cons_c(cons_c(a(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(a(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(b(cons_c(cons_c(b(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(b(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(b(cons_c(cons_c(cons_c(y0))), z1)) -> c2(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(cons_c(y0))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) ENCARG(b(a(a(y0, y1), y2), z1)) -> c2(ENCARG(a(a(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(a(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(a(y0, y1), y2))) ENCARG(b(a(y0, a(y1, y2)), z1)) -> c2(ENCARG(a(y0, a(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, a(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, a(y1, y2)))) ENCARG(b(a(b(y0, y1), y2), z1)) -> c2(ENCARG(a(b(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(b(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(b(y0, y1), y2))) ENCARG(b(a(y0, b(y1, y2)), z1)) -> c2(ENCARG(a(y0, b(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, b(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, b(y1, y2)))) ENCARG(b(a(cons_c(a(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(a(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(a(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(a(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(a(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(a(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(a(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(a(y1, y2))))) ENCARG(b(a(cons_c(b(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(b(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(b(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(b(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(b(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(b(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(b(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(b(y1, y2))))) ENCARG(b(a(cons_c(cons_c(y0)), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(y0)), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(y0)), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(y0)), y1))) ENCARG(b(a(y0, cons_c(cons_c(y1))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(y1)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(y1))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(y1))))) ENCARG(b(a(cons_c(cons_c(a(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(a(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(a(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(a(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(a(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(a(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(a(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(b(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(b(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(b(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(b(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(b(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(b(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(b(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(cons_c(y0))), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(cons_c(y0))), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(cons_c(y0))), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(cons_c(y0))), y1))) ENCARG(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(cons_c(y1))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(cons_c(y1)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(cons_c(y1)))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) S tuples: C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2, c2_2, c12_1 ---------------------------------------- (109) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(cons_c(a(z0, z1))) -> c4(ENCARG(a(z0, z1))) by ENCARG(cons_c(a(a(y0, y1), z1))) -> c4(ENCARG(a(a(y0, y1), z1))) ENCARG(cons_c(a(z0, a(y1, y2)))) -> c4(ENCARG(a(z0, a(y1, y2)))) ENCARG(cons_c(a(b(y0, y1), z1))) -> c4(ENCARG(a(b(y0, y1), z1))) ENCARG(cons_c(a(z0, b(y1, y2)))) -> c4(ENCARG(a(z0, b(y1, y2)))) ENCARG(cons_c(a(cons_c(a(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(a(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(a(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(a(y1, y2))))) ENCARG(cons_c(a(cons_c(b(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(b(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(b(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(b(y1, y2))))) ENCARG(cons_c(a(cons_c(cons_c(y0)), z1))) -> c4(ENCARG(a(cons_c(cons_c(y0)), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(y1))))) -> c4(ENCARG(a(z0, cons_c(cons_c(y1))))) ENCARG(cons_c(a(cons_c(cons_c(a(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(a(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(a(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(a(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(b(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(b(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(b(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(b(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(cons_c(y0))), z1))) -> c4(ENCARG(a(cons_c(cons_c(cons_c(y0))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(cons_c(y1)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(cons_c(y1)))))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) ENCARG(b(b(y0, y1), z1)) -> c2(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(b(z0, b(y0, y1))) -> c2(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(b(cons_c(a(y0, y1)), z1)) -> c2(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(a(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(b(cons_c(b(y0, y1)), z1)) -> c2(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(b(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(b(cons_c(cons_c(y0)), z1)) -> c2(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(y0)))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(b(cons_c(cons_c(a(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(a(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(b(cons_c(cons_c(b(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(b(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(b(cons_c(cons_c(cons_c(y0))), z1)) -> c2(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(cons_c(y0))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) ENCARG(b(a(a(y0, y1), y2), z1)) -> c2(ENCARG(a(a(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(a(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(a(y0, y1), y2))) ENCARG(b(a(y0, a(y1, y2)), z1)) -> c2(ENCARG(a(y0, a(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, a(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, a(y1, y2)))) ENCARG(b(a(b(y0, y1), y2), z1)) -> c2(ENCARG(a(b(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(b(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(b(y0, y1), y2))) ENCARG(b(a(y0, b(y1, y2)), z1)) -> c2(ENCARG(a(y0, b(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, b(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, b(y1, y2)))) ENCARG(b(a(cons_c(a(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(a(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(a(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(a(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(a(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(a(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(a(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(a(y1, y2))))) ENCARG(b(a(cons_c(b(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(b(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(b(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(b(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(b(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(b(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(b(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(b(y1, y2))))) ENCARG(b(a(cons_c(cons_c(y0)), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(y0)), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(y0)), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(y0)), y1))) ENCARG(b(a(y0, cons_c(cons_c(y1))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(y1)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(y1))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(y1))))) ENCARG(b(a(cons_c(cons_c(a(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(a(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(a(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(a(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(a(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(a(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(a(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(b(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(b(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(b(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(b(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(b(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(b(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(b(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(cons_c(y0))), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(cons_c(y0))), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(cons_c(y0))), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(cons_c(y0))), y1))) ENCARG(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(cons_c(y1))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(cons_c(y1)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(cons_c(y1)))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) ENCARG(cons_c(a(a(y0, y1), z1))) -> c4(ENCARG(a(a(y0, y1), z1))) ENCARG(cons_c(a(z0, a(y1, y2)))) -> c4(ENCARG(a(z0, a(y1, y2)))) ENCARG(cons_c(a(b(y0, y1), z1))) -> c4(ENCARG(a(b(y0, y1), z1))) ENCARG(cons_c(a(z0, b(y1, y2)))) -> c4(ENCARG(a(z0, b(y1, y2)))) ENCARG(cons_c(a(cons_c(a(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(a(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(a(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(a(y1, y2))))) ENCARG(cons_c(a(cons_c(b(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(b(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(b(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(b(y1, y2))))) ENCARG(cons_c(a(cons_c(cons_c(y0)), z1))) -> c4(ENCARG(a(cons_c(cons_c(y0)), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(y1))))) -> c4(ENCARG(a(z0, cons_c(cons_c(y1))))) ENCARG(cons_c(a(cons_c(cons_c(a(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(a(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(a(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(a(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(b(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(b(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(b(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(b(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(cons_c(y0))), z1))) -> c4(ENCARG(a(cons_c(cons_c(cons_c(y0))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(cons_c(y1)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(cons_c(y1)))))) S tuples: C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2, c2_2, c12_1 ---------------------------------------- (111) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace C(c_c(c_c(a(x0, c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))))) -> c11(C(c(c(a(0, c(c(a(z0, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2))))), C(c(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))), C(c_c(a(a(c_c(b(c_c(z0), 0)), 0), x2)))) by C(c_c(c_c(a(z0, c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))))) -> c11(C(c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2))))), C(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))), C(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(0)) -> c3(C(c(0))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) ENCARG(b(b(y0, y1), z1)) -> c2(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(b(z0, b(y0, y1))) -> c2(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(b(cons_c(a(y0, y1)), z1)) -> c2(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(a(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(b(cons_c(b(y0, y1)), z1)) -> c2(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(b(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(b(cons_c(cons_c(y0)), z1)) -> c2(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(y0)))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(b(cons_c(cons_c(a(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(a(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(b(cons_c(cons_c(b(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(b(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(b(cons_c(cons_c(cons_c(y0))), z1)) -> c2(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(cons_c(y0))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) ENCARG(b(a(a(y0, y1), y2), z1)) -> c2(ENCARG(a(a(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(a(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(a(y0, y1), y2))) ENCARG(b(a(y0, a(y1, y2)), z1)) -> c2(ENCARG(a(y0, a(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, a(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, a(y1, y2)))) ENCARG(b(a(b(y0, y1), y2), z1)) -> c2(ENCARG(a(b(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(b(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(b(y0, y1), y2))) ENCARG(b(a(y0, b(y1, y2)), z1)) -> c2(ENCARG(a(y0, b(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, b(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, b(y1, y2)))) ENCARG(b(a(cons_c(a(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(a(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(a(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(a(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(a(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(a(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(a(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(a(y1, y2))))) ENCARG(b(a(cons_c(b(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(b(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(b(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(b(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(b(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(b(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(b(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(b(y1, y2))))) ENCARG(b(a(cons_c(cons_c(y0)), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(y0)), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(y0)), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(y0)), y1))) ENCARG(b(a(y0, cons_c(cons_c(y1))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(y1)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(y1))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(y1))))) ENCARG(b(a(cons_c(cons_c(a(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(a(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(a(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(a(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(a(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(a(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(a(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(b(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(b(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(b(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(b(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(b(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(b(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(b(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(cons_c(y0))), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(cons_c(y0))), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(cons_c(y0))), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(cons_c(y0))), y1))) ENCARG(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(cons_c(y1))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(cons_c(y1)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(cons_c(y1)))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) ENCARG(cons_c(a(a(y0, y1), z1))) -> c4(ENCARG(a(a(y0, y1), z1))) ENCARG(cons_c(a(z0, a(y1, y2)))) -> c4(ENCARG(a(z0, a(y1, y2)))) ENCARG(cons_c(a(b(y0, y1), z1))) -> c4(ENCARG(a(b(y0, y1), z1))) ENCARG(cons_c(a(z0, b(y1, y2)))) -> c4(ENCARG(a(z0, b(y1, y2)))) ENCARG(cons_c(a(cons_c(a(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(a(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(a(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(a(y1, y2))))) ENCARG(cons_c(a(cons_c(b(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(b(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(b(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(b(y1, y2))))) ENCARG(cons_c(a(cons_c(cons_c(y0)), z1))) -> c4(ENCARG(a(cons_c(cons_c(y0)), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(y1))))) -> c4(ENCARG(a(z0, cons_c(cons_c(y1))))) ENCARG(cons_c(a(cons_c(cons_c(a(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(a(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(a(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(a(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(b(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(b(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(b(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(b(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(cons_c(y0))), z1))) -> c4(ENCARG(a(cons_c(cons_c(cons_c(y0))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(cons_c(y1)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(cons_c(y1)))))) C(c_c(c_c(a(z0, c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))))) -> c11(C(c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2))))), C(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))), C(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))) S tuples: C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) C(c_c(c_c(a(z0, c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))))) -> c11(C(c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2))))), C(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))), C(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2, c2_2, c12_1 ---------------------------------------- (113) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace ENCODE_C(cons_c(0)) -> c3(C(c(0))) by ENCODE_C(cons_c(0)) -> c3(C(c_c(0))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) ENCARG(b(b(y0, y1), z1)) -> c2(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(b(z0, b(y0, y1))) -> c2(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(b(cons_c(a(y0, y1)), z1)) -> c2(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(a(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(b(cons_c(b(y0, y1)), z1)) -> c2(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(b(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(b(cons_c(cons_c(y0)), z1)) -> c2(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(y0)))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(b(cons_c(cons_c(a(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(a(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(b(cons_c(cons_c(b(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(b(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(b(cons_c(cons_c(cons_c(y0))), z1)) -> c2(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(cons_c(y0))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) ENCARG(b(a(a(y0, y1), y2), z1)) -> c2(ENCARG(a(a(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(a(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(a(y0, y1), y2))) ENCARG(b(a(y0, a(y1, y2)), z1)) -> c2(ENCARG(a(y0, a(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, a(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, a(y1, y2)))) ENCARG(b(a(b(y0, y1), y2), z1)) -> c2(ENCARG(a(b(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(b(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(b(y0, y1), y2))) ENCARG(b(a(y0, b(y1, y2)), z1)) -> c2(ENCARG(a(y0, b(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, b(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, b(y1, y2)))) ENCARG(b(a(cons_c(a(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(a(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(a(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(a(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(a(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(a(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(a(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(a(y1, y2))))) ENCARG(b(a(cons_c(b(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(b(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(b(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(b(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(b(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(b(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(b(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(b(y1, y2))))) ENCARG(b(a(cons_c(cons_c(y0)), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(y0)), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(y0)), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(y0)), y1))) ENCARG(b(a(y0, cons_c(cons_c(y1))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(y1)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(y1))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(y1))))) ENCARG(b(a(cons_c(cons_c(a(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(a(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(a(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(a(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(a(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(a(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(a(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(b(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(b(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(b(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(b(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(b(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(b(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(b(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(cons_c(y0))), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(cons_c(y0))), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(cons_c(y0))), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(cons_c(y0))), y1))) ENCARG(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(cons_c(y1))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(cons_c(y1)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(cons_c(y1)))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) ENCARG(cons_c(a(a(y0, y1), z1))) -> c4(ENCARG(a(a(y0, y1), z1))) ENCARG(cons_c(a(z0, a(y1, y2)))) -> c4(ENCARG(a(z0, a(y1, y2)))) ENCARG(cons_c(a(b(y0, y1), z1))) -> c4(ENCARG(a(b(y0, y1), z1))) ENCARG(cons_c(a(z0, b(y1, y2)))) -> c4(ENCARG(a(z0, b(y1, y2)))) ENCARG(cons_c(a(cons_c(a(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(a(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(a(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(a(y1, y2))))) ENCARG(cons_c(a(cons_c(b(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(b(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(b(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(b(y1, y2))))) ENCARG(cons_c(a(cons_c(cons_c(y0)), z1))) -> c4(ENCARG(a(cons_c(cons_c(y0)), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(y1))))) -> c4(ENCARG(a(z0, cons_c(cons_c(y1))))) ENCARG(cons_c(a(cons_c(cons_c(a(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(a(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(a(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(a(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(b(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(b(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(b(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(b(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(cons_c(y0))), z1))) -> c4(ENCARG(a(cons_c(cons_c(cons_c(y0))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(cons_c(y1)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(cons_c(y1)))))) C(c_c(c_c(a(z0, c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))))) -> c11(C(c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2))))), C(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))), C(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))) ENCODE_C(cons_c(0)) -> c3(C(c_c(0))) S tuples: C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) C(c_c(c_c(a(z0, c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))))) -> c11(C(c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2))))), C(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))), C(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2, c2_2, c12_1 ---------------------------------------- (115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCODE_C(cons_c(0)) -> c3(C(c_c(0))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) ENCARG(b(b(y0, y1), z1)) -> c2(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(b(z0, b(y0, y1))) -> c2(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(b(cons_c(a(y0, y1)), z1)) -> c2(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(a(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(b(cons_c(b(y0, y1)), z1)) -> c2(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(b(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(b(cons_c(cons_c(y0)), z1)) -> c2(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(y0)))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(b(cons_c(cons_c(a(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(a(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(b(cons_c(cons_c(b(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(b(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(b(cons_c(cons_c(cons_c(y0))), z1)) -> c2(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(cons_c(y0))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) ENCARG(b(a(a(y0, y1), y2), z1)) -> c2(ENCARG(a(a(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(a(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(a(y0, y1), y2))) ENCARG(b(a(y0, a(y1, y2)), z1)) -> c2(ENCARG(a(y0, a(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, a(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, a(y1, y2)))) ENCARG(b(a(b(y0, y1), y2), z1)) -> c2(ENCARG(a(b(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(b(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(b(y0, y1), y2))) ENCARG(b(a(y0, b(y1, y2)), z1)) -> c2(ENCARG(a(y0, b(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, b(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, b(y1, y2)))) ENCARG(b(a(cons_c(a(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(a(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(a(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(a(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(a(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(a(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(a(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(a(y1, y2))))) ENCARG(b(a(cons_c(b(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(b(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(b(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(b(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(b(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(b(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(b(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(b(y1, y2))))) ENCARG(b(a(cons_c(cons_c(y0)), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(y0)), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(y0)), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(y0)), y1))) ENCARG(b(a(y0, cons_c(cons_c(y1))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(y1)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(y1))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(y1))))) ENCARG(b(a(cons_c(cons_c(a(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(a(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(a(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(a(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(a(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(a(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(a(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(b(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(b(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(b(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(b(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(b(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(b(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(b(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(cons_c(y0))), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(cons_c(y0))), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(cons_c(y0))), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(cons_c(y0))), y1))) ENCARG(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(cons_c(y1))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(cons_c(y1)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(cons_c(y1)))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) ENCARG(cons_c(a(a(y0, y1), z1))) -> c4(ENCARG(a(a(y0, y1), z1))) ENCARG(cons_c(a(z0, a(y1, y2)))) -> c4(ENCARG(a(z0, a(y1, y2)))) ENCARG(cons_c(a(b(y0, y1), z1))) -> c4(ENCARG(a(b(y0, y1), z1))) ENCARG(cons_c(a(z0, b(y1, y2)))) -> c4(ENCARG(a(z0, b(y1, y2)))) ENCARG(cons_c(a(cons_c(a(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(a(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(a(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(a(y1, y2))))) ENCARG(cons_c(a(cons_c(b(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(b(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(b(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(b(y1, y2))))) ENCARG(cons_c(a(cons_c(cons_c(y0)), z1))) -> c4(ENCARG(a(cons_c(cons_c(y0)), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(y1))))) -> c4(ENCARG(a(z0, cons_c(cons_c(y1))))) ENCARG(cons_c(a(cons_c(cons_c(a(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(a(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(a(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(a(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(b(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(b(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(b(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(b(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(cons_c(y0))), z1))) -> c4(ENCARG(a(cons_c(cons_c(cons_c(y0))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(cons_c(y1)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(cons_c(y1)))))) C(c_c(c_c(a(z0, c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))))) -> c11(C(c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2))))), C(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))), C(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))) S tuples: C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) C(c_c(c_c(a(z0, c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))))) -> c11(C(c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2))))), C(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))), C(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2, c2_2, c12_1 ---------------------------------------- (117) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) by C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) ENCARG(b(b(y0, y1), z1)) -> c2(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(b(z0, b(y0, y1))) -> c2(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(b(cons_c(a(y0, y1)), z1)) -> c2(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(a(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(b(cons_c(b(y0, y1)), z1)) -> c2(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(b(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(b(cons_c(cons_c(y0)), z1)) -> c2(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(y0)))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(b(cons_c(cons_c(a(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(a(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(b(cons_c(cons_c(b(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(b(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(b(cons_c(cons_c(cons_c(y0))), z1)) -> c2(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(cons_c(y0))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) ENCARG(b(a(a(y0, y1), y2), z1)) -> c2(ENCARG(a(a(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(a(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(a(y0, y1), y2))) ENCARG(b(a(y0, a(y1, y2)), z1)) -> c2(ENCARG(a(y0, a(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, a(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, a(y1, y2)))) ENCARG(b(a(b(y0, y1), y2), z1)) -> c2(ENCARG(a(b(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(b(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(b(y0, y1), y2))) ENCARG(b(a(y0, b(y1, y2)), z1)) -> c2(ENCARG(a(y0, b(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, b(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, b(y1, y2)))) ENCARG(b(a(cons_c(a(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(a(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(a(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(a(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(a(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(a(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(a(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(a(y1, y2))))) ENCARG(b(a(cons_c(b(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(b(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(b(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(b(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(b(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(b(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(b(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(b(y1, y2))))) ENCARG(b(a(cons_c(cons_c(y0)), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(y0)), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(y0)), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(y0)), y1))) ENCARG(b(a(y0, cons_c(cons_c(y1))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(y1)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(y1))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(y1))))) ENCARG(b(a(cons_c(cons_c(a(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(a(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(a(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(a(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(a(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(a(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(a(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(b(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(b(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(b(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(b(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(b(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(b(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(b(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(cons_c(y0))), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(cons_c(y0))), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(cons_c(y0))), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(cons_c(y0))), y1))) ENCARG(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(cons_c(y1))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(cons_c(y1)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(cons_c(y1)))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) ENCARG(cons_c(a(a(y0, y1), z1))) -> c4(ENCARG(a(a(y0, y1), z1))) ENCARG(cons_c(a(z0, a(y1, y2)))) -> c4(ENCARG(a(z0, a(y1, y2)))) ENCARG(cons_c(a(b(y0, y1), z1))) -> c4(ENCARG(a(b(y0, y1), z1))) ENCARG(cons_c(a(z0, b(y1, y2)))) -> c4(ENCARG(a(z0, b(y1, y2)))) ENCARG(cons_c(a(cons_c(a(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(a(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(a(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(a(y1, y2))))) ENCARG(cons_c(a(cons_c(b(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(b(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(b(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(b(y1, y2))))) ENCARG(cons_c(a(cons_c(cons_c(y0)), z1))) -> c4(ENCARG(a(cons_c(cons_c(y0)), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(y1))))) -> c4(ENCARG(a(z0, cons_c(cons_c(y1))))) ENCARG(cons_c(a(cons_c(cons_c(a(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(a(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(a(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(a(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(b(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(b(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(b(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(b(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(cons_c(y0))), z1))) -> c4(ENCARG(a(cons_c(cons_c(cons_c(y0))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(cons_c(y1)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(cons_c(y1)))))) C(c_c(c_c(a(z0, c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))))) -> c11(C(c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2))))), C(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))), C(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) S tuples: C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) C(c_c(c_c(a(z0, c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))))) -> c11(C(c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2))))), C(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))), C(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c4_1, c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2, c2_2, c12_1 ---------------------------------------- (119) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(cons_c(b(z0, z1))) -> c4(ENCARG(b(z0, z1))) by ENCARG(cons_c(b(b(y0, y1), z1))) -> c4(ENCARG(b(b(y0, y1), z1))) ENCARG(cons_c(b(z0, b(y1, y2)))) -> c4(ENCARG(b(z0, b(y1, y2)))) ENCARG(cons_c(b(cons_c(a(y0, y1)), z1))) -> c4(ENCARG(b(cons_c(a(y0, y1)), z1))) ENCARG(cons_c(b(z0, cons_c(a(y1, y2))))) -> c4(ENCARG(b(z0, cons_c(a(y1, y2))))) ENCARG(cons_c(b(cons_c(b(y0, y1)), z1))) -> c4(ENCARG(b(cons_c(b(y0, y1)), z1))) ENCARG(cons_c(b(z0, cons_c(b(y1, y2))))) -> c4(ENCARG(b(z0, cons_c(b(y1, y2))))) ENCARG(cons_c(b(cons_c(cons_c(y0)), z1))) -> c4(ENCARG(b(cons_c(cons_c(y0)), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(y1))))) -> c4(ENCARG(b(z0, cons_c(cons_c(y1))))) ENCARG(cons_c(b(cons_c(cons_c(a(y0, y1))), z1))) -> c4(ENCARG(b(cons_c(cons_c(a(y0, y1))), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(a(y1, y2)))))) -> c4(ENCARG(b(z0, cons_c(cons_c(a(y1, y2)))))) ENCARG(cons_c(b(cons_c(cons_c(b(y0, y1))), z1))) -> c4(ENCARG(b(cons_c(cons_c(b(y0, y1))), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(b(y1, y2)))))) -> c4(ENCARG(b(z0, cons_c(cons_c(b(y1, y2)))))) ENCARG(cons_c(b(cons_c(cons_c(cons_c(y0))), z1))) -> c4(ENCARG(b(cons_c(cons_c(cons_c(y0))), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(cons_c(y1)))))) -> c4(ENCARG(b(z0, cons_c(cons_c(cons_c(y1)))))) ENCARG(cons_c(b(a(a(y0, y1), y2), z1))) -> c4(ENCARG(b(a(a(y0, y1), y2), z1))) ENCARG(cons_c(b(z0, a(a(y1, y2), y3)))) -> c4(ENCARG(b(z0, a(a(y1, y2), y3)))) ENCARG(cons_c(b(a(y0, a(y1, y2)), z1))) -> c4(ENCARG(b(a(y0, a(y1, y2)), z1))) ENCARG(cons_c(b(z0, a(y1, a(y2, y3))))) -> c4(ENCARG(b(z0, a(y1, a(y2, y3))))) ENCARG(cons_c(b(a(b(y0, y1), y2), z1))) -> c4(ENCARG(b(a(b(y0, y1), y2), z1))) ENCARG(cons_c(b(z0, a(b(y1, y2), y3)))) -> c4(ENCARG(b(z0, a(b(y1, y2), y3)))) ENCARG(cons_c(b(a(y0, b(y1, y2)), z1))) -> c4(ENCARG(b(a(y0, b(y1, y2)), z1))) ENCARG(cons_c(b(z0, a(y1, b(y2, y3))))) -> c4(ENCARG(b(z0, a(y1, b(y2, y3))))) ENCARG(cons_c(b(a(cons_c(a(y0, y1)), y2), z1))) -> c4(ENCARG(b(a(cons_c(a(y0, y1)), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(a(y1, y2)), y3)))) -> c4(ENCARG(b(z0, a(cons_c(a(y1, y2)), y3)))) ENCARG(cons_c(b(a(y0, cons_c(a(y1, y2))), z1))) -> c4(ENCARG(b(a(y0, cons_c(a(y1, y2))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(a(y2, y3)))))) -> c4(ENCARG(b(z0, a(y1, cons_c(a(y2, y3)))))) ENCARG(cons_c(b(a(cons_c(b(y0, y1)), y2), z1))) -> c4(ENCARG(b(a(cons_c(b(y0, y1)), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(b(y1, y2)), y3)))) -> c4(ENCARG(b(z0, a(cons_c(b(y1, y2)), y3)))) ENCARG(cons_c(b(a(y0, cons_c(b(y1, y2))), z1))) -> c4(ENCARG(b(a(y0, cons_c(b(y1, y2))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(b(y2, y3)))))) -> c4(ENCARG(b(z0, a(y1, cons_c(b(y2, y3)))))) ENCARG(cons_c(b(a(cons_c(cons_c(y0)), y1), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(y0)), y1), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(y1)), y2)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(y1)), y2)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(y1))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(y1))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(y2)))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(y2)))))) ENCARG(cons_c(b(a(cons_c(cons_c(a(y0, y1))), y2), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(a(y0, y1))), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(a(y1, y2))), y3)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(a(y1, y2))), y3)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(a(y2, y3))))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(a(y2, y3))))))) ENCARG(cons_c(b(a(cons_c(cons_c(b(y0, y1))), y2), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(b(y0, y1))), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(b(y1, y2))), y3)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(b(y1, y2))), y3)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(b(y2, y3))))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(b(y2, y3))))))) ENCARG(cons_c(b(a(cons_c(cons_c(cons_c(y0))), y1), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(cons_c(y0))), y1), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(cons_c(y1))), y2)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(cons_c(y1))), y2)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(cons_c(y2))))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(cons_c(y2))))))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) ENCARG(b(b(y0, y1), z1)) -> c2(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(b(z0, b(y0, y1))) -> c2(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(b(cons_c(a(y0, y1)), z1)) -> c2(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(a(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(b(cons_c(b(y0, y1)), z1)) -> c2(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(b(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(b(cons_c(cons_c(y0)), z1)) -> c2(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(y0)))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(b(cons_c(cons_c(a(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(a(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(b(cons_c(cons_c(b(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(b(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(b(cons_c(cons_c(cons_c(y0))), z1)) -> c2(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(cons_c(y0))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) ENCARG(b(a(a(y0, y1), y2), z1)) -> c2(ENCARG(a(a(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(a(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(a(y0, y1), y2))) ENCARG(b(a(y0, a(y1, y2)), z1)) -> c2(ENCARG(a(y0, a(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, a(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, a(y1, y2)))) ENCARG(b(a(b(y0, y1), y2), z1)) -> c2(ENCARG(a(b(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(b(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(b(y0, y1), y2))) ENCARG(b(a(y0, b(y1, y2)), z1)) -> c2(ENCARG(a(y0, b(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, b(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, b(y1, y2)))) ENCARG(b(a(cons_c(a(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(a(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(a(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(a(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(a(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(a(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(a(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(a(y1, y2))))) ENCARG(b(a(cons_c(b(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(b(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(b(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(b(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(b(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(b(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(b(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(b(y1, y2))))) ENCARG(b(a(cons_c(cons_c(y0)), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(y0)), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(y0)), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(y0)), y1))) ENCARG(b(a(y0, cons_c(cons_c(y1))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(y1)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(y1))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(y1))))) ENCARG(b(a(cons_c(cons_c(a(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(a(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(a(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(a(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(a(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(a(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(a(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(b(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(b(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(b(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(b(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(b(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(b(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(b(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(cons_c(y0))), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(cons_c(y0))), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(cons_c(y0))), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(cons_c(y0))), y1))) ENCARG(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(cons_c(y1))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(cons_c(y1)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(cons_c(y1)))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) ENCARG(cons_c(a(a(y0, y1), z1))) -> c4(ENCARG(a(a(y0, y1), z1))) ENCARG(cons_c(a(z0, a(y1, y2)))) -> c4(ENCARG(a(z0, a(y1, y2)))) ENCARG(cons_c(a(b(y0, y1), z1))) -> c4(ENCARG(a(b(y0, y1), z1))) ENCARG(cons_c(a(z0, b(y1, y2)))) -> c4(ENCARG(a(z0, b(y1, y2)))) ENCARG(cons_c(a(cons_c(a(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(a(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(a(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(a(y1, y2))))) ENCARG(cons_c(a(cons_c(b(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(b(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(b(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(b(y1, y2))))) ENCARG(cons_c(a(cons_c(cons_c(y0)), z1))) -> c4(ENCARG(a(cons_c(cons_c(y0)), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(y1))))) -> c4(ENCARG(a(z0, cons_c(cons_c(y1))))) ENCARG(cons_c(a(cons_c(cons_c(a(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(a(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(a(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(a(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(b(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(b(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(b(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(b(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(cons_c(y0))), z1))) -> c4(ENCARG(a(cons_c(cons_c(cons_c(y0))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(cons_c(y1)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(cons_c(y1)))))) C(c_c(c_c(a(z0, c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))))) -> c11(C(c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2))))), C(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))), C(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(cons_c(b(b(y0, y1), z1))) -> c4(ENCARG(b(b(y0, y1), z1))) ENCARG(cons_c(b(z0, b(y1, y2)))) -> c4(ENCARG(b(z0, b(y1, y2)))) ENCARG(cons_c(b(cons_c(a(y0, y1)), z1))) -> c4(ENCARG(b(cons_c(a(y0, y1)), z1))) ENCARG(cons_c(b(z0, cons_c(a(y1, y2))))) -> c4(ENCARG(b(z0, cons_c(a(y1, y2))))) ENCARG(cons_c(b(cons_c(b(y0, y1)), z1))) -> c4(ENCARG(b(cons_c(b(y0, y1)), z1))) ENCARG(cons_c(b(z0, cons_c(b(y1, y2))))) -> c4(ENCARG(b(z0, cons_c(b(y1, y2))))) ENCARG(cons_c(b(cons_c(cons_c(y0)), z1))) -> c4(ENCARG(b(cons_c(cons_c(y0)), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(y1))))) -> c4(ENCARG(b(z0, cons_c(cons_c(y1))))) ENCARG(cons_c(b(cons_c(cons_c(a(y0, y1))), z1))) -> c4(ENCARG(b(cons_c(cons_c(a(y0, y1))), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(a(y1, y2)))))) -> c4(ENCARG(b(z0, cons_c(cons_c(a(y1, y2)))))) ENCARG(cons_c(b(cons_c(cons_c(b(y0, y1))), z1))) -> c4(ENCARG(b(cons_c(cons_c(b(y0, y1))), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(b(y1, y2)))))) -> c4(ENCARG(b(z0, cons_c(cons_c(b(y1, y2)))))) ENCARG(cons_c(b(cons_c(cons_c(cons_c(y0))), z1))) -> c4(ENCARG(b(cons_c(cons_c(cons_c(y0))), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(cons_c(y1)))))) -> c4(ENCARG(b(z0, cons_c(cons_c(cons_c(y1)))))) ENCARG(cons_c(b(a(a(y0, y1), y2), z1))) -> c4(ENCARG(b(a(a(y0, y1), y2), z1))) ENCARG(cons_c(b(z0, a(a(y1, y2), y3)))) -> c4(ENCARG(b(z0, a(a(y1, y2), y3)))) ENCARG(cons_c(b(a(y0, a(y1, y2)), z1))) -> c4(ENCARG(b(a(y0, a(y1, y2)), z1))) ENCARG(cons_c(b(z0, a(y1, a(y2, y3))))) -> c4(ENCARG(b(z0, a(y1, a(y2, y3))))) ENCARG(cons_c(b(a(b(y0, y1), y2), z1))) -> c4(ENCARG(b(a(b(y0, y1), y2), z1))) ENCARG(cons_c(b(z0, a(b(y1, y2), y3)))) -> c4(ENCARG(b(z0, a(b(y1, y2), y3)))) ENCARG(cons_c(b(a(y0, b(y1, y2)), z1))) -> c4(ENCARG(b(a(y0, b(y1, y2)), z1))) ENCARG(cons_c(b(z0, a(y1, b(y2, y3))))) -> c4(ENCARG(b(z0, a(y1, b(y2, y3))))) ENCARG(cons_c(b(a(cons_c(a(y0, y1)), y2), z1))) -> c4(ENCARG(b(a(cons_c(a(y0, y1)), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(a(y1, y2)), y3)))) -> c4(ENCARG(b(z0, a(cons_c(a(y1, y2)), y3)))) ENCARG(cons_c(b(a(y0, cons_c(a(y1, y2))), z1))) -> c4(ENCARG(b(a(y0, cons_c(a(y1, y2))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(a(y2, y3)))))) -> c4(ENCARG(b(z0, a(y1, cons_c(a(y2, y3)))))) ENCARG(cons_c(b(a(cons_c(b(y0, y1)), y2), z1))) -> c4(ENCARG(b(a(cons_c(b(y0, y1)), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(b(y1, y2)), y3)))) -> c4(ENCARG(b(z0, a(cons_c(b(y1, y2)), y3)))) ENCARG(cons_c(b(a(y0, cons_c(b(y1, y2))), z1))) -> c4(ENCARG(b(a(y0, cons_c(b(y1, y2))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(b(y2, y3)))))) -> c4(ENCARG(b(z0, a(y1, cons_c(b(y2, y3)))))) ENCARG(cons_c(b(a(cons_c(cons_c(y0)), y1), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(y0)), y1), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(y1)), y2)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(y1)), y2)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(y1))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(y1))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(y2)))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(y2)))))) ENCARG(cons_c(b(a(cons_c(cons_c(a(y0, y1))), y2), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(a(y0, y1))), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(a(y1, y2))), y3)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(a(y1, y2))), y3)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(a(y2, y3))))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(a(y2, y3))))))) ENCARG(cons_c(b(a(cons_c(cons_c(b(y0, y1))), y2), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(b(y0, y1))), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(b(y1, y2))), y3)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(b(y1, y2))), y3)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(b(y2, y3))))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(b(y2, y3))))))) ENCARG(cons_c(b(a(cons_c(cons_c(cons_c(y0))), y1), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(cons_c(y0))), y1), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(cons_c(y1))), y2)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(cons_c(y1))), y2)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(cons_c(y2))))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(cons_c(y2))))))) S tuples: C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) C(c_c(c_c(a(z0, c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))))) -> c11(C(c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2))))), C(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))), C(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: C_1, ENCARG_1, ENCODE_C_1 Compound Symbols: c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2, c2_2, c12_1, c4_1 ---------------------------------------- (121) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) by C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c_c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) ENCARG(b(b(y0, y1), z1)) -> c2(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(b(z0, b(y0, y1))) -> c2(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(b(cons_c(a(y0, y1)), z1)) -> c2(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(a(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(b(cons_c(b(y0, y1)), z1)) -> c2(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(b(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(b(cons_c(cons_c(y0)), z1)) -> c2(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(y0)))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(b(cons_c(cons_c(a(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(a(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(b(cons_c(cons_c(b(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(b(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(b(cons_c(cons_c(cons_c(y0))), z1)) -> c2(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(cons_c(y0))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) ENCARG(b(a(a(y0, y1), y2), z1)) -> c2(ENCARG(a(a(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(a(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(a(y0, y1), y2))) ENCARG(b(a(y0, a(y1, y2)), z1)) -> c2(ENCARG(a(y0, a(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, a(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, a(y1, y2)))) ENCARG(b(a(b(y0, y1), y2), z1)) -> c2(ENCARG(a(b(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(b(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(b(y0, y1), y2))) ENCARG(b(a(y0, b(y1, y2)), z1)) -> c2(ENCARG(a(y0, b(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, b(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, b(y1, y2)))) ENCARG(b(a(cons_c(a(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(a(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(a(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(a(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(a(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(a(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(a(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(a(y1, y2))))) ENCARG(b(a(cons_c(b(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(b(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(b(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(b(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(b(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(b(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(b(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(b(y1, y2))))) ENCARG(b(a(cons_c(cons_c(y0)), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(y0)), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(y0)), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(y0)), y1))) ENCARG(b(a(y0, cons_c(cons_c(y1))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(y1)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(y1))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(y1))))) ENCARG(b(a(cons_c(cons_c(a(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(a(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(a(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(a(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(a(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(a(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(a(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(b(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(b(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(b(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(b(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(b(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(b(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(b(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(cons_c(y0))), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(cons_c(y0))), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(cons_c(y0))), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(cons_c(y0))), y1))) ENCARG(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(cons_c(y1))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(cons_c(y1)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(cons_c(y1)))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) ENCARG(cons_c(a(a(y0, y1), z1))) -> c4(ENCARG(a(a(y0, y1), z1))) ENCARG(cons_c(a(z0, a(y1, y2)))) -> c4(ENCARG(a(z0, a(y1, y2)))) ENCARG(cons_c(a(b(y0, y1), z1))) -> c4(ENCARG(a(b(y0, y1), z1))) ENCARG(cons_c(a(z0, b(y1, y2)))) -> c4(ENCARG(a(z0, b(y1, y2)))) ENCARG(cons_c(a(cons_c(a(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(a(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(a(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(a(y1, y2))))) ENCARG(cons_c(a(cons_c(b(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(b(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(b(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(b(y1, y2))))) ENCARG(cons_c(a(cons_c(cons_c(y0)), z1))) -> c4(ENCARG(a(cons_c(cons_c(y0)), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(y1))))) -> c4(ENCARG(a(z0, cons_c(cons_c(y1))))) ENCARG(cons_c(a(cons_c(cons_c(a(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(a(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(a(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(a(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(b(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(b(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(b(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(b(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(cons_c(y0))), z1))) -> c4(ENCARG(a(cons_c(cons_c(cons_c(y0))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(cons_c(y1)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(cons_c(y1)))))) C(c_c(c_c(a(z0, c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))))) -> c11(C(c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2))))), C(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))), C(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(cons_c(b(b(y0, y1), z1))) -> c4(ENCARG(b(b(y0, y1), z1))) ENCARG(cons_c(b(z0, b(y1, y2)))) -> c4(ENCARG(b(z0, b(y1, y2)))) ENCARG(cons_c(b(cons_c(a(y0, y1)), z1))) -> c4(ENCARG(b(cons_c(a(y0, y1)), z1))) ENCARG(cons_c(b(z0, cons_c(a(y1, y2))))) -> c4(ENCARG(b(z0, cons_c(a(y1, y2))))) ENCARG(cons_c(b(cons_c(b(y0, y1)), z1))) -> c4(ENCARG(b(cons_c(b(y0, y1)), z1))) ENCARG(cons_c(b(z0, cons_c(b(y1, y2))))) -> c4(ENCARG(b(z0, cons_c(b(y1, y2))))) ENCARG(cons_c(b(cons_c(cons_c(y0)), z1))) -> c4(ENCARG(b(cons_c(cons_c(y0)), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(y1))))) -> c4(ENCARG(b(z0, cons_c(cons_c(y1))))) ENCARG(cons_c(b(cons_c(cons_c(a(y0, y1))), z1))) -> c4(ENCARG(b(cons_c(cons_c(a(y0, y1))), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(a(y1, y2)))))) -> c4(ENCARG(b(z0, cons_c(cons_c(a(y1, y2)))))) ENCARG(cons_c(b(cons_c(cons_c(b(y0, y1))), z1))) -> c4(ENCARG(b(cons_c(cons_c(b(y0, y1))), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(b(y1, y2)))))) -> c4(ENCARG(b(z0, cons_c(cons_c(b(y1, y2)))))) ENCARG(cons_c(b(cons_c(cons_c(cons_c(y0))), z1))) -> c4(ENCARG(b(cons_c(cons_c(cons_c(y0))), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(cons_c(y1)))))) -> c4(ENCARG(b(z0, cons_c(cons_c(cons_c(y1)))))) ENCARG(cons_c(b(a(a(y0, y1), y2), z1))) -> c4(ENCARG(b(a(a(y0, y1), y2), z1))) ENCARG(cons_c(b(z0, a(a(y1, y2), y3)))) -> c4(ENCARG(b(z0, a(a(y1, y2), y3)))) ENCARG(cons_c(b(a(y0, a(y1, y2)), z1))) -> c4(ENCARG(b(a(y0, a(y1, y2)), z1))) ENCARG(cons_c(b(z0, a(y1, a(y2, y3))))) -> c4(ENCARG(b(z0, a(y1, a(y2, y3))))) ENCARG(cons_c(b(a(b(y0, y1), y2), z1))) -> c4(ENCARG(b(a(b(y0, y1), y2), z1))) ENCARG(cons_c(b(z0, a(b(y1, y2), y3)))) -> c4(ENCARG(b(z0, a(b(y1, y2), y3)))) ENCARG(cons_c(b(a(y0, b(y1, y2)), z1))) -> c4(ENCARG(b(a(y0, b(y1, y2)), z1))) ENCARG(cons_c(b(z0, a(y1, b(y2, y3))))) -> c4(ENCARG(b(z0, a(y1, b(y2, y3))))) ENCARG(cons_c(b(a(cons_c(a(y0, y1)), y2), z1))) -> c4(ENCARG(b(a(cons_c(a(y0, y1)), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(a(y1, y2)), y3)))) -> c4(ENCARG(b(z0, a(cons_c(a(y1, y2)), y3)))) ENCARG(cons_c(b(a(y0, cons_c(a(y1, y2))), z1))) -> c4(ENCARG(b(a(y0, cons_c(a(y1, y2))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(a(y2, y3)))))) -> c4(ENCARG(b(z0, a(y1, cons_c(a(y2, y3)))))) ENCARG(cons_c(b(a(cons_c(b(y0, y1)), y2), z1))) -> c4(ENCARG(b(a(cons_c(b(y0, y1)), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(b(y1, y2)), y3)))) -> c4(ENCARG(b(z0, a(cons_c(b(y1, y2)), y3)))) ENCARG(cons_c(b(a(y0, cons_c(b(y1, y2))), z1))) -> c4(ENCARG(b(a(y0, cons_c(b(y1, y2))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(b(y2, y3)))))) -> c4(ENCARG(b(z0, a(y1, cons_c(b(y2, y3)))))) ENCARG(cons_c(b(a(cons_c(cons_c(y0)), y1), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(y0)), y1), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(y1)), y2)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(y1)), y2)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(y1))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(y1))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(y2)))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(y2)))))) ENCARG(cons_c(b(a(cons_c(cons_c(a(y0, y1))), y2), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(a(y0, y1))), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(a(y1, y2))), y3)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(a(y1, y2))), y3)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(a(y2, y3))))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(a(y2, y3))))))) ENCARG(cons_c(b(a(cons_c(cons_c(b(y0, y1))), y2), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(b(y0, y1))), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(b(y1, y2))), y3)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(b(y1, y2))), y3)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(b(y2, y3))))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(b(y2, y3))))))) ENCARG(cons_c(b(a(cons_c(cons_c(cons_c(y0))), y1), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(cons_c(y0))), y1), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(cons_c(y1))), y2)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(cons_c(y1))), y2)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(cons_c(y2))))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(cons_c(y2))))))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c_c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) S tuples: C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) C(c_c(c_c(a(z0, c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))))) -> c11(C(c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2))))), C(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))), C(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c_c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: C_1, ENCARG_1, ENCODE_C_1 Compound Symbols: c10_1, c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2, c2_2, c12_1, c4_1 ---------------------------------------- (123) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace C(c_c(b(c_c(x0), 0))) -> c10(C(c_c(a(x0, 0)))) by C(c_c(b(c_c(a(c_c(a(a(y0, 0), y1)), 0)), 0))) -> c10(C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), 0)))) C(c_c(b(c_c(a(c_c(b(c_c(y0), 0)), 0)), 0))) -> c10(C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, y1))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), 0)))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0, z1)) -> a(encArg(z0), encArg(z1)) encArg(b(z0, z1)) -> b(encArg(z0), encArg(z1)) encArg(0) -> 0 encArg(cons_c(z0)) -> c(encArg(z0)) c(z0) -> c_c(z0) c(c_c(b(c_c(z0), 0))) -> a(0, c(c(a(z0, 0)))) c(c_c(c_c(a(z0, z1)))) -> b(c(c(c(c(z1)))), z0) c(c_c(a(a(z0, 0), z1))) -> c(z0) Tuples: ENCARG(cons_c(cons_c(x0))) -> c4(C(c_c(encArg(x0))), ENCARG(cons_c(x0))) ENCARG(cons_c(cons_c(a(z0, z1)))) -> c4(C(c(a(encArg(z0), encArg(z1)))), ENCARG(cons_c(a(z0, z1)))) ENCARG(cons_c(cons_c(b(z0, z1)))) -> c4(C(c(b(encArg(z0), encArg(z1)))), ENCARG(cons_c(b(z0, z1)))) ENCARG(cons_c(cons_c(cons_c(z0)))) -> c4(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) ENCODE_C(cons_c(x0)) -> c3(C(c_c(encArg(x0)))) ENCODE_C(cons_c(a(z0, z1))) -> c3(C(c(a(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(b(z0, z1))) -> c3(C(c(b(encArg(z0), encArg(z1))))) ENCODE_C(cons_c(cons_c(z0))) -> c3(C(c(c(encArg(z0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(a(a(y0, y1), z1)) -> c1(ENCARG(a(y0, y1)), ENCARG(z1)) ENCARG(a(z0, a(y0, y1))) -> c1(ENCARG(z0), ENCARG(a(y0, y1))) ENCARG(a(b(y0, y1), z1)) -> c1(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(a(z0, b(y0, y1))) -> c1(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(a(cons_c(a(y0, y1)), z1)) -> c1(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(a(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(a(cons_c(b(y0, y1)), z1)) -> c1(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(a(z0, cons_c(b(y0, y1)))) -> c1(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(a(cons_c(cons_c(y0)), z1)) -> c1(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(y0)))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(a(cons_c(cons_c(a(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(a(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(a(cons_c(cons_c(b(y0, y1))), z1)) -> c1(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(b(y0, y1))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(a(cons_c(cons_c(cons_c(y0))), z1)) -> c1(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(a(z0, cons_c(cons_c(cons_c(y0))))) -> c1(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c_c(c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))))) -> c11(C(c(c(b(c(c(c(a(0, c(c_c(a(z2, 0))))))), z1)))), C(c(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0)))))))), C(c(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))), C(c_c(c_c(a(z1, c_c(b(c_c(z2), 0))))))) ENCARG(b(b(y0, y1), z1)) -> c2(ENCARG(b(y0, y1)), ENCARG(z1)) ENCARG(b(z0, b(y0, y1))) -> c2(ENCARG(z0), ENCARG(b(y0, y1))) ENCARG(b(cons_c(a(y0, y1)), z1)) -> c2(ENCARG(cons_c(a(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(a(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(a(y0, y1)))) ENCARG(b(cons_c(b(y0, y1)), z1)) -> c2(ENCARG(cons_c(b(y0, y1))), ENCARG(z1)) ENCARG(b(z0, cons_c(b(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_c(b(y0, y1)))) ENCARG(b(cons_c(cons_c(y0)), z1)) -> c2(ENCARG(cons_c(cons_c(y0))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(y0)))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(y0)))) ENCARG(b(cons_c(cons_c(a(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(a(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(a(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(a(y0, y1))))) ENCARG(b(cons_c(cons_c(b(y0, y1))), z1)) -> c2(ENCARG(cons_c(cons_c(b(y0, y1)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(b(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(b(y0, y1))))) ENCARG(b(cons_c(cons_c(cons_c(y0))), z1)) -> c2(ENCARG(cons_c(cons_c(cons_c(y0)))), ENCARG(z1)) ENCARG(b(z0, cons_c(cons_c(cons_c(y0))))) -> c2(ENCARG(z0), ENCARG(cons_c(cons_c(cons_c(y0))))) ENCARG(b(a(a(y0, y1), y2), z1)) -> c2(ENCARG(a(a(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(a(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(a(y0, y1), y2))) ENCARG(b(a(y0, a(y1, y2)), z1)) -> c2(ENCARG(a(y0, a(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, a(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, a(y1, y2)))) ENCARG(b(a(b(y0, y1), y2), z1)) -> c2(ENCARG(a(b(y0, y1), y2)), ENCARG(z1)) ENCARG(b(z0, a(b(y0, y1), y2))) -> c2(ENCARG(z0), ENCARG(a(b(y0, y1), y2))) ENCARG(b(a(y0, b(y1, y2)), z1)) -> c2(ENCARG(a(y0, b(y1, y2))), ENCARG(z1)) ENCARG(b(z0, a(y0, b(y1, y2)))) -> c2(ENCARG(z0), ENCARG(a(y0, b(y1, y2)))) ENCARG(b(a(cons_c(a(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(a(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(a(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(a(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(a(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(a(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(a(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(a(y1, y2))))) ENCARG(b(a(cons_c(b(y0, y1)), y2), z1)) -> c2(ENCARG(a(cons_c(b(y0, y1)), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(b(y0, y1)), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(b(y0, y1)), y2))) ENCARG(b(a(y0, cons_c(b(y1, y2))), z1)) -> c2(ENCARG(a(y0, cons_c(b(y1, y2)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(b(y1, y2))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(b(y1, y2))))) ENCARG(b(a(cons_c(cons_c(y0)), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(y0)), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(y0)), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(y0)), y1))) ENCARG(b(a(y0, cons_c(cons_c(y1))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(y1)))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(y1))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(y1))))) ENCARG(b(a(cons_c(cons_c(a(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(a(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(a(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(a(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(a(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(a(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(a(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(b(y0, y1))), y2), z1)) -> c2(ENCARG(a(cons_c(cons_c(b(y0, y1))), y2)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(b(y0, y1))), y2))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(b(y0, y1))), y2))) ENCARG(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(b(y1, y2))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(b(y1, y2)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(b(y1, y2)))))) ENCARG(b(a(cons_c(cons_c(cons_c(y0))), y1), z1)) -> c2(ENCARG(a(cons_c(cons_c(cons_c(y0))), y1)), ENCARG(z1)) ENCARG(b(z0, a(cons_c(cons_c(cons_c(y0))), y1))) -> c2(ENCARG(z0), ENCARG(a(cons_c(cons_c(cons_c(y0))), y1))) ENCARG(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1)) -> c2(ENCARG(a(y0, cons_c(cons_c(cons_c(y1))))), ENCARG(z1)) ENCARG(b(z0, a(y0, cons_c(cons_c(cons_c(y1)))))) -> c2(ENCARG(z0), ENCARG(a(y0, cons_c(cons_c(cons_c(y1)))))) C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), z1))) -> c12(C(c_c(a(a(y0, 0), y1)))) C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), z1))) -> c12(C(c_c(b(c_c(y0), 0)))) C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), z1))) -> c12(C(c_c(c_c(a(y0, y1))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(y1, y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) ENCARG(cons_c(a(a(y0, y1), z1))) -> c4(ENCARG(a(a(y0, y1), z1))) ENCARG(cons_c(a(z0, a(y1, y2)))) -> c4(ENCARG(a(z0, a(y1, y2)))) ENCARG(cons_c(a(b(y0, y1), z1))) -> c4(ENCARG(a(b(y0, y1), z1))) ENCARG(cons_c(a(z0, b(y1, y2)))) -> c4(ENCARG(a(z0, b(y1, y2)))) ENCARG(cons_c(a(cons_c(a(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(a(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(a(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(a(y1, y2))))) ENCARG(cons_c(a(cons_c(b(y0, y1)), z1))) -> c4(ENCARG(a(cons_c(b(y0, y1)), z1))) ENCARG(cons_c(a(z0, cons_c(b(y1, y2))))) -> c4(ENCARG(a(z0, cons_c(b(y1, y2))))) ENCARG(cons_c(a(cons_c(cons_c(y0)), z1))) -> c4(ENCARG(a(cons_c(cons_c(y0)), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(y1))))) -> c4(ENCARG(a(z0, cons_c(cons_c(y1))))) ENCARG(cons_c(a(cons_c(cons_c(a(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(a(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(a(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(a(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(b(y0, y1))), z1))) -> c4(ENCARG(a(cons_c(cons_c(b(y0, y1))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(b(y1, y2)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(b(y1, y2)))))) ENCARG(cons_c(a(cons_c(cons_c(cons_c(y0))), z1))) -> c4(ENCARG(a(cons_c(cons_c(cons_c(y0))), z1))) ENCARG(cons_c(a(z0, cons_c(cons_c(cons_c(y1)))))) -> c4(ENCARG(a(z0, cons_c(cons_c(cons_c(y1)))))) C(c_c(c_c(a(z0, c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))))) -> c11(C(c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2))))), C(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))), C(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) ENCARG(cons_c(b(b(y0, y1), z1))) -> c4(ENCARG(b(b(y0, y1), z1))) ENCARG(cons_c(b(z0, b(y1, y2)))) -> c4(ENCARG(b(z0, b(y1, y2)))) ENCARG(cons_c(b(cons_c(a(y0, y1)), z1))) -> c4(ENCARG(b(cons_c(a(y0, y1)), z1))) ENCARG(cons_c(b(z0, cons_c(a(y1, y2))))) -> c4(ENCARG(b(z0, cons_c(a(y1, y2))))) ENCARG(cons_c(b(cons_c(b(y0, y1)), z1))) -> c4(ENCARG(b(cons_c(b(y0, y1)), z1))) ENCARG(cons_c(b(z0, cons_c(b(y1, y2))))) -> c4(ENCARG(b(z0, cons_c(b(y1, y2))))) ENCARG(cons_c(b(cons_c(cons_c(y0)), z1))) -> c4(ENCARG(b(cons_c(cons_c(y0)), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(y1))))) -> c4(ENCARG(b(z0, cons_c(cons_c(y1))))) ENCARG(cons_c(b(cons_c(cons_c(a(y0, y1))), z1))) -> c4(ENCARG(b(cons_c(cons_c(a(y0, y1))), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(a(y1, y2)))))) -> c4(ENCARG(b(z0, cons_c(cons_c(a(y1, y2)))))) ENCARG(cons_c(b(cons_c(cons_c(b(y0, y1))), z1))) -> c4(ENCARG(b(cons_c(cons_c(b(y0, y1))), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(b(y1, y2)))))) -> c4(ENCARG(b(z0, cons_c(cons_c(b(y1, y2)))))) ENCARG(cons_c(b(cons_c(cons_c(cons_c(y0))), z1))) -> c4(ENCARG(b(cons_c(cons_c(cons_c(y0))), z1))) ENCARG(cons_c(b(z0, cons_c(cons_c(cons_c(y1)))))) -> c4(ENCARG(b(z0, cons_c(cons_c(cons_c(y1)))))) ENCARG(cons_c(b(a(a(y0, y1), y2), z1))) -> c4(ENCARG(b(a(a(y0, y1), y2), z1))) ENCARG(cons_c(b(z0, a(a(y1, y2), y3)))) -> c4(ENCARG(b(z0, a(a(y1, y2), y3)))) ENCARG(cons_c(b(a(y0, a(y1, y2)), z1))) -> c4(ENCARG(b(a(y0, a(y1, y2)), z1))) ENCARG(cons_c(b(z0, a(y1, a(y2, y3))))) -> c4(ENCARG(b(z0, a(y1, a(y2, y3))))) ENCARG(cons_c(b(a(b(y0, y1), y2), z1))) -> c4(ENCARG(b(a(b(y0, y1), y2), z1))) ENCARG(cons_c(b(z0, a(b(y1, y2), y3)))) -> c4(ENCARG(b(z0, a(b(y1, y2), y3)))) ENCARG(cons_c(b(a(y0, b(y1, y2)), z1))) -> c4(ENCARG(b(a(y0, b(y1, y2)), z1))) ENCARG(cons_c(b(z0, a(y1, b(y2, y3))))) -> c4(ENCARG(b(z0, a(y1, b(y2, y3))))) ENCARG(cons_c(b(a(cons_c(a(y0, y1)), y2), z1))) -> c4(ENCARG(b(a(cons_c(a(y0, y1)), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(a(y1, y2)), y3)))) -> c4(ENCARG(b(z0, a(cons_c(a(y1, y2)), y3)))) ENCARG(cons_c(b(a(y0, cons_c(a(y1, y2))), z1))) -> c4(ENCARG(b(a(y0, cons_c(a(y1, y2))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(a(y2, y3)))))) -> c4(ENCARG(b(z0, a(y1, cons_c(a(y2, y3)))))) ENCARG(cons_c(b(a(cons_c(b(y0, y1)), y2), z1))) -> c4(ENCARG(b(a(cons_c(b(y0, y1)), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(b(y1, y2)), y3)))) -> c4(ENCARG(b(z0, a(cons_c(b(y1, y2)), y3)))) ENCARG(cons_c(b(a(y0, cons_c(b(y1, y2))), z1))) -> c4(ENCARG(b(a(y0, cons_c(b(y1, y2))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(b(y2, y3)))))) -> c4(ENCARG(b(z0, a(y1, cons_c(b(y2, y3)))))) ENCARG(cons_c(b(a(cons_c(cons_c(y0)), y1), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(y0)), y1), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(y1)), y2)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(y1)), y2)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(y1))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(y1))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(y2)))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(y2)))))) ENCARG(cons_c(b(a(cons_c(cons_c(a(y0, y1))), y2), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(a(y0, y1))), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(a(y1, y2))), y3)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(a(y1, y2))), y3)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(a(y1, y2)))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(a(y2, y3))))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(a(y2, y3))))))) ENCARG(cons_c(b(a(cons_c(cons_c(b(y0, y1))), y2), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(b(y0, y1))), y2), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(b(y1, y2))), y3)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(b(y1, y2))), y3)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(b(y1, y2)))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(b(y2, y3))))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(b(y2, y3))))))) ENCARG(cons_c(b(a(cons_c(cons_c(cons_c(y0))), y1), z1))) -> c4(ENCARG(b(a(cons_c(cons_c(cons_c(y0))), y1), z1))) ENCARG(cons_c(b(z0, a(cons_c(cons_c(cons_c(y1))), y2)))) -> c4(ENCARG(b(z0, a(cons_c(cons_c(cons_c(y1))), y2)))) ENCARG(cons_c(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1))) -> c4(ENCARG(b(a(y0, cons_c(cons_c(cons_c(y1)))), z1))) ENCARG(cons_c(b(z0, a(y1, cons_c(cons_c(cons_c(y2))))))) -> c4(ENCARG(b(z0, a(y1, cons_c(cons_c(cons_c(y2))))))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c_c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(b(c_c(a(c_c(a(a(y0, 0), y1)), 0)), 0))) -> c10(C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), 0)))) C(c_c(b(c_c(a(c_c(b(c_c(y0), 0)), 0)), 0))) -> c10(C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, y1))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), 0)))) S tuples: C(c_c(c_c(a(x0, x1)))) -> c11(C(c_c(c_c(c(x1)))), C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, z0)))) -> c11(C(c_c(c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c_c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c_c(c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, z0)))) -> c11(C(c(c_c(c_c(z0)))), C(c(c(z0))), C(c(z0)), C(z0)) C(c_c(c_c(a(x0, c_c(c_c(a(z0, z1))))))) -> c11(C(c(c_c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(c_c(a(z0, z1)))))), C(c(c_c(c_c(a(z0, z1))))), C(c_c(c_c(a(z0, z1))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), z1)))))) -> c11(C(c(c_c(c(z0)))), C(c(c(c_c(a(a(z0, 0), z1))))), C(c(c_c(a(a(z0, 0), z1)))), C(c_c(a(a(z0, 0), z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1)))) C(c_c(c_c(a(x0, c_c(a(z0, z1)))))) -> c11(C(c(b(c(c(c(c(z1)))), z0))), C(c(c(c_c(a(z0, z1))))), C(c(c_c(a(z0, z1)))), C(c_c(a(z0, z1)))) C(c_c(c_c(a(x0, x1)))) -> c11(C(c(c(x1))), C(c(x1)), C(x1)) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(a(0, c(c_c(a(x1, 0))))))), C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(b(c_c(x1), 0)))))) -> c11(C(c(c(c_c(b(c_c(x1), 0))))), C(c(c_c(b(c_c(x1), 0)))), C(c_c(b(c_c(x1), 0)))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c_c(c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c_c(c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(b(c(c(c_c(c(x2)))), x1)))), C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2))))), C(c_c(c_c(a(x1, x2))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, z0))))))) -> c11(C(c(c(b(c(c(c(c_c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, z0)))))), C(c(c_c(c_c(a(x1, z0))))), C(c_c(c_c(a(x1, z0))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))))) -> c11(C(c(c(b(c(c(c(b(c(c(c(c(z1)))), z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1))))))))), C(c(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))), C(c_c(c_c(a(x1, c_c(c_c(a(z0, z1)))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))))) -> c11(C(c(c(b(c(c(c(c(z0)))), x1)))), C(c(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1)))))))), C(c(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))), C(c_c(c_c(a(x1, c_c(a(a(z0, 0), z1))))))) C(c_c(c_c(a(x0, c_c(c_c(a(x1, x2))))))) -> c11(C(c(c(c_c(c_c(a(x1, x2)))))), C(c(c_c(c_c(a(x1, x2)))))) C(c_c(c_c(a(x0, c_c(a(a(z0, 0), x2)))))) -> c11(C(c(c(c_c(z0)))), C(c(c(c_c(a(a(z0, 0), x2))))), C(c(c_c(a(a(z0, 0), x2)))), C(c_c(a(a(z0, 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))))) -> c11(C(c(c(b(c(c(c(c(z1)))), z0)))), C(c(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2))))), C(c(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))), C(c_c(a(a(c_c(c_c(a(z0, z1))), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))))) -> c11(C(c(c(c(z0)))), C(c(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2))))), C(c(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))), C(c_c(a(a(c_c(a(a(z0, 0), z1)), 0), x2)))) C(c_c(c_c(a(x0, c_c(a(a(x1, 0), x2)))))) -> c11(C(c(c(c_c(a(a(x1, 0), x2))))), C(c(c_c(a(a(x1, 0), x2))))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c_c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, c_c(b(c_c(z1), 0)))))) -> c11(C(c(c_c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(b(c_c(z1), 0))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) 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c12(C(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))))) C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, b(c_c(y1), 0)))))) C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), z1))) -> c12(C(c_c(c_c(a(y0, a(a(y1, 0), y2)))))) C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), z1))) -> c12(C(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))))) C(c_c(c_c(a(z0, c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))))) -> c11(C(c(c(a(0, c(c_c(a(z1, 0))))))), C(c(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2))))), C(c(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))), C(c_c(a(a(c_c(b(c_c(z1), 0)), 0), z2)))) C(c_c(c_c(a(z0, b(c_c(z1), 0))))) -> c11(C(c(a(0, c(c(a(z1, 0)))))), C(c(c_c(b(c_c(z1), 0)))), C(c_c(b(c_c(z1), 0)))) C(c_c(c_c(a(z0, a(a(z1, 0), z2))))) -> c11(C(c(c(z1))), C(c(c_c(a(a(z1, 0), z2)))), C(c_c(a(a(z1, 0), z2)))) C(c_c(b(c_c(a(c_c(a(a(y0, 0), y1)), 0)), 0))) -> c10(C(c_c(a(a(c_c(a(a(y0, 0), y1)), 0), 0)))) C(c_c(b(c_c(a(c_c(b(c_c(y0), 0)), 0)), 0))) -> c10(C(c_c(a(a(c_c(b(c_c(y0), 0)), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, y1))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, y1))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, y2)))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(y1, 0), y2))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(a(y1, y2))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(b(c_c(y1), 0))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(c_c(a(y2, y3))))))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(a(a(y2, 0), y3)))))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(b(c_c(y1), 0)), 0), y2))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(c_c(a(y1, y2))), 0), y3))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(a(a(c_c(a(a(y1, 0), y2)), 0), y3))))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, b(c_c(y1), 0)))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, a(a(y1, 0), y2)))), 0), 0)))) C(c_c(b(c_c(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0)), 0))) -> c10(C(c_c(a(a(c_c(c_c(a(y0, c_c(c_c(a(y1, c_c(b(c_c(y2), 0)))))))), 0), 0)))) K tuples:none Defined Rule Symbols: encArg_1, c_1 Defined Pair Symbols: ENCARG_1, C_1, ENCODE_C_1 Compound Symbols: c4_2, c11_4, c11_1, c11_3, c11_2, c3_1, c1_2, c2_2, c12_1, c4_1, c10_1