/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- KILLED proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF).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), 158 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 681 ms] (14) BOUNDS(1, INF) (15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (16) CpxTRS (17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (18) CpxRelTRS (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 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), 5 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 [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (44) CdtProblem (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 4 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtRewritingProof [BOTH BOUNDS(ID, ID), 3 ms] (116) CdtProblem (117) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 62 ms] (118) CdtProblem (119) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 221 ms] (120) CdtProblem (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1263 ms] (124) CdtProblem (125) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 2376 ms] (126) 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: f(f(a, a), x) -> f(a, f(b, f(a, x))) f(x, f(y, z)) -> f(f(x, y), z) 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) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b ---------------------------------------- (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: f(f(a, a), x) -> f(a, f(b, f(a, x))) f(x, f(y, z)) -> f(f(x, y), z) The (relative) TRS S consists of the following rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b 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: f(f(a, a), x) -> f(a, f(b, f(a, x))) f(x, f(y, z)) -> f(f(x, y), z) The (relative) TRS S consists of the following rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b Rewrite Strategy: FULL ---------------------------------------- (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (6) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: f(f(a, a), x) -> f(a, f(b, f(a, x))) f(x, f(y, z)) -> f(f(x, y), z) The (relative) TRS S consists of the following rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b Rewrite Strategy: FULL ---------------------------------------- (7) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (8) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: f(f(a, a), x) -> f(a, f(b, f(a, x))) f(x, f(y, z)) -> f(f(x, y), z) The (relative) TRS S consists of the following rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b Rewrite Strategy: FULL ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: TRS: Rules: f(f(a, a), x) -> f(a, f(b, f(a, x))) f(x, f(y, z)) -> f(f(x, y), z) encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b Types: f :: a:b:cons_f -> a:b:cons_f -> a:b:cons_f a :: a:b:cons_f b :: a:b:cons_f encArg :: a:b:cons_f -> a:b:cons_f cons_f :: a:b:cons_f -> a:b:cons_f -> a:b:cons_f encode_f :: a:b:cons_f -> a:b:cons_f -> a:b:cons_f encode_a :: a:b:cons_f encode_b :: a:b:cons_f hole_a:b:cons_f1_0 :: a:b:cons_f gen_a:b:cons_f2_0 :: Nat -> a:b:cons_f ---------------------------------------- (11) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: f, encArg They will be analysed ascendingly in the following order: f < encArg ---------------------------------------- (12) Obligation: TRS: Rules: f(f(a, a), x) -> f(a, f(b, f(a, x))) f(x, f(y, z)) -> f(f(x, y), z) encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b Types: f :: a:b:cons_f -> a:b:cons_f -> a:b:cons_f a :: a:b:cons_f b :: a:b:cons_f encArg :: a:b:cons_f -> a:b:cons_f cons_f :: a:b:cons_f -> a:b:cons_f -> a:b:cons_f encode_f :: a:b:cons_f -> a:b:cons_f -> a:b:cons_f encode_a :: a:b:cons_f encode_b :: a:b:cons_f hole_a:b:cons_f1_0 :: a:b:cons_f gen_a:b:cons_f2_0 :: Nat -> a:b:cons_f Generator Equations: gen_a:b:cons_f2_0(0) <=> a gen_a:b:cons_f2_0(+(x, 1)) <=> cons_f(a, gen_a:b:cons_f2_0(x)) The following defined symbols remain to be analysed: f, encArg They will be analysed ascendingly in the following order: f < encArg ---------------------------------------- (13) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_a:b:cons_f2_0(n15_0)) -> *3_0, rt in Omega(0) Induction Base: encArg(gen_a:b:cons_f2_0(0)) Induction Step: encArg(gen_a:b:cons_f2_0(+(n15_0, 1))) ->_R^Omega(0) f(encArg(a), encArg(gen_a:b:cons_f2_0(n15_0))) ->_R^Omega(0) f(a, encArg(gen_a:b:cons_f2_0(n15_0))) ->_IH f(a, *3_0) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (14) BOUNDS(1, INF) ---------------------------------------- (15) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (16) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: f(f(a, a), x) -> f(a, f(b, f(a, x))) f(x, f(y, z)) -> f(f(x, y), z) encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b 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: f(x, c_f(y, z)) -> f(f(x, y), z) f(c_f(a, a), x) -> f(a, f(b, f(a, x))) The (relative) TRS S consists of the following rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b f(x0, x1) -> c_f(x0, x1) 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: f(x, c_f(y, z)) -> f(f(x, y), z) f(c_f(a, a), x) -> f(a, f(b, f(a, x))) The (relative) TRS S consists of the following rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b f(x0, x1) -> c_f(x0, x1) 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: f(x, c_f(y, z)) -> f(f(x, y), z) [1] f(c_f(a, a), x) -> f(a, f(b, f(a, x))) [1] encArg(a) -> a [0] encArg(b) -> b [0] encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0] encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0] encode_a -> a [0] encode_b -> b [0] f(x0, x1) -> c_f(x0, x1) [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: f(x, c_f(y, z)) -> f(f(x, y), z) [1] f(c_f(a, a), x) -> f(a, f(b, f(a, x))) [1] encArg(a) -> a [0] encArg(b) -> b [0] encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0] encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0] encode_a -> a [0] encode_b -> b [0] f(x0, x1) -> c_f(x0, x1) [0] The TRS has the following type information: f :: c_f:a:b:cons_f -> c_f:a:b:cons_f -> c_f:a:b:cons_f c_f :: c_f:a:b:cons_f -> c_f:a:b:cons_f -> c_f:a:b:cons_f a :: c_f:a:b:cons_f b :: c_f:a:b:cons_f encArg :: c_f:a:b:cons_f -> c_f:a:b:cons_f cons_f :: c_f:a:b:cons_f -> c_f:a:b:cons_f -> c_f:a:b:cons_f encode_f :: c_f:a:b:cons_f -> c_f:a:b:cons_f -> c_f:a:b:cons_f encode_a :: c_f:a:b:cons_f encode_b :: c_f:a:b:cons_f 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_f_2 encode_a encode_b f_2 Due to the following rules being added: encArg(v0) -> null_encArg [0] encode_f(v0, v1) -> null_encode_f [0] encode_a -> null_encode_a [0] encode_b -> null_encode_b [0] f(v0, v1) -> null_f [0] And the following fresh constants: null_encArg, null_encode_f, null_encode_a, null_encode_b, null_f ---------------------------------------- (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: f(x, c_f(y, z)) -> f(f(x, y), z) [1] f(c_f(a, a), x) -> f(a, f(b, f(a, x))) [1] encArg(a) -> a [0] encArg(b) -> b [0] encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0] encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0] encode_a -> a [0] encode_b -> b [0] f(x0, x1) -> c_f(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_f(v0, v1) -> null_encode_f [0] encode_a -> null_encode_a [0] encode_b -> null_encode_b [0] f(v0, v1) -> null_f [0] The TRS has the following type information: f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f c_f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f a :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f b :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encArg :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f cons_f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_a :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_b :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encArg :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_a :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_b :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f 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: f(x, c_f(c_f(y', z'), z)) -> f(f(f(x, y'), z'), z) [2] f(c_f(a, a), c_f(y, z)) -> f(f(a, f(b, f(a, y))), z) [2] f(x, c_f(y, z)) -> f(c_f(x, y), z) [1] f(x, c_f(y, z)) -> f(null_f, z) [1] f(c_f(a, a), c_f(y'', z'')) -> f(a, f(b, f(f(a, y''), z''))) [2] f(c_f(a, a), x) -> f(a, f(b, c_f(a, x))) [1] f(c_f(a, a), x) -> f(a, f(b, null_f)) [1] encArg(a) -> a [0] encArg(b) -> b [0] encArg(cons_f(a, a)) -> f(a, a) [0] encArg(cons_f(a, b)) -> f(a, b) [0] encArg(cons_f(a, cons_f(x_1'', x_2''))) -> f(a, f(encArg(x_1''), encArg(x_2''))) [0] encArg(cons_f(a, x_2)) -> f(a, null_encArg) [0] encArg(cons_f(b, a)) -> f(b, a) [0] encArg(cons_f(b, b)) -> f(b, b) [0] encArg(cons_f(b, cons_f(x_11, x_21))) -> f(b, f(encArg(x_11), encArg(x_21))) [0] encArg(cons_f(b, x_2)) -> f(b, null_encArg) [0] encArg(cons_f(cons_f(x_1', x_2'), a)) -> f(f(encArg(x_1'), encArg(x_2')), a) [0] encArg(cons_f(cons_f(x_1', x_2'), b)) -> f(f(encArg(x_1'), encArg(x_2')), b) [0] encArg(cons_f(cons_f(x_1', x_2'), cons_f(x_12, x_22))) -> f(f(encArg(x_1'), encArg(x_2')), f(encArg(x_12), encArg(x_22))) [0] encArg(cons_f(cons_f(x_1', x_2'), x_2)) -> f(f(encArg(x_1'), encArg(x_2')), null_encArg) [0] encArg(cons_f(x_1, a)) -> f(null_encArg, a) [0] encArg(cons_f(x_1, b)) -> f(null_encArg, b) [0] encArg(cons_f(x_1, cons_f(x_13, x_23))) -> f(null_encArg, f(encArg(x_13), encArg(x_23))) [0] encArg(cons_f(x_1, x_2)) -> f(null_encArg, null_encArg) [0] encode_f(a, a) -> f(a, a) [0] encode_f(a, b) -> f(a, b) [0] encode_f(a, cons_f(x_15, x_25)) -> f(a, f(encArg(x_15), encArg(x_25))) [0] encode_f(a, x_2) -> f(a, null_encArg) [0] encode_f(b, a) -> f(b, a) [0] encode_f(b, b) -> f(b, b) [0] encode_f(b, cons_f(x_16, x_26)) -> f(b, f(encArg(x_16), encArg(x_26))) [0] encode_f(b, x_2) -> f(b, null_encArg) [0] encode_f(cons_f(x_14, x_24), a) -> f(f(encArg(x_14), encArg(x_24)), a) [0] encode_f(cons_f(x_14, x_24), b) -> f(f(encArg(x_14), encArg(x_24)), b) [0] encode_f(cons_f(x_14, x_24), cons_f(x_17, x_27)) -> f(f(encArg(x_14), encArg(x_24)), f(encArg(x_17), encArg(x_27))) [0] encode_f(cons_f(x_14, x_24), x_2) -> f(f(encArg(x_14), encArg(x_24)), null_encArg) [0] encode_f(x_1, a) -> f(null_encArg, a) [0] encode_f(x_1, b) -> f(null_encArg, b) [0] encode_f(x_1, cons_f(x_18, x_28)) -> f(null_encArg, f(encArg(x_18), encArg(x_28))) [0] encode_f(x_1, x_2) -> f(null_encArg, null_encArg) [0] encode_a -> a [0] encode_b -> b [0] f(x0, x1) -> c_f(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_f(v0, v1) -> null_encode_f [0] encode_a -> null_encode_a [0] encode_b -> null_encode_b [0] f(v0, v1) -> null_f [0] The TRS has the following type information: f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f c_f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f a :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f b :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encArg :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f cons_f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_a :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_b :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encArg :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_a :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_b :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f 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: a => 0 b => 1 null_encArg => 0 null_encode_f => 0 null_encode_a => 0 null_encode_b => 0 null_f => 0 ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: encArg(z1) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), f(encArg(x_12), encArg(x_22))) :|: z1 = 1 + (1 + x_1' + x_2') + (1 + x_12 + x_22), x_2' >= 0, x_1' >= 0, x_12 >= 0, x_22 >= 0 encArg(z1) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 1) :|: x_2' >= 0, x_1' >= 0, z1 = 1 + (1 + x_1' + x_2') + 1 encArg(z1) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, x_1' >= 0, z1 = 1 + (1 + x_1' + x_2') + 0 encArg(z1) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 0) :|: z1 = 1 + (1 + x_1' + x_2') + x_2, x_2' >= 0, x_1' >= 0, x_2 >= 0 encArg(z1) -{ 0 }-> f(1, f(encArg(x_11), encArg(x_21))) :|: x_11 >= 0, z1 = 1 + 1 + (1 + x_11 + x_21), x_21 >= 0 encArg(z1) -{ 0 }-> f(1, 1) :|: z1 = 1 + 1 + 1 encArg(z1) -{ 0 }-> f(1, 0) :|: z1 = 1 + 1 + 0 encArg(z1) -{ 0 }-> f(1, 0) :|: x_2 >= 0, z1 = 1 + 1 + x_2 encArg(z1) -{ 0 }-> f(0, f(encArg(x_1''), encArg(x_2''))) :|: x_1'' >= 0, x_2'' >= 0, z1 = 1 + 0 + (1 + x_1'' + x_2'') encArg(z1) -{ 0 }-> f(0, f(encArg(x_13), encArg(x_23))) :|: x_1 >= 0, x_13 >= 0, x_23 >= 0, z1 = 1 + x_1 + (1 + x_13 + x_23) encArg(z1) -{ 0 }-> f(0, 1) :|: z1 = 1 + 0 + 1 encArg(z1) -{ 0 }-> f(0, 1) :|: x_1 >= 0, z1 = 1 + x_1 + 1 encArg(z1) -{ 0 }-> f(0, 0) :|: z1 = 1 + 0 + 0 encArg(z1) -{ 0 }-> f(0, 0) :|: z1 = 1 + 0 + x_2, x_2 >= 0 encArg(z1) -{ 0 }-> f(0, 0) :|: x_1 >= 0, z1 = 1 + x_1 + 0 encArg(z1) -{ 0 }-> f(0, 0) :|: x_1 >= 0, z1 = 1 + x_1 + x_2, x_2 >= 0 encArg(z1) -{ 0 }-> 1 :|: z1 = 1 encArg(z1) -{ 0 }-> 0 :|: z1 = 0 encArg(z1) -{ 0 }-> 0 :|: z1 = v0, v0 >= 0 encode_a -{ 0 }-> 0 :|: encode_b -{ 0 }-> 1 :|: encode_b -{ 0 }-> 0 :|: encode_f(z1, z2) -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), f(encArg(x_17), encArg(x_27))) :|: x_14 >= 0, z2 = 1 + x_17 + x_27, x_17 >= 0, x_24 >= 0, x_27 >= 0, z1 = 1 + x_14 + x_24 encode_f(z1, z2) -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), 1) :|: x_14 >= 0, z2 = 1, x_24 >= 0, z1 = 1 + x_14 + x_24 encode_f(z1, z2) -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), 0) :|: x_14 >= 0, z2 = 0, x_24 >= 0, z1 = 1 + x_14 + x_24 encode_f(z1, z2) -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), 0) :|: x_14 >= 0, z2 = x_2, x_24 >= 0, x_2 >= 0, z1 = 1 + x_14 + x_24 encode_f(z1, z2) -{ 0 }-> f(1, f(encArg(x_16), encArg(x_26))) :|: x_16 >= 0, x_26 >= 0, z1 = 1, z2 = 1 + x_16 + x_26 encode_f(z1, z2) -{ 0 }-> f(1, 1) :|: z2 = 1, z1 = 1 encode_f(z1, z2) -{ 0 }-> f(1, 0) :|: z2 = 0, z1 = 1 encode_f(z1, z2) -{ 0 }-> f(1, 0) :|: z1 = 1, z2 = x_2, x_2 >= 0 encode_f(z1, z2) -{ 0 }-> f(0, f(encArg(x_15), encArg(x_25))) :|: x_15 >= 0, z1 = 0, x_25 >= 0, z2 = 1 + x_15 + x_25 encode_f(z1, z2) -{ 0 }-> f(0, f(encArg(x_18), encArg(x_28))) :|: x_1 >= 0, z1 = x_1, z2 = 1 + x_18 + x_28, x_18 >= 0, x_28 >= 0 encode_f(z1, z2) -{ 0 }-> f(0, 1) :|: z1 = 0, z2 = 1 encode_f(z1, z2) -{ 0 }-> f(0, 1) :|: x_1 >= 0, z1 = x_1, z2 = 1 encode_f(z1, z2) -{ 0 }-> f(0, 0) :|: z1 = 0, z2 = 0 encode_f(z1, z2) -{ 0 }-> f(0, 0) :|: z1 = 0, z2 = x_2, x_2 >= 0 encode_f(z1, z2) -{ 0 }-> f(0, 0) :|: x_1 >= 0, z1 = x_1, z2 = 0 encode_f(z1, z2) -{ 0 }-> f(0, 0) :|: x_1 >= 0, z1 = x_1, z2 = x_2, x_2 >= 0 encode_f(z1, z2) -{ 0 }-> 0 :|: z1 = v0, v0 >= 0, z2 = v1, v1 >= 0 f(z1, z2) -{ 2 }-> f(f(f(x, y'), z'), z) :|: z >= 0, x >= 0, z' >= 0, y' >= 0, z2 = 1 + (1 + y' + z') + z, z1 = x f(z1, z2) -{ 2 }-> f(f(0, f(1, f(0, y))), z) :|: z2 = 1 + y + z, z >= 0, y >= 0, z1 = 1 + 0 + 0 f(z1, z2) -{ 1 }-> f(0, z) :|: z2 = 1 + y + z, z >= 0, x >= 0, y >= 0, z1 = x f(z1, z2) -{ 2 }-> f(0, f(1, f(f(0, y''), z''))) :|: z2 = 1 + y'' + z'', z'' >= 0, z1 = 1 + 0 + 0, y'' >= 0 f(z1, z2) -{ 1 }-> f(0, f(1, 0)) :|: z2 = x, x >= 0, z1 = 1 + 0 + 0 f(z1, z2) -{ 1 }-> f(0, f(1, 1 + 0 + x)) :|: z2 = x, x >= 0, z1 = 1 + 0 + 0 f(z1, z2) -{ 1 }-> f(1 + x + y, z) :|: z2 = 1 + y + z, z >= 0, x >= 0, y >= 0, z1 = x f(z1, z2) -{ 0 }-> 0 :|: z1 = v0, v0 >= 0, z2 = v1, v1 >= 0 f(z1, z2) -{ 0 }-> 1 + x0 + x1 :|: z1 = x0, x0 >= 0, x1 >= 0, z2 = x1 ---------------------------------------- (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: encArg(z1) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), f(encArg(x_12), encArg(x_22))) :|: z1 = 1 + (1 + x_1' + x_2') + (1 + x_12 + x_22), x_2' >= 0, x_1' >= 0, x_12 >= 0, x_22 >= 0 encArg(z1) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 1) :|: x_2' >= 0, x_1' >= 0, z1 = 1 + (1 + x_1' + x_2') + 1 encArg(z1) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, x_1' >= 0, z1 = 1 + (1 + x_1' + x_2') + 0 encArg(z1) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 0) :|: z1 = 1 + (1 + x_1' + x_2') + x_2, x_2' >= 0, x_1' >= 0, x_2 >= 0 encArg(z1) -{ 0 }-> f(1, f(encArg(x_11), encArg(x_21))) :|: x_11 >= 0, z1 = 1 + 1 + (1 + x_11 + x_21), x_21 >= 0 encArg(z1) -{ 0 }-> f(1, 1) :|: z1 = 1 + 1 + 1 encArg(z1) -{ 0 }-> f(1, 0) :|: z1 = 1 + 1 + 0 encArg(z1) -{ 0 }-> f(1, 0) :|: z1 - 2 >= 0 encArg(z1) -{ 0 }-> f(0, f(encArg(x_1''), encArg(x_2''))) :|: x_1'' >= 0, x_2'' >= 0, z1 = 1 + 0 + (1 + x_1'' + x_2'') encArg(z1) -{ 0 }-> f(0, f(encArg(x_13), encArg(x_23))) :|: x_1 >= 0, x_13 >= 0, x_23 >= 0, z1 = 1 + x_1 + (1 + x_13 + x_23) encArg(z1) -{ 0 }-> f(0, 1) :|: z1 = 1 + 0 + 1 encArg(z1) -{ 0 }-> f(0, 1) :|: z1 - 2 >= 0 encArg(z1) -{ 0 }-> f(0, 0) :|: z1 = 1 + 0 + 0 encArg(z1) -{ 0 }-> f(0, 0) :|: z1 - 1 >= 0 encArg(z1) -{ 0 }-> f(0, 0) :|: x_1 >= 0, z1 = 1 + x_1 + x_2, x_2 >= 0 encArg(z1) -{ 0 }-> 1 :|: z1 = 1 encArg(z1) -{ 0 }-> 0 :|: z1 = 0 encArg(z1) -{ 0 }-> 0 :|: z1 >= 0 encode_a -{ 0 }-> 0 :|: encode_b -{ 0 }-> 1 :|: encode_b -{ 0 }-> 0 :|: encode_f(z1, z2) -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), f(encArg(x_17), encArg(x_27))) :|: x_14 >= 0, z2 = 1 + x_17 + x_27, x_17 >= 0, x_24 >= 0, x_27 >= 0, z1 = 1 + x_14 + x_24 encode_f(z1, z2) -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), 1) :|: x_14 >= 0, z2 = 1, x_24 >= 0, z1 = 1 + x_14 + x_24 encode_f(z1, z2) -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), 0) :|: x_14 >= 0, z2 = 0, x_24 >= 0, z1 = 1 + x_14 + x_24 encode_f(z1, z2) -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), 0) :|: x_14 >= 0, x_24 >= 0, z2 >= 0, z1 = 1 + x_14 + x_24 encode_f(z1, z2) -{ 0 }-> f(1, f(encArg(x_16), encArg(x_26))) :|: x_16 >= 0, x_26 >= 0, z1 = 1, z2 = 1 + x_16 + x_26 encode_f(z1, z2) -{ 0 }-> f(1, 1) :|: z2 = 1, z1 = 1 encode_f(z1, z2) -{ 0 }-> f(1, 0) :|: z2 = 0, z1 = 1 encode_f(z1, z2) -{ 0 }-> f(1, 0) :|: z1 = 1, z2 >= 0 encode_f(z1, z2) -{ 0 }-> f(0, f(encArg(x_15), encArg(x_25))) :|: x_15 >= 0, z1 = 0, x_25 >= 0, z2 = 1 + x_15 + x_25 encode_f(z1, z2) -{ 0 }-> f(0, f(encArg(x_18), encArg(x_28))) :|: z1 >= 0, z2 = 1 + x_18 + x_28, x_18 >= 0, x_28 >= 0 encode_f(z1, z2) -{ 0 }-> f(0, 1) :|: z1 = 0, z2 = 1 encode_f(z1, z2) -{ 0 }-> f(0, 1) :|: z1 >= 0, z2 = 1 encode_f(z1, z2) -{ 0 }-> f(0, 0) :|: z1 = 0, z2 = 0 encode_f(z1, z2) -{ 0 }-> f(0, 0) :|: z1 = 0, z2 >= 0 encode_f(z1, z2) -{ 0 }-> f(0, 0) :|: z1 >= 0, z2 = 0 encode_f(z1, z2) -{ 0 }-> f(0, 0) :|: z1 >= 0, z2 >= 0 encode_f(z1, z2) -{ 0 }-> 0 :|: z1 >= 0, z2 >= 0 f(z1, z2) -{ 2 }-> f(f(f(z1, y'), z'), z) :|: z >= 0, z1 >= 0, z' >= 0, y' >= 0, z2 = 1 + (1 + y' + z') + z f(z1, z2) -{ 2 }-> f(f(0, f(1, f(0, y))), z) :|: z2 = 1 + y + z, z >= 0, y >= 0, z1 = 1 + 0 + 0 f(z1, z2) -{ 1 }-> f(0, z) :|: z2 = 1 + y + z, z >= 0, z1 >= 0, y >= 0 f(z1, z2) -{ 2 }-> f(0, f(1, f(f(0, y''), z''))) :|: z2 = 1 + y'' + z'', z'' >= 0, z1 = 1 + 0 + 0, y'' >= 0 f(z1, z2) -{ 1 }-> f(0, f(1, 0)) :|: z2 >= 0, z1 = 1 + 0 + 0 f(z1, z2) -{ 1 }-> f(0, f(1, 1 + 0 + z2)) :|: z2 >= 0, z1 = 1 + 0 + 0 f(z1, z2) -{ 1 }-> f(1 + z1 + y, z) :|: z2 = 1 + y + z, z >= 0, z1 >= 0, y >= 0 f(z1, z2) -{ 0 }-> 0 :|: z1 >= 0, z2 >= 0 f(z1, z2) -{ 0 }-> 1 + z1 + z2 :|: z1 >= 0, z2 >= 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_f(v0, v1) -> null_encode_f [0] encode_a -> null_encode_a [0] encode_b -> null_encode_b [0] f(v0, v1) -> null_f [0] And the following fresh constants: null_encArg, null_encode_f, null_encode_a, null_encode_b, null_f ---------------------------------------- (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: f(x, c_f(y, z)) -> f(f(x, y), z) [1] f(c_f(a, a), x) -> f(a, f(b, f(a, x))) [1] encArg(a) -> a [0] encArg(b) -> b [0] encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0] encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0] encode_a -> a [0] encode_b -> b [0] f(x0, x1) -> c_f(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_f(v0, v1) -> null_encode_f [0] encode_a -> null_encode_a [0] encode_b -> null_encode_b [0] f(v0, v1) -> null_f [0] The TRS has the following type information: f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f c_f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f a :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f b :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encArg :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f cons_f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_a :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_b :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encArg :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_a :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_b :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_f :: c_f:a:b:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f 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: a => 0 b => 1 null_encArg => 0 null_encode_f => 0 null_encode_a => 0 null_encode_b => 0 null_f => 0 ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: encArg(z') -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2 encArg(z') -{ 0 }-> 1 :|: z' = 1 encArg(z') -{ 0 }-> 0 :|: z' = 0 encArg(z') -{ 0 }-> 0 :|: v0 >= 0, z' = v0 encode_a -{ 0 }-> 0 :|: encode_b -{ 0 }-> 1 :|: encode_b -{ 0 }-> 0 :|: encode_f(z', z'') -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z' = x_1, x_2 >= 0, z'' = x_2 encode_f(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0 f(z', z'') -{ 1 }-> f(f(x, y), z) :|: z >= 0, z' = x, x >= 0, y >= 0, z'' = 1 + y + z f(z', z'') -{ 1 }-> f(0, f(1, f(0, x))) :|: z' = 1 + 0 + 0, x >= 0, z'' = x f(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0 f(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = x1, x0 >= 0, x1 >= 0, z' = x0 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) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) encode_f(z0, z1) -> f(encArg(z0), encArg(z1)) encode_a -> a encode_b -> b f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(a) -> c ENCARG(b) -> c1 ENCARG(cons_f(z0, z1)) -> c2(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_F(z0, z1) -> c3(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_A -> c4 ENCODE_B -> c5 F(z0, z1) -> c6 F(z0, c_f(z1, z2)) -> c7(F(f(z0, z1), z2), F(z0, z1)) F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) S tuples: F(z0, c_f(z1, z2)) -> c7(F(f(z0, z1), z2), F(z0, z1)) F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) K tuples:none Defined Rule Symbols: f_2, encArg_1, encode_f_2, encode_a, encode_b Defined Pair Symbols: ENCARG_1, ENCODE_F_2, ENCODE_A, ENCODE_B, F_2 Compound Symbols: c, c1, c2_3, c3_3, c4, c5, c6, c7_2, c8_3 ---------------------------------------- (39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing nodes: ENCODE_A -> c4 F(z0, z1) -> c6 ENCARG(b) -> c1 ENCODE_B -> c5 ENCARG(a) -> c ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) encode_f(z0, z1) -> f(encArg(z0), encArg(z1)) encode_a -> a encode_b -> b f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(z0, z1)) -> c2(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_F(z0, z1) -> c3(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) F(z0, c_f(z1, z2)) -> c7(F(f(z0, z1), z2), F(z0, z1)) F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) S tuples: F(z0, c_f(z1, z2)) -> c7(F(f(z0, z1), z2), F(z0, z1)) F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) K tuples:none Defined Rule Symbols: f_2, encArg_1, encode_f_2, encode_a, encode_b Defined Pair Symbols: ENCARG_1, ENCODE_F_2, F_2 Compound Symbols: c2_3, c3_3, c7_2, c8_3 ---------------------------------------- (41) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) encode_f(z0, z1) -> f(encArg(z0), encArg(z1)) encode_a -> a encode_b -> b f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(z0, z1)) -> c2(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) F(z0, c_f(z1, z2)) -> c7(F(f(z0, z1), z2), F(z0, z1)) F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) ENCODE_F(z0, z1) -> c(ENCARG(z0)) ENCODE_F(z0, z1) -> c(ENCARG(z1)) S tuples: F(z0, c_f(z1, z2)) -> c7(F(f(z0, z1), z2), F(z0, z1)) F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) K tuples:none Defined Rule Symbols: f_2, encArg_1, encode_f_2, encode_a, encode_b Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c7_2, c8_3, c_1 ---------------------------------------- (43) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 2 leading nodes: ENCODE_F(z0, z1) -> c(ENCARG(z0)) ENCODE_F(z0, z1) -> c(ENCARG(z1)) ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) encode_f(z0, z1) -> f(encArg(z0), encArg(z1)) encode_a -> a encode_b -> b f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(z0, z1)) -> c2(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) F(z0, c_f(z1, z2)) -> c7(F(f(z0, z1), z2), F(z0, z1)) F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) S tuples: F(z0, c_f(z1, z2)) -> c7(F(f(z0, z1), z2), F(z0, z1)) F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) K tuples:none Defined Rule Symbols: f_2, encArg_1, encode_f_2, encode_a, encode_b Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c7_2, c8_3, c_1 ---------------------------------------- (45) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_f(z0, z1) -> f(encArg(z0), encArg(z1)) encode_a -> a encode_b -> b ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(z0, z1)) -> c2(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) F(z0, c_f(z1, z2)) -> c7(F(f(z0, z1), z2), F(z0, z1)) F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) S tuples: F(z0, c_f(z1, z2)) -> c7(F(f(z0, z1), z2), F(z0, z1)) F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c7_2, c8_3, c_1 ---------------------------------------- (47) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_f(z0, z1)) -> c2(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_f(x0, a)) -> c2(F(encArg(x0), a), ENCARG(x0), ENCARG(a)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0), ENCARG(b)) ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(a), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(b), ENCARG(x1)) ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, z2)) -> c7(F(f(z0, z1), z2), F(z0, z1)) F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) ENCARG(cons_f(x0, a)) -> c2(F(encArg(x0), a), ENCARG(x0), ENCARG(a)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0), ENCARG(b)) ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(a), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(b), ENCARG(x1)) ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) S tuples: F(z0, c_f(z1, z2)) -> c7(F(f(z0, z1), z2), F(z0, z1)) F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c8_3, c_1, c2_3 ---------------------------------------- (49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, z2)) -> c7(F(f(z0, z1), z2), F(z0, z1)) F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ENCARG(cons_f(x0, a)) -> c2(F(encArg(x0), a), ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(x1)) S tuples: F(z0, c_f(z1, z2)) -> c7(F(f(z0, z1), z2), F(z0, z1)) F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c8_3, c_1, c2_3, c2_2 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace F(z0, c_f(z1, z2)) -> c7(F(f(z0, z1), z2), F(z0, z1)) by F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ENCARG(cons_f(x0, a)) -> c2(F(encArg(x0), a), ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(x1)) F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) S tuples: F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c8_3, c_1, c2_3, c2_2, c7_2 ---------------------------------------- (53) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace F(c_f(a, a), z0) -> c8(F(a, f(b, f(a, z0))), F(b, f(a, z0)), F(a, z0)) by F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ENCARG(cons_f(x0, a)) -> c2(F(encArg(x0), a), ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(x1)) F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCODE_F_2, ENCARG_1, F_2 Compound Symbols: c_1, c2_3, c2_2, c7_2, c8_3 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) by ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ENCARG(cons_f(x0, a)) -> c2(F(encArg(x0), a), ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(x1)) F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c2_2, c7_2, c8_3, c_1 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) by ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(a), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(b), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ENCARG(cons_f(x0, a)) -> c2(F(encArg(x0), a), ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(x1)) F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(a), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(b), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c2_2, c7_2, c8_3, c_1 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ENCARG(cons_f(x0, a)) -> c2(F(encArg(x0), a), ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(x1)) F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c2_2, c7_2, c8_3, c_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) by ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)), ENCARG(a)) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)), ENCARG(b)) ENCARG(cons_f(cons_f(x0, x1), cons_f(z0, z1))) -> c2(F(f(encArg(x0), encArg(x1)), f(encArg(z0), encArg(z1))), ENCARG(cons_f(x0, x1)), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(x0, a)) -> c2(F(encArg(x0), a), ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(x1)) F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)), ENCARG(a)) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)), ENCARG(b)) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_2, c7_2, c8_3, c_1, c2_3 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(x0, a)) -> c2(F(encArg(x0), a), ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(x1)) F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_2, c7_2, c8_3, c_1, c2_3 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_f(x0, a)) -> c2(F(encArg(x0), a), ENCARG(x0)) by ENCARG(cons_f(a, a)) -> c2(F(a, a), ENCARG(a)) ENCARG(cons_f(b, a)) -> c2(F(b, a), ENCARG(b)) ENCARG(cons_f(cons_f(z0, z1), a)) -> c2(F(f(encArg(z0), encArg(z1)), a), ENCARG(cons_f(z0, z1))) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(x1)) F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(a, a)) -> c2(F(a, a), ENCARG(a)) ENCARG(cons_f(b, a)) -> c2(F(b, a), ENCARG(b)) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_2, c7_2, c8_3, c_1, c2_3 ---------------------------------------- (67) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_f(a, a)) -> c2(F(a, a), ENCARG(a)) ENCARG(cons_f(b, a)) -> c2(F(b, a), ENCARG(b)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(x1)) F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_2, c7_2, c8_3, c_1, c2_3 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) by ENCARG(cons_f(a, b)) -> c2(F(a, b), ENCARG(a)) ENCARG(cons_f(b, b)) -> c2(F(b, b), ENCARG(b)) ENCARG(cons_f(cons_f(z0, z1), b)) -> c2(F(f(encArg(z0), encArg(z1)), b), ENCARG(cons_f(z0, z1))) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(x1)) F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(a, b)) -> c2(F(a, b), ENCARG(a)) ENCARG(cons_f(b, b)) -> c2(F(b, b), ENCARG(b)) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_2, c7_2, c8_3, c_1, c2_3 ---------------------------------------- (71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_f(a, b)) -> c2(F(a, b), ENCARG(a)) ENCARG(cons_f(b, b)) -> c2(F(b, b), ENCARG(b)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(x1)) F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_2, c7_2, c8_3, c_1, c2_3 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) by ENCARG(cons_f(a, a)) -> c2(F(a, a), ENCARG(a)) ENCARG(cons_f(a, b)) -> c2(F(a, b), ENCARG(b)) ENCARG(cons_f(a, cons_f(z0, z1))) -> c2(F(a, f(encArg(z0), encArg(z1))), ENCARG(cons_f(z0, z1))) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(x1)) F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(a, a)) -> c2(F(a, a), ENCARG(a)) ENCARG(cons_f(a, b)) -> c2(F(a, b), ENCARG(b)) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_2, c7_2, c8_3, c_1, c2_3 ---------------------------------------- (75) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_f(a, a)) -> c2(F(a, a), ENCARG(a)) ENCARG(cons_f(a, b)) -> c2(F(a, b), ENCARG(b)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(x1)) F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_2, c7_2, c8_3, c_1, c2_3 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(x1)) by ENCARG(cons_f(b, a)) -> c2(F(b, a), ENCARG(a)) ENCARG(cons_f(b, b)) -> c2(F(b, b), ENCARG(b)) ENCARG(cons_f(b, cons_f(z0, z1))) -> c2(F(b, f(encArg(z0), encArg(z1))), ENCARG(cons_f(z0, z1))) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(b, a)) -> c2(F(b, a), ENCARG(a)) ENCARG(cons_f(b, b)) -> c2(F(b, b), ENCARG(b)) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c8_3, c_1, c2_3, c2_2 ---------------------------------------- (79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_f(b, a)) -> c2(F(b, a), ENCARG(a)) ENCARG(cons_f(b, b)) -> c2(F(b, b), ENCARG(b)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c8_3, c_1, c2_3, c2_2 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace F(z0, c_f(c_f(z1, z2), x2)) -> c7(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) by F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c8_3, c_1, c2_3, c2_2, c7_1 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace F(c_f(a, a), c_f(z0, x2)) -> c7(F(f(a, f(b, f(a, z0))), x2), F(c_f(a, a), z0)) by F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c8_3, c_1, c2_3, c2_2, c7_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace F(c_f(a, a), x0) -> c8(F(a, c_f(b, f(a, x0))), F(b, f(a, x0)), F(a, x0)) by F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c8_3, c_1, c2_3, c2_2, c7_1 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace F(c_f(a, a), z1) -> c8(F(a, f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) by F(c_f(a, a), x0) -> c8(F(a, c_f(b, c_f(a, x0))), F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c8_3, c_1, c2_3, c2_2, c7_1, c8_2 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) by F(c_f(a, a), c_f(x0, x1)) -> c8(F(a, c_f(b, f(f(a, x0), x1))), F(b, f(a, c_f(x0, x1))), F(a, c_f(x0, x1))) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c_1, c2_3, c2_2, c7_1, c8_3, c8_2, c8_1 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_F(x0, a) -> c(F(encArg(x0), a)) by ENCODE_F(a, a) -> c(F(a, a)) ENCODE_F(b, a) -> c(F(b, a)) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(a, a) -> c(F(a, a)) ENCODE_F(b, a) -> c(F(b, a)) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c_1, c2_3, c2_2, c7_1, c8_3, c8_2, c8_1 ---------------------------------------- (93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_F(b, a) -> c(F(b, a)) ENCODE_F(a, a) -> c(F(a, a)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c_1, c2_3, c2_2, c7_1, c8_3, c8_2, c8_1 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_F(x0, b) -> c(F(encArg(x0), b)) by ENCODE_F(a, b) -> c(F(a, b)) ENCODE_F(b, b) -> c(F(b, b)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(a, b) -> c(F(a, b)) ENCODE_F(b, b) -> c(F(b, b)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c_1, c2_3, c2_2, c7_1, c8_3, c8_2, c8_1 ---------------------------------------- (97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_F(a, b) -> c(F(a, b)) ENCODE_F(b, b) -> c(F(b, b)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c_1, c2_3, c2_2, c7_1, c8_3, c8_2, c8_1 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) by ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c_1, c2_3, c2_2, c7_1, c8_3, c8_2, c8_1 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_F(a, x1) -> c(F(a, encArg(x1))) by ENCODE_F(a, a) -> c(F(a, a)) ENCODE_F(a, b) -> c(F(a, b)) ENCODE_F(a, cons_f(z0, z1)) -> c(F(a, f(encArg(z0), encArg(z1)))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(a, a) -> c(F(a, a)) ENCODE_F(a, b) -> c(F(a, b)) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c_1, c2_3, c2_2, c7_1, c8_3, c8_2, c8_1 ---------------------------------------- (103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_F(a, b) -> c(F(a, b)) ENCODE_F(a, a) -> c(F(a, a)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c_1, c2_3, c2_2, c7_1, c8_3, c8_2, c8_1 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_F(b, x1) -> c(F(b, encArg(x1))) by ENCODE_F(b, a) -> c(F(b, a)) ENCODE_F(b, b) -> c(F(b, b)) ENCODE_F(b, cons_f(z0, z1)) -> c(F(b, f(encArg(z0), encArg(z1)))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(b, a) -> c(F(b, a)) ENCODE_F(b, b) -> c(F(b, b)) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c_1, c2_3, c2_2, c7_1, c8_3, c8_2, c8_1 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_F(b, a) -> c(F(b, a)) ENCODE_F(b, b) -> c(F(b, b)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_2, c_1, c2_3, c2_2, c7_1, c8_3, c8_2, c8_1 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) by ENCODE_F(cons_f(x0, x1), a) -> c(F(f(encArg(x0), encArg(x1)), a)) ENCODE_F(cons_f(x0, x1), b) -> c(F(f(encArg(x0), encArg(x1)), b)) ENCODE_F(cons_f(x0, x1), cons_f(z0, z1)) -> c(F(f(encArg(x0), encArg(x1)), f(encArg(z0), encArg(z1)))) ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2))) ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(b, x1), x2) -> c(F(f(b, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2))) ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(b, x1), x2) -> c(F(f(b, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) S tuples: F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCARG_1, ENCODE_F_2 Compound Symbols: c7_2, c2_3, c2_2, c7_1, c8_3, c8_2, c8_1, c_1 ---------------------------------------- (111) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(z0, c_f(z1, x2)) -> c7(F(c_f(z0, z1), x2), F(z0, z1)) by F(z0, c_f(z1, c_f(y1, y2))) -> c7(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1)) F(z0, c_f(c_f(y1, y2), z2)) -> c7(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1)), F(a, a)) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2), F(a, a)) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2))), F(a, a)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2))) ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(b, x1), x2) -> c(F(f(b, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) F(z0, c_f(z1, c_f(y1, y2))) -> c7(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1)) F(z0, c_f(c_f(y1, y2), z2)) -> c7(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1)), F(a, a)) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2), F(a, a)) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2))), F(a, a)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) S tuples: F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) F(z0, c_f(z1, c_f(y1, y2))) -> c7(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1)) F(z0, c_f(c_f(y1, y2), z2)) -> c7(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1)), F(a, a)) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2), F(a, a)) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2))), F(a, a)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c2_2, c7_2, c7_1, c8_3, c8_2, c8_1, c_1 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2))) ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(b, x1), x2) -> c(F(f(b, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) F(z0, c_f(z1, c_f(y1, y2))) -> c7(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1)) F(z0, c_f(c_f(y1, y2), z2)) -> c7(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2)))) S tuples: F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) F(z0, c_f(z1, c_f(y1, y2))) -> c7(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1)) F(z0, c_f(c_f(y1, y2), z2)) -> c7(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2)))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c2_2, c7_2, c7_1, c8_3, c8_2, c8_1, c_1 ---------------------------------------- (115) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace F(c_f(a, a), z2) -> c8(F(a, f(f(b, a), z2)), F(b, f(a, z2)), F(a, z2)) by F(c_f(a, a), z0) -> c8(F(a, f(c_f(b, a), z0)), F(b, f(a, z0)), F(a, z0)) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2))) ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(b, x1), x2) -> c(F(f(b, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) F(z0, c_f(z1, c_f(y1, y2))) -> c7(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1)) F(z0, c_f(c_f(y1, y2), z2)) -> c7(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(c_f(a, a), z0) -> c8(F(a, f(c_f(b, a), z0)), F(b, f(a, z0)), F(a, z0)) S tuples: F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) F(z0, c_f(z1, c_f(y1, y2))) -> c7(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1)) F(z0, c_f(c_f(y1, y2), z2)) -> c7(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(c_f(a, a), z0) -> c8(F(a, f(c_f(b, a), z0)), F(b, f(a, z0)), F(a, z0)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c2_2, c7_2, c7_1, c8_3, c8_2, c8_1, c_1 ---------------------------------------- (117) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(x0, c_f(c_f(x1, x2), x3)) -> c7(F(x0, c_f(x1, x2))) by F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c7(F(z0, c_f(c_f(y1, y2), z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), z2))) F(c_f(a, a), c_f(c_f(z1, z2), z3)) -> c7(F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c7(F(c_f(a, a), c_f(z1, c_f(y1, y2)))) F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c7(F(z0, c_f(z1, c_f(y2, y3)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(a, c_f(a, c_f(y0, c_f(y1, y2))))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2))) ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(b, x1), x2) -> c(F(f(b, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) F(z0, c_f(z1, c_f(y1, y2))) -> c7(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1)) F(z0, c_f(c_f(y1, y2), z2)) -> c7(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(c_f(a, a), z0) -> c8(F(a, f(c_f(b, a), z0)), F(b, f(a, z0)), F(a, z0)) F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c7(F(z0, c_f(c_f(y1, y2), z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), z2))) F(c_f(a, a), c_f(c_f(z1, z2), z3)) -> c7(F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c7(F(c_f(a, a), c_f(z1, c_f(y1, y2)))) F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c7(F(z0, c_f(z1, c_f(y2, y3)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(a, c_f(a, c_f(y0, c_f(y1, y2))))) S tuples: F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) F(z0, c_f(z1, c_f(y1, y2))) -> c7(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1)) F(z0, c_f(c_f(y1, y2), z2)) -> c7(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(c_f(a, a), z0) -> c8(F(a, f(c_f(b, a), z0)), F(b, f(a, z0)), F(a, z0)) F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c7(F(z0, c_f(c_f(y1, y2), z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), z2))) F(c_f(a, a), c_f(c_f(z1, z2), z3)) -> c7(F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c7(F(c_f(a, a), c_f(z1, c_f(y1, y2)))) F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c7(F(z0, c_f(z1, c_f(y2, y3)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(a, c_f(a, c_f(y0, c_f(y1, y2))))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c2_2, c7_2, c7_1, c8_3, c8_2, c8_1, c_1 ---------------------------------------- (119) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(z0, c_f(z1, c_f(y1, y2))) -> c7(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1)) by F(z0, c_f(z1, c_f(c_f(y1, y2), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(a, c_f(a, c_f(c_f(y0, y1), z3))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), z3)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(z2, z3))) -> c7(F(c_f(a, a), c_f(z2, z3)), F(a, a)) F(c_f(a, a), c_f(c_f(y0, y1), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), c_f(z2, z3)), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), z1), c_f(z2, z3)), F(c_f(a, a), z1)) F(a, c_f(a, c_f(z2, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(z2, c_f(y1, y2))), F(a, a)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) F(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z3)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3))) F(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z3)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, y1))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, y0), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, y0)), c_f(z2, z3)), F(a, c_f(a, y0))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) F(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))) F(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), y2)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, y1)), y2))) F(a, c_f(c_f(c_f(a, y0), y1), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, y0), y1)), c_f(z2, z3)), F(a, c_f(c_f(a, y0), y1))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2))) ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(b, x1), x2) -> c(F(f(b, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) F(z0, c_f(c_f(y1, y2), z2)) -> c7(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(c_f(a, a), z0) -> c8(F(a, f(c_f(b, a), z0)), F(b, f(a, z0)), F(a, z0)) F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c7(F(z0, c_f(c_f(y1, y2), z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), z2))) F(c_f(a, a), c_f(c_f(z1, z2), z3)) -> c7(F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c7(F(c_f(a, a), c_f(z1, c_f(y1, y2)))) F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c7(F(z0, c_f(z1, c_f(y2, y3)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(a, c_f(a, c_f(c_f(y0, y1), z3))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), z3)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(z2, z3))) -> c7(F(c_f(a, a), c_f(z2, z3)), F(a, a)) F(c_f(a, a), c_f(c_f(y0, y1), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), c_f(z2, z3)), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), z1), c_f(z2, z3)), F(c_f(a, a), z1)) F(a, c_f(a, c_f(z2, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(z2, c_f(y1, y2))), F(a, a)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) F(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z3)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3))) F(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z3)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, y1))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, y0), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, y0)), c_f(z2, z3)), F(a, c_f(a, y0))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) F(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))) F(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), y2)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, y1)), y2))) F(a, c_f(c_f(c_f(a, y0), y1), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, y0), y1)), c_f(z2, z3)), F(a, c_f(c_f(a, y0), y1))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3))) S tuples: F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) F(z0, c_f(c_f(y1, y2), z2)) -> c7(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(c_f(a, a), z0) -> c8(F(a, f(c_f(b, a), z0)), F(b, f(a, z0)), F(a, z0)) F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c7(F(z0, c_f(c_f(y1, y2), z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), z2))) F(c_f(a, a), c_f(c_f(z1, z2), z3)) -> c7(F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c7(F(c_f(a, a), c_f(z1, c_f(y1, y2)))) F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c7(F(z0, c_f(z1, c_f(y2, y3)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(a, c_f(a, c_f(c_f(y0, y1), z3))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), z3)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(z2, z3))) -> c7(F(c_f(a, a), c_f(z2, z3)), F(a, a)) F(c_f(a, a), c_f(c_f(y0, y1), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), c_f(z2, z3)), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), z1), c_f(z2, z3)), F(c_f(a, a), z1)) F(a, c_f(a, c_f(z2, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(z2, c_f(y1, y2))), F(a, a)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) F(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z3)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3))) F(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z3)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, y1))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, y0), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, y0)), c_f(z2, z3)), F(a, c_f(a, y0))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) F(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))) F(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)), F(a, a)) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), y2)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, y1)), y2))) F(a, c_f(c_f(c_f(a, y0), y1), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, y0), y1)), c_f(z2, z3)), F(a, c_f(c_f(a, y0), y1))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c2_2, c7_2, c7_1, c8_3, c8_2, c8_1, c_1 ---------------------------------------- (121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2))) ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(b, x1), x2) -> c(F(f(b, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) F(z0, c_f(c_f(y1, y2), z2)) -> c7(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(c_f(a, a), z0) -> c8(F(a, f(c_f(b, a), z0)), F(b, f(a, z0)), F(a, z0)) F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c7(F(z0, c_f(c_f(y1, y2), z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), z2))) F(c_f(a, a), c_f(c_f(z1, z2), z3)) -> c7(F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c7(F(c_f(a, a), c_f(z1, c_f(y1, y2)))) F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c7(F(z0, c_f(z1, c_f(y2, y3)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), c_f(z2, z3)), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), z1), c_f(z2, z3)), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, y1))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, y0), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, y0)), c_f(z2, z3)), F(a, c_f(a, y0))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), y2)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, y1)), y2))) F(a, c_f(c_f(c_f(a, y0), y1), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, y0), y1)), c_f(z2, z3)), F(a, c_f(c_f(a, y0), y1))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3))) F(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z3))) F(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z3))) F(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) F(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) S tuples: F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) F(z0, c_f(c_f(y1, y2), z2)) -> c7(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(c_f(a, a), z0) -> c8(F(a, f(c_f(b, a), z0)), F(b, f(a, z0)), F(a, z0)) F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c7(F(z0, c_f(c_f(y1, y2), z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), z2))) F(c_f(a, a), c_f(c_f(z1, z2), z3)) -> c7(F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c7(F(c_f(a, a), c_f(z1, c_f(y1, y2)))) F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c7(F(z0, c_f(z1, c_f(y2, y3)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), c_f(z2, z3)), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), z1), c_f(z2, z3)), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, y1))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, y0), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, y0)), c_f(z2, z3)), F(a, c_f(a, y0))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), y2)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, y1)), y2))) F(a, c_f(c_f(c_f(a, y0), y1), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, y0), y1)), c_f(z2, z3)), F(a, c_f(c_f(a, y0), y1))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3))) F(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z3))) F(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z3))) F(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) F(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c2_2, c7_2, c7_1, c8_3, c8_2, c8_1, c_1 ---------------------------------------- (123) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(z0, c_f(c_f(y1, y2), z2)) -> c7(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2))) by F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, y2), y3)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), z2)), z3), F(z0, c_f(c_f(y1, y2), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), z2)), z3), F(z0, c_f(c_f(y1, c_f(y2, y3)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), z2)), z3), F(z0, c_f(c_f(c_f(y1, y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), z2)), z3), F(c_f(a, a), c_f(c_f(y0, y1), z2))) F(c_f(a, a), c_f(c_f(z1, z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(z1, z2)), z3), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c7(F(c_f(c_f(a, a), c_f(z1, c_f(y1, y2))), z3), F(c_f(a, a), c_f(z1, c_f(y1, y2)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, y3), y4)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, y3), y4))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, y3), y4))), z3), F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)), z3), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)), z3), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, y1), y2))), z3), F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(c_f(a, c_f(a, c_f(y0, y1))), z3), F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(c_f(a, c_f(a, z2)), z3), F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(c_f(a, c_f(a, c_f(y0, c_f(y1, y2)))), z3), F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2)), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2)), z3), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z2)), z3), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z2))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), z2)), z3), F(a, c_f(c_f(a, c_f(y0, y1)), z2))) F(a, c_f(c_f(c_f(a, y0), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, y0), z2)), z3), F(a, c_f(c_f(a, y0), z2))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z2)), z3), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), z3), F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4))), z3), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), c_f(y2, y3))), z3), F(c_f(a, a), c_f(c_f(y0, y1), c_f(y2, y3)))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4))), z3), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(y3, y4))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(y3, y4)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(y3, y4))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(y3, y4)))), z3), F(z0, c_f(z1, c_f(y2, c_f(y3, y4))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), z3), F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5))), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5))), z3), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4))), z3), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4)))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3)), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3))), z3), F(a, c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3)))) F(a, c_f(c_f(c_f(a, y0), c_f(y1, y2)), z3)) -> c7(F(c_f(a, c_f(c_f(a, y0), c_f(y1, y2))), z3), F(a, c_f(c_f(a, y0), c_f(y1, y2)))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(y3, y4))), z3), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(y3, y4)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6))), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6))), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)))) F(a, c_f(c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5))), z3), F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)))) F(a, c_f(c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(y3, y4)), z3)) -> c7(F(c_f(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(y3, y4))), z3), F(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(y3, y4)))) F(a, c_f(c_f(c_f(c_f(a, y0), y1), c_f(y2, y3)), z3)) -> c7(F(c_f(a, c_f(c_f(c_f(a, y0), y1), c_f(y2, y3))), z3), F(a, c_f(c_f(c_f(a, y0), y1), c_f(y2, y3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5))), z3), F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)))) F(a, c_f(c_f(a, c_f(c_f(c_f(y0, y1), y2), y3)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), y3))), z3), F(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), y3)))) F(a, c_f(c_f(a, c_f(c_f(y0, c_f(y1, y2)), y3)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), y3))), z3), F(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), y3)))) F(a, c_f(c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))), z3), F(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)))) F(a, c_f(c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))), z3), F(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2))) ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(b, x1), x2) -> c(F(f(b, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(c_f(a, a), z0) -> c8(F(a, f(c_f(b, a), z0)), F(b, f(a, z0)), F(a, z0)) F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c7(F(z0, c_f(c_f(y1, y2), z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), z2))) F(c_f(a, a), c_f(c_f(z1, z2), z3)) -> c7(F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c7(F(c_f(a, a), c_f(z1, c_f(y1, y2)))) F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c7(F(z0, c_f(z1, c_f(y2, y3)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), c_f(z2, z3)), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), z1), c_f(z2, z3)), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, y1))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, y0), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, y0)), c_f(z2, z3)), F(a, c_f(a, y0))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), y2)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, y1)), y2))) F(a, c_f(c_f(c_f(a, y0), y1), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, y0), y1)), c_f(z2, z3)), F(a, c_f(c_f(a, y0), y1))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3))) F(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z3))) F(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z3))) F(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) F(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, y2), y3)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, y3), y4)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, y3), y4))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, y3), y4))), z3), F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)), z3), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)), z3), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, y1), y2))), z3), F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(c_f(a, c_f(a, c_f(y0, y1))), z3), F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(c_f(a, c_f(a, z2)), z3), F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(c_f(a, c_f(a, c_f(y0, c_f(y1, y2)))), z3), F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2)), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2)), z3), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z2)), z3), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z2))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), z2)), z3), F(a, c_f(c_f(a, c_f(y0, y1)), z2))) F(a, c_f(c_f(c_f(a, y0), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, y0), z2)), z3), F(a, c_f(c_f(a, y0), z2))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z2)), z3), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), z3), F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4))), z3), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), c_f(y2, y3))), z3), F(c_f(a, a), c_f(c_f(y0, y1), c_f(y2, y3)))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4))), z3), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(y3, y4))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(y3, y4)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(y3, y4))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(y3, y4)))), z3), F(z0, c_f(z1, c_f(y2, c_f(y3, y4))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), z3), F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5))), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5))), z3), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4))), z3), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4)))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3)), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3))), z3), F(a, c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3)))) F(a, c_f(c_f(c_f(a, y0), c_f(y1, y2)), z3)) -> c7(F(c_f(a, c_f(c_f(a, y0), c_f(y1, y2))), z3), F(a, c_f(c_f(a, y0), c_f(y1, y2)))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(y3, y4))), z3), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(y3, y4)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6))), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6))), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)))) F(a, c_f(c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5))), z3), F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)))) F(a, c_f(c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(y3, y4)), z3)) -> c7(F(c_f(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(y3, y4))), z3), F(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(y3, y4)))) F(a, c_f(c_f(c_f(c_f(a, y0), y1), c_f(y2, y3)), z3)) -> c7(F(c_f(a, c_f(c_f(c_f(a, y0), y1), c_f(y2, y3))), z3), F(a, c_f(c_f(c_f(a, y0), y1), c_f(y2, y3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5))), z3), F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)))) F(a, c_f(c_f(a, c_f(c_f(c_f(y0, y1), y2), y3)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), y3))), z3), F(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), y3)))) F(a, c_f(c_f(a, c_f(c_f(y0, c_f(y1, y2)), y3)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), y3))), z3), F(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), y3)))) F(a, c_f(c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))), z3), F(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)))) F(a, c_f(c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))), z3), F(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)))) S tuples: F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(c_f(a, a), z0) -> c8(F(a, f(c_f(b, a), z0)), F(b, f(a, z0)), F(a, z0)) F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c7(F(z0, c_f(c_f(y1, y2), z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), z2))) F(c_f(a, a), c_f(c_f(z1, z2), z3)) -> c7(F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c7(F(c_f(a, a), c_f(z1, c_f(y1, y2)))) F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c7(F(z0, c_f(z1, c_f(y2, y3)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), c_f(z2, z3)), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), z1), c_f(z2, z3)), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, y1))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, y0), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, y0)), c_f(z2, z3)), F(a, c_f(a, y0))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), y2)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, y1)), y2))) F(a, c_f(c_f(c_f(a, y0), y1), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, y0), y1)), c_f(z2, z3)), F(a, c_f(c_f(a, y0), y1))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3))) F(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z3))) F(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z3))) F(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) F(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, y2), y3)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, y3), y4)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, y3), y4))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, y3), y4))), z3), F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)), z3), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)), z3), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, y1), y2))), z3), F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(c_f(a, c_f(a, c_f(y0, y1))), z3), F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(c_f(a, c_f(a, z2)), z3), F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(c_f(a, c_f(a, c_f(y0, c_f(y1, y2)))), z3), F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2)), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2)), z3), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z2)), z3), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z2))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), z2)), z3), F(a, c_f(c_f(a, c_f(y0, y1)), z2))) F(a, c_f(c_f(c_f(a, y0), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, y0), z2)), z3), F(a, c_f(c_f(a, y0), z2))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z2)), z3), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), z3), F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4))), z3), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), c_f(y2, y3))), z3), F(c_f(a, a), c_f(c_f(y0, y1), c_f(y2, y3)))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4))), z3), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(y3, y4))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(y3, y4)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(y3, y4))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(y3, y4)))), z3), F(z0, c_f(z1, c_f(y2, c_f(y3, y4))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), z3), F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5))), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5))), z3), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4))), z3), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4)))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3)), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3))), z3), F(a, c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3)))) F(a, c_f(c_f(c_f(a, y0), c_f(y1, y2)), z3)) -> c7(F(c_f(a, c_f(c_f(a, y0), c_f(y1, y2))), z3), F(a, c_f(c_f(a, y0), c_f(y1, y2)))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(y3, y4))), z3), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(y3, y4)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6))), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6))), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)))) F(a, c_f(c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5))), z3), F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)))) F(a, c_f(c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(y3, y4)), z3)) -> c7(F(c_f(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(y3, y4))), z3), F(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(y3, y4)))) F(a, c_f(c_f(c_f(c_f(a, y0), y1), c_f(y2, y3)), z3)) -> c7(F(c_f(a, c_f(c_f(c_f(a, y0), y1), c_f(y2, y3))), z3), F(a, c_f(c_f(c_f(a, y0), y1), c_f(y2, y3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5))), z3), F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)))) F(a, c_f(c_f(a, c_f(c_f(c_f(y0, y1), y2), y3)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), y3))), z3), F(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), y3)))) F(a, c_f(c_f(a, c_f(c_f(y0, c_f(y1, y2)), y3)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), y3))), z3), F(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), y3)))) F(a, c_f(c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))), z3), F(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)))) F(a, c_f(c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))), z3), F(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c2_2, c7_2, c7_1, c8_3, c8_2, c8_1, c_1 ---------------------------------------- (125) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c7(F(z0, c_f(z1, c_f(y2, y3)))) by F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(z1, c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(z1, c_f(z2, z3)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), z3)), z4)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, y3), z3)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), z3)), z4)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), z3)))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3)))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), z3)), z4)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), z3)))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3)))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), z3)), z4)) -> c7(F(a, c_f(a, c_f(c_f(y0, y1), z3)))) F(a, c_f(c_f(a, c_f(z2, z3)), z4)) -> c7(F(a, c_f(a, c_f(z2, z3)))) F(a, c_f(c_f(a, c_f(z2, c_f(y1, y2))), z4)) -> c7(F(a, c_f(a, c_f(z2, c_f(y1, y2))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(y0, y1)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, y0), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, y0), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(z2, z3)))) F(z0, c_f(c_f(z1, c_f(z2, c_f(y3, y4))), z4)) -> c7(F(z0, c_f(z1, c_f(z2, c_f(y3, y4))))) F(z0, c_f(c_f(z1, c_f(z2, c_f(c_f(y3, y4), y5))), z4)) -> c7(F(z0, c_f(z1, c_f(z2, c_f(c_f(y3, y4), y5))))) F(z0, c_f(c_f(z1, c_f(z2, c_f(c_f(y3, c_f(y4, y5)), y6))), z4)) -> c7(F(z0, c_f(z1, c_f(z2, c_f(c_f(y3, c_f(y4, y5)), y6))))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), z3)), z4)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), z3)))) F(z0, c_f(c_f(z1, c_f(z2, c_f(c_f(c_f(y3, y4), y5), y6))), z4)) -> c7(F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y3, y4), y5), y6))))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), z3)), z4)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), z3)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), z3)), z4)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), z3)))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), z3)), z4)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), z3)))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3)))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), z3)), z4)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), z3)))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), z3)), z4)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), z3)))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3)))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), z3)), z4)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), z3)))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, y0), y1), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, y0), y1), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3)))) F(a, c_f(c_f(a, c_f(c_f(c_f(y0, y1), y2), z3)), z4)) -> c7(F(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), z3)))) F(a, c_f(c_f(a, c_f(c_f(y0, c_f(y1, y2)), z3)), z4)) -> c7(F(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), z3)))) F(a, c_f(c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)), z4)) -> c7(F(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)))) F(a, c_f(c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)), z4)) -> c7(F(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, y4), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, y4), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, y5), y6))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, y5), y6))))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(y5, y6)), y7))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(y5, y6)), y7))))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, y5), y6), y7))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, y5), y6), y7))))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), c_f(y6, y7))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), c_f(y6, y7))))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), c_f(y7, y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), c_f(y7, y8))))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), c_f(y7, y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), c_f(y7, y8))))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(y5, y6)))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(y5, y6)))))) F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(y3, y4))), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, c_f(y3, y4))), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), c_f(y6, y7))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), c_f(y6, y7))))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, y6), y7)))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, y6), y7)))))) F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), c_f(y7, y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), c_f(y7, y8))))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)))))) F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), c_f(y8, y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), c_f(y8, y9))))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), c_f(y8, y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), c_f(y8, y9))))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)))))) F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), c_f(y8, y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), c_f(y8, y9))))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), c_f(y8, y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), c_f(y8, y9))))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, y0), c_f(y1, y2)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, y0), c_f(y1, y2)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, y6), y7)), y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, y6), y7)), y8))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, y5), y6)), y7), c_f(y8, y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, y5), y6)), y7), c_f(y8, y9))))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)), y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)), y9))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), y8), c_f(y9, y10))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), y8), c_f(y9, y10))))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8), y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8), y9))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), y8), c_f(y9, y10))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), y8), c_f(y9, y10))))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)), y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)), y9))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), y8), c_f(y9, y10))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), y8), c_f(y9, y10))))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8), y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8), y9))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), y8), c_f(y9, y10))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), y8), c_f(y9, y10))))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(y3, y4)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(c_f(a, y0), y1), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(c_f(a, y0), y1), c_f(y2, y3)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)))) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(z0, z1) -> c_f(z0, z1) f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2) f(c_f(a, a), z0) -> f(a, f(b, f(a, z0))) Tuples: ENCARG(cons_f(x0, cons_f(x1, x2))) -> c2(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), x2)) -> c2(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) ENCODE_F(cons_f(z0, z1), a) -> c(F(f(encArg(z0), encArg(z1)), a)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2))) ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(b, x1), x2) -> c(F(f(b, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(c_f(a, a), z0) -> c8(F(a, f(c_f(b, a), z0)), F(b, f(a, z0)), F(a, z0)) F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c7(F(z0, c_f(c_f(y1, y2), z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), z2))) F(c_f(a, a), c_f(c_f(z1, z2), z3)) -> c7(F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c7(F(c_f(a, a), c_f(z1, c_f(y1, y2)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), c_f(z2, z3)), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), z1), c_f(z2, z3)), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, y1))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, y0), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, y0)), c_f(z2, z3)), F(a, c_f(a, y0))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), y2)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, y1)), y2))) F(a, c_f(c_f(c_f(a, y0), y1), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, y0), y1)), c_f(z2, z3)), F(a, c_f(c_f(a, y0), y1))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3))) F(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z3))) F(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z3))) F(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) F(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, y2), y3)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, y3), y4)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, y3), y4))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, y3), y4))), z3), F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)), z3), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)), z3), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, y1), y2))), z3), F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(c_f(a, c_f(a, c_f(y0, y1))), z3), F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(c_f(a, c_f(a, z2)), z3), F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(c_f(a, c_f(a, c_f(y0, c_f(y1, y2)))), z3), F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2)), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2)), z3), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z2)), z3), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z2))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), z2), z3)) -> c7(F(c_f(a, 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y4), c_f(y5, y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4))), z3), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), c_f(y2, y3))), z3), F(c_f(a, a), c_f(c_f(y0, y1), c_f(y2, y3)))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4))), z3), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(y3, y4))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(y3, y4)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(y3, y4))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(y3, y4)))), z3), F(z0, c_f(z1, c_f(y2, c_f(y3, y4))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), z3), F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5))), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5))), z3), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4))), z3), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4)))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3)), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), 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c_f(z2, z3)))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(y0, y1)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, y0), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, y0), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(z2, z3)))) F(z0, c_f(c_f(z1, c_f(z2, c_f(y3, y4))), z4)) -> c7(F(z0, c_f(z1, c_f(z2, c_f(y3, y4))))) F(z0, c_f(c_f(z1, c_f(z2, c_f(c_f(y3, 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z3)))) F(a, c_f(c_f(a, c_f(c_f(y0, c_f(y1, y2)), z3)), z4)) -> c7(F(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), z3)))) F(a, c_f(c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)), z4)) -> c7(F(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)))) F(a, c_f(c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)), z4)) -> c7(F(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, y4), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, y4), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, y5), y6))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, y5), y6))))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(y5, y6)), y7))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(y5, y6)), y7))))) F(z0, 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y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), c_f(y6, y7))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), c_f(y6, y7))))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), c_f(y7, y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), c_f(y7, y8))))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), c_f(y7, y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), c_f(y7, y8))))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(y5, y6)))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(y5, y6)))))) F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(y3, y4))), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, c_f(y3, y4))), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), c_f(y6, y7))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), c_f(y6, y7))))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, y6), y7)))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, y6), y7)))))) F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), c_f(y7, y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), c_f(y7, y8))))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)))))) F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), c_f(y8, y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), c_f(y8, y9))))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), c_f(y8, y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), c_f(y8, y9))))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, 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c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), c_f(y8, y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), c_f(y8, y9))))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, y0), c_f(y1, y2)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, y0), c_f(y1, y2)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, y6), y7)), y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, y6), y7)), y8))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, y5), y6)), y7), c_f(y8, y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, y5), y6)), y7), c_f(y8, y9))))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)), y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)), y9))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), y8), c_f(y9, y10))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), y8), c_f(y9, y10))))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8), y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8), y9))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), y8), c_f(y9, y10))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), y8), c_f(y9, y10))))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)), y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)), y9))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), y8), c_f(y9, y10))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), y8), c_f(y9, y10))))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8), y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8), y9))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), y8), c_f(y9, y10))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), y8), c_f(y9, y10))))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(y3, y4)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(c_f(a, y0), y1), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(c_f(a, y0), y1), c_f(y2, y3)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)))) S tuples: F(x0, c_f(c_f(x1, z1), x3)) -> c7(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1))) F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c7(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2)))) F(z0, c_f(c_f(z1, x2), x3)) -> c7(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2))) F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c7(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2))) F(c_f(a, a), c_f(c_f(z0, x2), x3)) -> c7(F(f(f(a, f(b, f(a, z0))), x2), x3), F(c_f(a, a), c_f(z0, x2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(x0, x1)) -> c7(F(f(a, c_f(b, f(a, x0))), x1), F(c_f(a, a), x0)) F(c_f(a, a), c_f(z1, x1)) -> c7(F(f(a, f(b, c_f(a, z1))), x1), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c7(F(f(a, f(b, f(f(a, z1), z2))), x1), F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(x0, x1)) -> c7(F(c_f(a, a), x0)) F(c_f(a, a), z1) -> c8(F(a, c_f(b, c_f(a, z1))), F(b, f(a, z1)), F(a, z1)) F(c_f(a, a), c_f(z1, z2)) -> c8(F(a, c_f(b, f(f(a, z1), z2))), F(b, f(a, c_f(z1, z2))), F(a, c_f(z1, z2))) F(c_f(a, a), x0) -> c8(F(b, f(a, x0)), F(a, x0)) F(c_f(a, a), c_f(x0, z1)) -> c8(F(a, f(b, c_f(f(a, x0), z1))), F(b, f(a, c_f(x0, z1))), F(a, c_f(x0, z1))) F(c_f(a, a), c_f(x0, c_f(z1, z2))) -> c8(F(a, f(b, f(f(f(a, x0), z1), z2))), F(b, f(a, c_f(x0, c_f(z1, z2)))), F(a, c_f(x0, c_f(z1, z2)))) F(c_f(a, a), c_f(z1, x1)) -> c8(F(a, f(b, f(c_f(a, z1), x1))), F(b, f(a, c_f(z1, x1))), F(a, c_f(z1, x1))) F(c_f(a, a), c_f(c_f(z1, z2), x1)) -> c8(F(a, f(b, f(f(f(a, z1), z2), x1))), F(b, f(a, c_f(c_f(z1, z2), x1))), F(a, c_f(c_f(z1, z2), x1))) F(c_f(a, a), c_f(x0, x1)) -> c8(F(b, f(a, c_f(x0, x1)))) F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), z2), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), z2), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, z2)) -> c7(F(c_f(c_f(a, a), z1), z2), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), z2), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(a, c_f(a, c_f(c_f(y0, y1), y2))) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(a, c_f(a, c_f(y0, y1))) -> c7(F(c_f(a, a), c_f(y0, y1))) F(a, c_f(a, z2)) -> c7(F(c_f(a, a), z2)) F(a, c_f(a, c_f(y0, c_f(y1, y2)))) -> c7(F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(c_f(a, a), z0) -> c8(F(a, f(c_f(b, a), z0)), F(b, f(a, z0)), F(a, z0)) F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c7(F(z0, c_f(c_f(y1, y2), z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, y1), z2))) F(c_f(a, a), c_f(c_f(z1, z2), z3)) -> c7(F(c_f(a, a), c_f(z1, z2))) F(c_f(a, a), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c7(F(c_f(a, a), c_f(z1, c_f(y1, y2)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, y1), y2))) F(c_f(a, a), c_f(c_f(y0, y1), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, y1)), c_f(z2, z3)), F(c_f(a, a), c_f(y0, y1))) F(c_f(a, a), c_f(z1, c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), z1), c_f(z2, z3)), F(c_f(a, a), z1)) F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(a, a), c_f(y0, c_f(y1, y2)))) F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c7(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1)) F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), y3))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), y3))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, y1))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, y0), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, y0)), c_f(z2, z3)), F(a, c_f(a, y0))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c7(F(c_f(a, c_f(a, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c7(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1)) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), y2)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, y1)), y2))) F(a, c_f(c_f(c_f(a, y0), y1), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, y0), y1)), c_f(z2, z3)), F(a, c_f(c_f(a, y0), y1))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3))) F(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z3))) F(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c7(F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z3))) F(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) F(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, y2), y3))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, y2), y3)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), y4))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), y4))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, y3), y4)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, y3), y4))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, y3), y4))), z3), F(z0, c_f(z1, c_f(c_f(y2, y3), y4)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2)), z3), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), z2))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2)), z3), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), z2))) F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z3)) -> c7(F(c_f(a, c_f(a, c_f(c_f(y0, y1), y2))), z3), F(a, c_f(a, c_f(c_f(y0, y1), y2)))) F(a, c_f(c_f(a, c_f(y0, y1)), z3)) -> c7(F(c_f(a, c_f(a, c_f(y0, y1))), z3), F(a, c_f(a, c_f(y0, y1)))) F(a, c_f(c_f(a, z2), z3)) -> c7(F(c_f(a, c_f(a, z2)), z3), F(a, c_f(a, z2))) F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z3)) -> c7(F(c_f(a, c_f(a, c_f(y0, c_f(y1, y2)))), z3), F(a, c_f(a, c_f(y0, c_f(y1, y2))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2)), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2)), z3), F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z2)), z3), F(a, c_f(c_f(a, c_f(c_f(y0, y1), y2)), z2))) F(a, c_f(c_f(c_f(a, c_f(y0, y1)), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, y1)), z2)), z3), F(a, c_f(c_f(a, c_f(y0, y1)), z2))) F(a, c_f(c_f(c_f(a, y0), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, y0), z2)), z3), F(a, c_f(c_f(a, y0), z2))) F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), z2), z3)) -> c7(F(c_f(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z2)), z3), F(a, c_f(c_f(a, c_f(y0, c_f(y1, y2))), z2))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), z3), F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4))), z3), F(c_f(a, a), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)))) F(c_f(a, a), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, y1), c_f(y2, y3))), z3), F(c_f(a, a), c_f(c_f(y0, y1), c_f(y2, y3)))) F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4))), z3), F(c_f(a, a), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(y3, y4))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(y3, y4)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(y3, y4))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(y3, y4)))), z3), F(z0, c_f(z1, c_f(y2, c_f(y3, y4))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), z3), F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))))) F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)))) F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), z3)) -> c7(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)))) F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)))) -> c7(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), z3)) -> c7(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5))), z3), F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), z3)) -> c7(F(c_f(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5))), z3), F(c_f(a, a), c_f(c_f(c_f(y0, 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y0), y1), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, y0), y1), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3)))) F(a, c_f(c_f(a, c_f(c_f(c_f(y0, y1), y2), z3)), z4)) -> c7(F(a, c_f(a, c_f(c_f(c_f(y0, y1), y2), z3)))) F(a, c_f(c_f(a, c_f(c_f(y0, c_f(y1, y2)), z3)), z4)) -> c7(F(a, c_f(a, c_f(c_f(y0, c_f(y1, y2)), z3)))) F(a, c_f(c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)), z4)) -> c7(F(a, c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)))) F(a, c_f(c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)), z4)) -> c7(F(a, c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, y4), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, y4), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, y5), y6))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, y5), y6))))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(y5, y6)), y7))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(y5, y6)), y7))))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, y5), y6), y7))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, y5), y6), y7))))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), z3)), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), c_f(y6, y7))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), c_f(y6, y7))))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), c_f(y7, y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), c_f(y7, y8))))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), c_f(y7, y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), c_f(y7, y8))))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, y1), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(y5, y6)))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(y5, y6)))))) F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(y3, y4))), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, c_f(y3, y4))), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), c_f(y6, y7))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), c_f(y6, y7))))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, y6), y7)))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, y6), y7)))))) F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), c_f(y7, y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), c_f(y7, y8))))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)))))) F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), c_f(y8, y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), c_f(y8, y9))))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), c_f(y8, y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), c_f(y8, y9))))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)))))) F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), c_f(y8, y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), c_f(y8, y9))))) F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), c_f(y8, y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), c_f(y8, y9))))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, c_f(y0, y1)), c_f(y2, y3)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, y0), c_f(y1, y2)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, y0), c_f(y1, y2)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, y6), y7)), y8))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, y6), y7)), y8))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, y5), y6)), y7), c_f(y8, y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, y5), y6)), y7), c_f(y8, y9))))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)), y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)), y9))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), y8), c_f(y9, y10))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), y8), c_f(y9, y10))))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8), y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8), y9))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), y8), c_f(y9, y10))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), y8), c_f(y9, y10))))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)), y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)), y9))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), y8), c_f(y9, y10))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), y8), c_f(y9, y10))))) F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8), y9))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8), y9))))) F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), c_f(z2, z3)))) F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), y8), c_f(y9, y10))), z4)) -> c7(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), y8), c_f(y9, y10))))) F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c7(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)))) F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c7(F(c_f(a, a), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(c_f(a, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(c_f(a, c_f(y0, y1)), y2), c_f(y3, y4)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(c_f(a, y0), y1), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(c_f(a, y0), y1), c_f(y2, y3)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(c_f(c_f(a, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)))) F(a, c_f(c_f(c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), z4)) -> c7(F(a, c_f(c_f(a, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c2_2, c7_2, c7_1, c8_3, c8_2, c8_1, c_1