/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 176 ms] (4) CpxRelTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxWeightedTrs (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxTypedWeightedTrs (11) CompletionProof [UPPER BOUND(ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) CompleteCoflocoProof [FINISHED, 34.9 s] (16) BOUNDS(1, n^3) (17) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRelTRS (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (20) typed CpxTrs (21) OrderProof [LOWER BOUND(ID), 0 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 306 ms] (24) BEST (25) proven lower bound (26) LowerBoundPropagationProof [FINISHED, 0 ms] (27) BOUNDS(n^1, INF) (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 85 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 36 ms] (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 16 ms] (34) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: min(x, 0) -> 0 min(0, y) -> 0 min(s(x), s(y)) -> s(min(x, y)) max(x, 0) -> x max(0, y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0) -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_max(x_1, x_2)) -> max(encArg(x_1), encArg(x_2)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_max(x_1, x_2) -> max(encArg(x_1), encArg(x_2)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: min(x, 0) -> 0 min(0, y) -> 0 min(s(x), s(y)) -> s(min(x, y)) max(x, 0) -> x max(0, y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0) -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_max(x_1, x_2)) -> max(encArg(x_1), encArg(x_2)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_max(x_1, x_2) -> max(encArg(x_1), encArg(x_2)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: min(x, 0) -> 0 min(0, y) -> 0 min(s(x), s(y)) -> s(min(x, y)) max(x, 0) -> x max(0, y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0) -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_max(x_1, x_2)) -> max(encArg(x_1), encArg(x_2)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_max(x_1, x_2) -> max(encArg(x_1), encArg(x_2)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). The TRS R consists of the following rules: min(x, 0) -> 0 [1] min(0, y) -> 0 [1] min(s(x), s(y)) -> s(min(x, y)) [1] max(x, 0) -> x [1] max(0, y) -> y [1] max(s(x), s(y)) -> s(max(x, y)) [1] -(x, 0) -> x [1] -(s(x), s(y)) -> -(x, y) [1] gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) [0] encArg(cons_max(x_1, x_2)) -> max(encArg(x_1), encArg(x_2)) [0] encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) [0] encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) [0] encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_max(x_1, x_2) -> max(encArg(x_1), encArg(x_2)) [0] encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) [0] encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (7) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) Renamed defined symbols to avoid conflicts with arithmetic symbols: - => minus ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). The TRS R consists of the following rules: min(x, 0) -> 0 [1] min(0, y) -> 0 [1] min(s(x), s(y)) -> s(min(x, y)) [1] max(x, 0) -> x [1] max(0, y) -> y [1] max(s(x), s(y)) -> s(max(x, y)) [1] minus(x, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] gcd(s(x), s(y)) -> gcd(minus(s(max(x, y)), s(min(x, y))), s(min(x, y))) [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) [0] encArg(cons_max(x_1, x_2)) -> max(encArg(x_1), encArg(x_2)) [0] encArg(cons_-(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) [0] encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_max(x_1, x_2) -> max(encArg(x_1), encArg(x_2)) [0] encode_-(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: min(x, 0) -> 0 [1] min(0, y) -> 0 [1] min(s(x), s(y)) -> s(min(x, y)) [1] max(x, 0) -> x [1] max(0, y) -> y [1] max(s(x), s(y)) -> s(max(x, y)) [1] minus(x, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] gcd(s(x), s(y)) -> gcd(minus(s(max(x, y)), s(min(x, y))), s(min(x, y))) [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) [0] encArg(cons_max(x_1, x_2)) -> max(encArg(x_1), encArg(x_2)) [0] encArg(cons_-(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) [0] encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_max(x_1, x_2) -> max(encArg(x_1), encArg(x_2)) [0] encode_-(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) [0] The TRS has the following type information: min :: 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd 0 :: 0:s:cons_min:cons_max:cons_-:cons_gcd s :: 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd max :: 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd minus :: 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd gcd :: 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd encArg :: 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd cons_min :: 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd cons_max :: 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd cons_- :: 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd cons_gcd :: 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd encode_min :: 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd encode_0 :: 0:s:cons_min:cons_max:cons_-:cons_gcd encode_s :: 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd encode_max :: 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd encode_- :: 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd encode_gcd :: 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd Rewrite Strategy: INNERMOST ---------------------------------------- (11) 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_min(v0, v1) -> null_encode_min [0] encode_0 -> null_encode_0 [0] encode_s(v0) -> null_encode_s [0] encode_max(v0, v1) -> null_encode_max [0] encode_-(v0, v1) -> null_encode_- [0] encode_gcd(v0, v1) -> null_encode_gcd [0] min(v0, v1) -> null_min [0] max(v0, v1) -> null_max [0] minus(v0, v1) -> null_minus [0] gcd(v0, v1) -> null_gcd [0] And the following fresh constants: null_encArg, null_encode_min, null_encode_0, null_encode_s, null_encode_max, null_encode_-, null_encode_gcd, null_min, null_max, null_minus, null_gcd ---------------------------------------- (12) 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: min(x, 0) -> 0 [1] min(0, y) -> 0 [1] min(s(x), s(y)) -> s(min(x, y)) [1] max(x, 0) -> x [1] max(0, y) -> y [1] max(s(x), s(y)) -> s(max(x, y)) [1] minus(x, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] gcd(s(x), s(y)) -> gcd(minus(s(max(x, y)), s(min(x, y))), s(min(x, y))) [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) [0] encArg(cons_max(x_1, x_2)) -> max(encArg(x_1), encArg(x_2)) [0] encArg(cons_-(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) [0] encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_max(x_1, x_2) -> max(encArg(x_1), encArg(x_2)) [0] encode_-(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) [0] encArg(v0) -> null_encArg [0] encode_min(v0, v1) -> null_encode_min [0] encode_0 -> null_encode_0 [0] encode_s(v0) -> null_encode_s [0] encode_max(v0, v1) -> null_encode_max [0] encode_-(v0, v1) -> null_encode_- [0] encode_gcd(v0, v1) -> null_encode_gcd [0] min(v0, v1) -> null_min [0] max(v0, v1) -> null_max [0] minus(v0, v1) -> null_minus [0] gcd(v0, v1) -> null_gcd [0] The TRS has the following type information: min :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd 0 :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd s :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd max :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd minus :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd gcd :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd encArg :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd cons_min :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd cons_max :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd cons_- :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd cons_gcd :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd encode_min :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd encode_0 :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd encode_s :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd encode_max :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd encode_- :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd encode_gcd :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd -> 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd null_encArg :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd null_encode_min :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd null_encode_0 :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd null_encode_s :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd null_encode_max :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd null_encode_- :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd null_encode_gcd :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd null_min :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd null_max :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd null_minus :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd null_gcd :: 0:s:cons_min:cons_max:cons_-:cons_gcd:null_encArg:null_encode_min:null_encode_0:null_encode_s:null_encode_max:null_encode_-:null_encode_gcd:null_min:null_max:null_minus:null_gcd Rewrite Strategy: INNERMOST ---------------------------------------- (13) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 null_encArg => 0 null_encode_min => 0 null_encode_0 => 0 null_encode_s => 0 null_encode_max => 0 null_encode_- => 0 null_encode_gcd => 0 null_min => 0 null_max => 0 null_minus => 0 null_gcd => 0 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: encArg(z) -{ 0 }-> minus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> min(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> max(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> gcd(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0 encode_-(z, z') -{ 0 }-> minus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_-(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_0 -{ 0 }-> 0 :|: encode_gcd(z, z') -{ 0 }-> gcd(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_gcd(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_max(z, z') -{ 0 }-> max(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_max(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_min(z, z') -{ 0 }-> min(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_min(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_s(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 gcd(z, z') -{ 1 }-> gcd(minus(1 + max(x, y), 1 + min(x, y)), 1 + min(x, y)) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x gcd(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 max(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0 max(z, z') -{ 1 }-> y :|: y >= 0, z = 0, z' = y max(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 max(z, z') -{ 1 }-> 1 + max(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x min(z, z') -{ 1 }-> 0 :|: x >= 0, z = x, z' = 0 min(z, z') -{ 1 }-> 0 :|: y >= 0, z = 0, z' = y min(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 min(z, z') -{ 1 }-> 1 + min(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x minus(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0 minus(z, z') -{ 1 }-> minus(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (15) CompleteCoflocoProof (FINISHED) Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: eq(start(V1, V),0,[min(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V),0,[max(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V),0,[minus(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V),0,[gcd(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V),0,[encArg(V1, Out)],[V1 >= 0]). eq(start(V1, V),0,[fun(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V),0,[fun1(Out)],[]). eq(start(V1, V),0,[fun2(V1, Out)],[V1 >= 0]). eq(start(V1, V),0,[fun3(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V),0,[fun4(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V),0,[fun5(V1, V, Out)],[V1 >= 0,V >= 0]). eq(min(V1, V, Out),1,[],[Out = 0,V2 >= 0,V1 = V2,V = 0]). eq(min(V1, V, Out),1,[],[Out = 0,V3 >= 0,V1 = 0,V = V3]). eq(min(V1, V, Out),1,[min(V4, V5, Ret1)],[Out = 1 + Ret1,V = 1 + V5,V4 >= 0,V5 >= 0,V1 = 1 + V4]). eq(max(V1, V, Out),1,[],[Out = V6,V6 >= 0,V1 = V6,V = 0]). eq(max(V1, V, Out),1,[],[Out = V7,V7 >= 0,V1 = 0,V = V7]). eq(max(V1, V, Out),1,[max(V8, V9, Ret11)],[Out = 1 + Ret11,V = 1 + V9,V8 >= 0,V9 >= 0,V1 = 1 + V8]). eq(minus(V1, V, Out),1,[],[Out = V10,V10 >= 0,V1 = V10,V = 0]). eq(minus(V1, V, Out),1,[minus(V12, V11, Ret)],[Out = Ret,V = 1 + V11,V12 >= 0,V11 >= 0,V1 = 1 + V12]). eq(gcd(V1, V, Out),1,[max(V14, V13, Ret001),min(V14, V13, Ret011),minus(1 + Ret001, 1 + Ret011, Ret0),min(V14, V13, Ret111),gcd(Ret0, 1 + Ret111, Ret2)],[Out = Ret2,V = 1 + V13,V14 >= 0,V13 >= 0,V1 = 1 + V14]). eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]). eq(encArg(V1, Out),0,[encArg(V15, Ret12)],[Out = 1 + Ret12,V1 = 1 + V15,V15 >= 0]). eq(encArg(V1, Out),0,[encArg(V16, Ret01),encArg(V17, Ret13),min(Ret01, Ret13, Ret3)],[Out = Ret3,V16 >= 0,V1 = 1 + V16 + V17,V17 >= 0]). eq(encArg(V1, Out),0,[encArg(V18, Ret02),encArg(V19, Ret14),max(Ret02, Ret14, Ret4)],[Out = Ret4,V18 >= 0,V1 = 1 + V18 + V19,V19 >= 0]). eq(encArg(V1, Out),0,[encArg(V21, Ret03),encArg(V20, Ret15),minus(Ret03, Ret15, Ret5)],[Out = Ret5,V21 >= 0,V1 = 1 + V20 + V21,V20 >= 0]). eq(encArg(V1, Out),0,[encArg(V23, Ret04),encArg(V22, Ret16),gcd(Ret04, Ret16, Ret6)],[Out = Ret6,V23 >= 0,V1 = 1 + V22 + V23,V22 >= 0]). eq(fun(V1, V, Out),0,[encArg(V24, Ret05),encArg(V25, Ret17),min(Ret05, Ret17, Ret7)],[Out = Ret7,V24 >= 0,V25 >= 0,V1 = V24,V = V25]). eq(fun1(Out),0,[],[Out = 0]). eq(fun2(V1, Out),0,[encArg(V26, Ret18)],[Out = 1 + Ret18,V26 >= 0,V1 = V26]). eq(fun3(V1, V, Out),0,[encArg(V28, Ret06),encArg(V27, Ret19),max(Ret06, Ret19, Ret8)],[Out = Ret8,V28 >= 0,V27 >= 0,V1 = V28,V = V27]). eq(fun4(V1, V, Out),0,[encArg(V30, Ret07),encArg(V29, Ret110),minus(Ret07, Ret110, Ret9)],[Out = Ret9,V30 >= 0,V29 >= 0,V1 = V30,V = V29]). eq(fun5(V1, V, Out),0,[encArg(V31, Ret08),encArg(V32, Ret112),gcd(Ret08, Ret112, Ret10)],[Out = Ret10,V31 >= 0,V32 >= 0,V1 = V31,V = V32]). eq(encArg(V1, Out),0,[],[Out = 0,V33 >= 0,V1 = V33]). eq(fun(V1, V, Out),0,[],[Out = 0,V35 >= 0,V34 >= 0,V1 = V35,V = V34]). eq(fun2(V1, Out),0,[],[Out = 0,V36 >= 0,V1 = V36]). eq(fun3(V1, V, Out),0,[],[Out = 0,V37 >= 0,V38 >= 0,V1 = V37,V = V38]). eq(fun4(V1, V, Out),0,[],[Out = 0,V39 >= 0,V40 >= 0,V1 = V39,V = V40]). eq(fun5(V1, V, Out),0,[],[Out = 0,V41 >= 0,V42 >= 0,V1 = V41,V = V42]). eq(min(V1, V, Out),0,[],[Out = 0,V44 >= 0,V43 >= 0,V1 = V44,V = V43]). eq(max(V1, V, Out),0,[],[Out = 0,V45 >= 0,V46 >= 0,V1 = V45,V = V46]). eq(minus(V1, V, Out),0,[],[Out = 0,V47 >= 0,V48 >= 0,V1 = V47,V = V48]). eq(gcd(V1, V, Out),0,[],[Out = 0,V49 >= 0,V50 >= 0,V1 = V49,V = V50]). input_output_vars(min(V1,V,Out),[V1,V],[Out]). input_output_vars(max(V1,V,Out),[V1,V],[Out]). input_output_vars(minus(V1,V,Out),[V1,V],[Out]). input_output_vars(gcd(V1,V,Out),[V1,V],[Out]). input_output_vars(encArg(V1,Out),[V1],[Out]). input_output_vars(fun(V1,V,Out),[V1,V],[Out]). input_output_vars(fun1(Out),[],[Out]). input_output_vars(fun2(V1,Out),[V1],[Out]). input_output_vars(fun3(V1,V,Out),[V1,V],[Out]). input_output_vars(fun4(V1,V,Out),[V1,V],[Out]). input_output_vars(fun5(V1,V,Out),[V1,V],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [max/3] 1. recursive : [min/3] 2. recursive : [minus/3] 3. recursive : [gcd/3] 4. recursive [non_tail,multiple] : [encArg/2] 5. non_recursive : [fun/3] 6. non_recursive : [fun1/1] 7. non_recursive : [fun2/2] 8. non_recursive : [fun3/3] 9. non_recursive : [fun4/3] 10. non_recursive : [fun5/3] 11. non_recursive : [start/2] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into max/3 1. SCC is partially evaluated into min/3 2. SCC is partially evaluated into minus/3 3. SCC is partially evaluated into gcd/3 4. SCC is partially evaluated into encArg/2 5. SCC is partially evaluated into fun/3 6. SCC is completely evaluated into other SCCs 7. SCC is partially evaluated into fun2/2 8. SCC is partially evaluated into fun3/3 9. SCC is partially evaluated into fun4/3 10. SCC is partially evaluated into fun5/3 11. SCC is partially evaluated into start/2 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations max/3 * CE 19 is refined into CE [41] * CE 16 is refined into CE [42] * CE 17 is refined into CE [43] * CE 18 is refined into CE [44] ### Cost equations --> "Loop" of max/3 * CEs [44] --> Loop 22 * CEs [41] --> Loop 23 * CEs [42] --> Loop 24 * CEs [43] --> Loop 25 ### Ranking functions of CR max(V1,V,Out) * RF of phase [22]: [V,V1] #### Partial ranking functions of CR max(V1,V,Out) * Partial RF of phase [22]: - RF of loop [22:1]: V V1 ### Specialization of cost equations min/3 * CE 12 is refined into CE [45] * CE 13 is refined into CE [46] * CE 15 is refined into CE [47] * CE 14 is refined into CE [48] ### Cost equations --> "Loop" of min/3 * CEs [48] --> Loop 26 * CEs [45] --> Loop 27 * CEs [46,47] --> Loop 28 ### Ranking functions of CR min(V1,V,Out) * RF of phase [26]: [V,V1] #### Partial ranking functions of CR min(V1,V,Out) * Partial RF of phase [26]: - RF of loop [26:1]: V V1 ### Specialization of cost equations minus/3 * CE 22 is refined into CE [49] * CE 20 is refined into CE [50] * CE 21 is refined into CE [51] ### Cost equations --> "Loop" of minus/3 * CEs [51] --> Loop 29 * CEs [49] --> Loop 30 * CEs [50] --> Loop 31 ### Ranking functions of CR minus(V1,V,Out) * RF of phase [29]: [V,V1] #### Partial ranking functions of CR minus(V1,V,Out) * Partial RF of phase [29]: - RF of loop [29:1]: V V1 ### Specialization of cost equations gcd/3 * CE 24 is refined into CE [52] * CE 23 is refined into CE [53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86] ### Cost equations --> "Loop" of gcd/3 * CEs [70] --> Loop 32 * CEs [78] --> Loop 33 * CEs [82] --> Loop 34 * CEs [74] --> Loop 35 * CEs [66] --> Loop 36 * CEs [69] --> Loop 37 * CEs [77] --> Loop 38 * CEs [81] --> Loop 39 * CEs [85] --> Loop 40 * CEs [73] --> Loop 41 * CEs [65] --> Loop 42 * CEs [64,68] --> Loop 43 * CEs [58,60,62,72,76,80,84,86] --> Loop 44 * CEs [56] --> Loop 45 * CEs [55] --> Loop 46 * CEs [54] --> Loop 47 * CEs [53,57,59,61,63,67,71,75,79,83] --> Loop 48 * CEs [52] --> Loop 49 ### Ranking functions of CR gcd(V1,V,Out) * RF of phase [32,33,34,35,36,44]: [V1+V-3] * RF of phase [45,47]: [V1+V-1] #### Partial ranking functions of CR gcd(V1,V,Out) * Partial RF of phase [32,33,34,35,36,44]: - RF of loop [32:1,34:1,36:1,44:1]: V1-1 depends on loops [33:1,35:1] - RF of loop [33:1,34:1,35:1,44:1]: V1+V-3 * Partial RF of phase [45,47]: - RF of loop [45:1]: V1 depends on loops [47:1] - RF of loop [47:1]: V1+V-1 ### Specialization of cost equations encArg/2 * CE 25 is refined into CE [87] * CE 27 is refined into CE [88,89] * CE 28 is refined into CE [90,91,92,93,94,95] * CE 29 is refined into CE [96,97,98] * CE 30 is refined into CE [99] * CE 26 is refined into CE [100] ### Cost equations --> "Loop" of encArg/2 * CEs [100] --> Loop 50 * CEs [89,95] --> Loop 51 * CEs [98] --> Loop 52 * CEs [94] --> Loop 53 * CEs [93] --> Loop 54 * CEs [91,96] --> Loop 55 * CEs [90] --> Loop 56 * CEs [88,92,97,99] --> Loop 57 * CEs [87] --> Loop 58 ### Ranking functions of CR encArg(V1,Out) * RF of phase [50,51,52,53,54,55,56,57]: [V1] #### Partial ranking functions of CR encArg(V1,Out) * Partial RF of phase [50,51,52,53,54,55,56,57]: - RF of loop [50:1,51:1,51:2,52:1,52:2,53:1,53:2,54:1,54:2,55:1,55:2,56:1,56:2,57:1,57:2]: V1 ### Specialization of cost equations fun/3 * CE 31 is refined into CE [101,102,103,104,105] * CE 32 is refined into CE [106] ### Cost equations --> "Loop" of fun/3 * CEs [105] --> Loop 59 * CEs [101,102,103,104,106] --> Loop 60 ### Ranking functions of CR fun(V1,V,Out) #### Partial ranking functions of CR fun(V1,V,Out) ### Specialization of cost equations fun2/2 * CE 33 is refined into CE [107,108] * CE 34 is refined into CE [109] ### Cost equations --> "Loop" of fun2/2 * CEs [108] --> Loop 61 * CEs [107] --> Loop 62 * CEs [109] --> Loop 63 ### Ranking functions of CR fun2(V1,Out) #### Partial ranking functions of CR fun2(V1,Out) ### Specialization of cost equations fun3/3 * CE 35 is refined into CE [110,111,112,113,114,115,116,117,118,119,120,121,122,123,124] * CE 36 is refined into CE [125] ### Cost equations --> "Loop" of fun3/3 * CEs [117,120,122] --> Loop 64 * CEs [113,119,123,124] --> Loop 65 * CEs [110,111,112,114,115,116,118,121,125] --> Loop 66 ### Ranking functions of CR fun3(V1,V,Out) #### Partial ranking functions of CR fun3(V1,V,Out) ### Specialization of cost equations fun4/3 * CE 37 is refined into CE [126,127,128,129,130,131,132,133,134] * CE 38 is refined into CE [135] ### Cost equations --> "Loop" of fun4/3 * CEs [130,132,134] --> Loop 67 * CEs [126,127,128,129,131,133,135] --> Loop 68 ### Ranking functions of CR fun4(V1,V,Out) #### Partial ranking functions of CR fun4(V1,V,Out) ### Specialization of cost equations fun5/3 * CE 39 is refined into CE [136,137,138,139] * CE 40 is refined into CE [140] ### Cost equations --> "Loop" of fun5/3 * CEs [136,137,138,139,140] --> Loop 69 ### Ranking functions of CR fun5(V1,V,Out) #### Partial ranking functions of CR fun5(V1,V,Out) ### Specialization of cost equations start/2 * CE 1 is refined into CE [141,142] * CE 2 is refined into CE [143,144,145,146,147,148] * CE 3 is refined into CE [149,150,151] * CE 4 is refined into CE [152] * CE 5 is refined into CE [153,154] * CE 6 is refined into CE [155,156] * CE 7 is refined into CE [157] * CE 8 is refined into CE [158,159,160] * CE 9 is refined into CE [161,162,163] * CE 10 is refined into CE [164,165] * CE 11 is refined into CE [166] ### Cost equations --> "Loop" of start/2 * CEs [141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166] --> Loop 70 ### Ranking functions of CR start(V1,V) #### Partial ranking functions of CR start(V1,V) Computing Bounds ===================================== #### Cost of chains of max(V1,V,Out): * Chain [[22],25]: 1*it(22)+1 Such that:it(22) =< V1 with precondition: [V=Out,V1>=1,V>=V1] * Chain [[22],24]: 1*it(22)+1 Such that:it(22) =< V with precondition: [V1=Out,V>=1,V1>=V] * Chain [[22],23]: 1*it(22)+0 Such that:it(22) =< Out with precondition: [Out>=1,V1>=Out,V>=Out] * Chain [25]: 1 with precondition: [V1=0,V=Out,V>=0] * Chain [24]: 1 with precondition: [V=0,V1=Out,V1>=0] * Chain [23]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of min(V1,V,Out): * Chain [[26],28]: 1*it(26)+1 Such that:it(26) =< Out with precondition: [Out>=1,V1>=Out,V>=Out] * Chain [[26],27]: 1*it(26)+1 Such that:it(26) =< Out with precondition: [V=Out,V>=1,V1>=V] * Chain [28]: 1 with precondition: [Out=0,V1>=0,V>=0] * Chain [27]: 1 with precondition: [V=0,Out=0,V1>=0] #### Cost of chains of minus(V1,V,Out): * Chain [[29],31]: 1*it(29)+1 Such that:it(29) =< V with precondition: [V1=Out+V,V>=1,V1>=V] * Chain [[29],30]: 1*it(29)+0 Such that:it(29) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [31]: 1 with precondition: [V=0,V1=Out,V1>=0] * Chain [30]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of gcd(V1,V,Out): * Chain [[45,47],49]: 5*it(45)+6*it(47)+1*s(8)+0 Such that:aux(13) =< V1 aux(14) =< V1+V aux(15) =< V aux(6) =< aux(14) it(45) =< aux(14) it(47) =< aux(14) aux(6) =< aux(15)+aux(13) it(45) =< aux(15)+aux(13) s(8) =< aux(6) with precondition: [Out=0,V1>=1,V>=1] * Chain [[45,47],48,49]: 5*it(45)+15*it(47)+1*s(8)+15*s(10)+4 Such that:aux(23) =< 1 aux(24) =< V1 aux(25) =< V1+V aux(26) =< V s(10) =< aux(23) it(47) =< aux(25) aux(6) =< aux(25) it(45) =< aux(25) aux(6) =< aux(26)+aux(24) it(45) =< aux(26)+aux(24) s(8) =< aux(6) with precondition: [Out=0,V1>=1,V>=1,V+V1>=3] * Chain [[45,47],46,49]: 5*it(45)+6*it(47)+1*s(8)+1*s(34)+4 Such that:s(34) =< 1 aux(27) =< V1 aux(28) =< V1+V aux(29) =< V aux(6) =< aux(28) it(45) =< aux(28) it(47) =< aux(28) aux(6) =< aux(29)+aux(27) it(45) =< aux(29)+aux(27) s(8) =< aux(6) with precondition: [Out=0,V1>=1,V>=1,V+V1>=3] * Chain [[32,33,34,35,36,44],[45,47],49]: 18*it(32)+20*it(33)+5*it(45)+1*s(8)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+0 Such that:aux(90) =< V1 aux(91) =< V1+V aux(92) =< V aux(6) =< aux(91) it(45) =< aux(91) it(33) =< aux(91) aux(6) =< aux(91)+aux(91) it(45) =< aux(91)+aux(91) s(8) =< aux(6) aux(61) =< aux(91) it(32) =< aux(91) aux(55) =< aux(91) aux(52) =< aux(92) aux(62) =< aux(91)-1 aux(61) =< aux(92)+aux(92)+aux(90) it(32) =< aux(92)+aux(92)+aux(90) s(133) =< it(33)*aux(91) s(132) =< aux(92)+aux(92)+aux(90) s(155) =< aux(92)+aux(92)+aux(90) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(92) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2] * Chain [[32,33,34,35,36,44],[45,47],48,49]: 18*it(32)+29*it(33)+5*it(45)+1*s(8)+15*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4 Such that:aux(23) =< 1 aux(93) =< V1 aux(94) =< V1+V aux(95) =< V s(10) =< aux(23) it(33) =< aux(94) aux(6) =< aux(94) it(45) =< aux(94) aux(6) =< aux(94)+aux(94) it(45) =< aux(94)+aux(94) s(8) =< aux(6) aux(61) =< aux(94) it(32) =< aux(94) aux(55) =< aux(94) aux(52) =< aux(95) aux(62) =< aux(94)-1 aux(61) =< aux(95)+aux(95)+aux(93) it(32) =< aux(95)+aux(95)+aux(93) s(133) =< it(33)*aux(94) s(132) =< aux(95)+aux(95)+aux(93) s(155) =< aux(95)+aux(95)+aux(93) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(95) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2] * Chain [[32,33,34,35,36,44],[45,47],46,49]: 18*it(32)+20*it(33)+5*it(45)+1*s(8)+1*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4 Such that:s(34) =< 1 aux(96) =< V1 aux(97) =< V1+V aux(98) =< V aux(6) =< aux(97) it(45) =< aux(97) it(33) =< aux(97) aux(6) =< aux(97)+aux(97) it(45) =< aux(97)+aux(97) s(8) =< aux(6) aux(61) =< aux(97) it(32) =< aux(97) aux(55) =< aux(97) aux(52) =< aux(98) aux(62) =< aux(97)-1 aux(61) =< aux(98)+aux(98)+aux(96) it(32) =< aux(98)+aux(98)+aux(96) s(133) =< it(33)*aux(97) s(132) =< aux(98)+aux(98)+aux(96) s(155) =< aux(98)+aux(98)+aux(96) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(98) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2] * Chain [[32,33,34,35,36,44],49]: 18*it(32)+14*it(33)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+0 Such that:aux(99) =< V1 aux(100) =< V1+V aux(101) =< V aux(61) =< aux(100) it(32) =< aux(100) it(33) =< aux(100) aux(55) =< aux(100) aux(52) =< aux(101) aux(62) =< aux(100)-1 aux(61) =< aux(101)+aux(101)+aux(99) it(32) =< aux(101)+aux(101)+aux(99) s(133) =< it(33)*aux(100) s(132) =< aux(101)+aux(101)+aux(99) s(155) =< aux(101)+aux(101)+aux(99) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(101) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2] * Chain [[32,33,34,35,36,44],48,49]: 18*it(32)+32*it(33)+6*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4 Such that:aux(20) =< 1 aux(102) =< V1 aux(103) =< V1+V aux(104) =< V s(10) =< aux(20) it(33) =< aux(103) aux(61) =< aux(103) it(32) =< aux(103) aux(55) =< aux(103) aux(52) =< aux(104) aux(62) =< aux(103)-1 aux(61) =< aux(104)+aux(104)+aux(102) it(32) =< aux(104)+aux(104)+aux(102) s(133) =< it(33)*aux(103) s(132) =< aux(104)+aux(104)+aux(102) s(155) =< aux(104)+aux(104)+aux(102) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(104) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2] * Chain [[32,33,34,35,36,44],43,49]: 18*it(32)+14*it(33)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9*s(160)+1*s(161)+4 Such that:s(161) =< 1 aux(109) =< V1 aux(110) =< V1+V aux(111) =< V s(160) =< aux(111) aux(61) =< aux(110) it(32) =< aux(110) it(33) =< aux(110) aux(55) =< aux(110) aux(52) =< aux(111) aux(62) =< aux(110)-1 aux(61) =< aux(111)+aux(111)+aux(109) it(32) =< aux(111)+aux(111)+aux(109) s(133) =< it(33)*aux(110) s(132) =< aux(111)+aux(111)+aux(109) s(155) =< aux(111)+aux(111)+aux(109) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(111) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],42,[45,47],49]: 18*it(32)+21*it(33)+5*it(45)+1*s(8)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(171)+5 Such that:aux(112) =< 1 aux(114) =< V1 aux(115) =< V1+V aux(116) =< V it(33) =< aux(115) s(171) =< aux(112) aux(6) =< aux(115) it(45) =< aux(115) aux(6) =< aux(112)+aux(115) it(45) =< aux(112)+aux(115) s(8) =< aux(6) aux(61) =< aux(115) it(32) =< aux(115) aux(55) =< aux(115) aux(52) =< aux(116) aux(62) =< aux(115)-1 aux(61) =< aux(116)+aux(116)+aux(114) it(32) =< aux(116)+aux(116)+aux(114) s(133) =< it(33)*aux(115) s(132) =< aux(116)+aux(116)+aux(114) s(155) =< aux(116)+aux(116)+aux(114) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(116) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],42,[45,47],48,49]: 18*it(32)+30*it(33)+5*it(45)+1*s(8)+16*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(117) =< 1 aux(119) =< V1 aux(120) =< V1+V aux(121) =< V it(33) =< aux(120) s(10) =< aux(117) aux(6) =< aux(120) it(45) =< aux(120) aux(6) =< aux(117)+aux(120) it(45) =< aux(117)+aux(120) s(8) =< aux(6) aux(61) =< aux(120) it(32) =< aux(120) aux(55) =< aux(120) aux(52) =< aux(121) aux(62) =< aux(120)-1 aux(61) =< aux(121)+aux(121)+aux(119) it(32) =< aux(121)+aux(121)+aux(119) s(133) =< it(33)*aux(120) s(132) =< aux(121)+aux(121)+aux(119) s(155) =< aux(121)+aux(121)+aux(119) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(121) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=6] * Chain [[32,33,34,35,36,44],42,[45,47],46,49]: 18*it(32)+21*it(33)+5*it(45)+1*s(8)+2*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(122) =< 1 aux(124) =< V1 aux(125) =< V1+V aux(126) =< V it(33) =< aux(125) s(34) =< aux(122) aux(6) =< aux(125) it(45) =< aux(125) aux(6) =< aux(122)+aux(125) it(45) =< aux(122)+aux(125) s(8) =< aux(6) aux(61) =< aux(125) it(32) =< aux(125) aux(55) =< aux(125) aux(52) =< aux(126) aux(62) =< aux(125)-1 aux(61) =< aux(126)+aux(126)+aux(124) it(32) =< aux(126)+aux(126)+aux(124) s(133) =< it(33)*aux(125) s(132) =< aux(126)+aux(126)+aux(124) s(155) =< aux(126)+aux(126)+aux(124) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(126) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=6] * Chain [[32,33,34,35,36,44],42,49]: 18*it(32)+14*it(33)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(170)+1*s(171)+5 Such that:s(171) =< 1 aux(127) =< V1 aux(128) =< V1+V aux(129) =< V s(170) =< aux(129) aux(61) =< aux(128) it(32) =< aux(128) it(33) =< aux(128) aux(55) =< aux(128) aux(52) =< aux(129) aux(62) =< aux(128)-1 aux(61) =< aux(129)+aux(129)+aux(127) it(32) =< aux(129)+aux(129)+aux(127) s(133) =< it(33)*aux(128) s(132) =< aux(129)+aux(129)+aux(127) s(155) =< aux(129)+aux(129)+aux(127) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(129) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],42,48,49]: 18*it(32)+24*it(33)+16*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(130) =< 1 aux(131) =< V1 aux(132) =< V1+V aux(133) =< V it(33) =< aux(132) s(10) =< aux(130) aux(61) =< aux(132) it(32) =< aux(132) aux(55) =< aux(132) aux(52) =< aux(133) aux(62) =< aux(132)-1 aux(61) =< aux(133)+aux(133)+aux(131) it(32) =< aux(133)+aux(133)+aux(131) s(133) =< it(33)*aux(132) s(132) =< aux(133)+aux(133)+aux(131) s(155) =< aux(133)+aux(133)+aux(131) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(133) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],42,46,49]: 18*it(32)+14*it(33)+2*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(170)+9 Such that:aux(134) =< 1 aux(135) =< V1 aux(136) =< V1+V aux(137) =< V s(170) =< aux(137) s(34) =< aux(134) aux(61) =< aux(136) it(32) =< aux(136) it(33) =< aux(136) aux(55) =< aux(136) aux(52) =< aux(137) aux(62) =< aux(136)-1 aux(61) =< aux(137)+aux(137)+aux(135) it(32) =< aux(137)+aux(137)+aux(135) s(133) =< it(33)*aux(136) s(132) =< aux(137)+aux(137)+aux(135) s(155) =< aux(137)+aux(137)+aux(135) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(137) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],41,[45,47],49]: 18*it(32)+21*it(33)+5*it(45)+1*s(8)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(173)+5 Such that:aux(138) =< 1 aux(140) =< V1 aux(141) =< V1+V aux(142) =< V it(33) =< aux(141) s(173) =< aux(138) aux(6) =< aux(141) it(45) =< aux(141) aux(6) =< aux(138)+aux(141) it(45) =< aux(138)+aux(141) s(8) =< aux(6) aux(61) =< aux(141) it(32) =< aux(141) aux(55) =< aux(141) aux(52) =< aux(142) aux(62) =< aux(141)-1 aux(61) =< aux(142)+aux(142)+aux(140) it(32) =< aux(142)+aux(142)+aux(140) s(133) =< it(33)*aux(141) s(132) =< aux(142)+aux(142)+aux(140) s(155) =< aux(142)+aux(142)+aux(140) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(142) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],41,[45,47],48,49]: 18*it(32)+30*it(33)+5*it(45)+1*s(8)+16*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(143) =< 1 aux(145) =< V1 aux(146) =< V1+V aux(147) =< V it(33) =< aux(146) s(10) =< aux(143) aux(6) =< aux(146) it(45) =< aux(146) aux(6) =< aux(143)+aux(146) it(45) =< aux(143)+aux(146) s(8) =< aux(6) aux(61) =< aux(146) it(32) =< aux(146) aux(55) =< aux(146) aux(52) =< aux(147) aux(62) =< aux(146)-1 aux(61) =< aux(147)+aux(147)+aux(145) it(32) =< aux(147)+aux(147)+aux(145) s(133) =< it(33)*aux(146) s(132) =< aux(147)+aux(147)+aux(145) s(155) =< aux(147)+aux(147)+aux(145) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(147) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3] * Chain [[32,33,34,35,36,44],41,[45,47],46,49]: 18*it(32)+21*it(33)+5*it(45)+1*s(8)+2*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(148) =< 1 aux(150) =< V1 aux(151) =< V1+V aux(152) =< V it(33) =< aux(151) s(34) =< aux(148) aux(6) =< aux(151) it(45) =< aux(151) aux(6) =< aux(148)+aux(151) it(45) =< aux(148)+aux(151) s(8) =< aux(6) aux(61) =< aux(151) it(32) =< aux(151) aux(55) =< aux(151) aux(52) =< aux(152) aux(62) =< aux(151)-1 aux(61) =< aux(152)+aux(152)+aux(150) it(32) =< aux(152)+aux(152)+aux(150) s(133) =< it(33)*aux(151) s(132) =< aux(152)+aux(152)+aux(150) s(155) =< aux(152)+aux(152)+aux(150) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(152) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3] * Chain [[32,33,34,35,36,44],41,49]: 18*it(32)+14*it(33)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(172)+1*s(173)+5 Such that:s(173) =< 1 aux(153) =< V1 aux(154) =< V1+V aux(155) =< V s(172) =< aux(153) aux(61) =< aux(154) it(32) =< aux(154) it(33) =< aux(154) aux(55) =< aux(154) aux(52) =< aux(155) aux(62) =< aux(154)-1 aux(61) =< aux(155)+aux(155)+aux(153) it(32) =< aux(155)+aux(155)+aux(153) s(133) =< it(33)*aux(154) s(132) =< aux(155)+aux(155)+aux(153) s(155) =< aux(155)+aux(155)+aux(153) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(155) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],41,48,49]: 18*it(32)+24*it(33)+16*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(156) =< 1 aux(157) =< V1 aux(158) =< V1+V aux(159) =< V it(33) =< aux(158) s(10) =< aux(156) aux(61) =< aux(158) it(32) =< aux(158) aux(55) =< aux(158) aux(52) =< aux(159) aux(62) =< aux(158)-1 aux(61) =< aux(159)+aux(159)+aux(157) it(32) =< aux(159)+aux(159)+aux(157) s(133) =< it(33)*aux(158) s(132) =< aux(159)+aux(159)+aux(157) s(155) =< aux(159)+aux(159)+aux(157) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(159) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],41,46,49]: 18*it(32)+14*it(33)+2*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(172)+9 Such that:aux(160) =< 1 aux(161) =< V1 aux(162) =< V1+V aux(163) =< V s(172) =< aux(161) s(34) =< aux(160) aux(61) =< aux(162) it(32) =< aux(162) it(33) =< aux(162) aux(55) =< aux(162) aux(52) =< aux(163) aux(62) =< aux(162)-1 aux(61) =< aux(163)+aux(163)+aux(161) it(32) =< aux(163)+aux(163)+aux(161) s(133) =< it(33)*aux(162) s(132) =< aux(163)+aux(163)+aux(161) s(155) =< aux(163)+aux(163)+aux(161) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(163) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],40,[45,47],49]: 18*it(32)+24*it(33)+5*it(45)+1*s(8)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4 Such that:aux(15) =< 1 aux(88) =< V aux(89) =< V+1 aux(166) =< V1 aux(167) =< V1+V it(33) =< aux(167) aux(6) =< aux(167) it(45) =< aux(167) aux(6) =< aux(15)+aux(167) it(45) =< aux(15)+aux(167) s(8) =< aux(6) aux(61) =< aux(167) it(32) =< aux(167) aux(39) =< aux(88) aux(39) =< aux(89) aux(55) =< aux(167) aux(52) =< aux(88) aux(62) =< aux(167)-1 aux(61) =< aux(39)+aux(39)+aux(166) it(32) =< aux(39)+aux(39)+aux(166) s(133) =< it(33)*aux(167) s(132) =< aux(39)+aux(39)+aux(166) s(155) =< aux(39)+aux(39)+aux(166) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(88) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3,V+V1>=7] * Chain [[32,33,34,35,36,44],40,[45,47],48,49]: 18*it(32)+33*it(33)+5*it(45)+1*s(8)+15*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+8 Such that:aux(168) =< 1 aux(88) =< V aux(89) =< V+1 aux(170) =< V1 aux(171) =< V1+V it(33) =< aux(171) s(10) =< aux(168) aux(6) =< aux(171) it(45) =< aux(171) aux(6) =< aux(168)+aux(171) it(45) =< aux(168)+aux(171) s(8) =< aux(6) aux(61) =< aux(171) it(32) =< aux(171) aux(39) =< aux(88) aux(39) =< aux(89) aux(55) =< aux(171) aux(52) =< aux(88) aux(62) =< aux(171)-1 aux(61) =< aux(39)+aux(39)+aux(170) it(32) =< aux(39)+aux(39)+aux(170) s(133) =< it(33)*aux(171) s(132) =< aux(39)+aux(39)+aux(170) s(155) =< aux(39)+aux(39)+aux(170) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(88) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=4,V>=4,V+V1>=9] * Chain [[32,33,34,35,36,44],40,[45,47],46,49]: 18*it(32)+24*it(33)+5*it(45)+1*s(8)+1*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+8 Such that:aux(172) =< 1 aux(88) =< V aux(89) =< V+1 aux(174) =< V1 aux(175) =< V1+V s(34) =< aux(172) it(33) =< aux(175) aux(6) =< aux(175) it(45) =< aux(175) aux(6) =< aux(172)+aux(175) it(45) =< aux(172)+aux(175) s(8) =< aux(6) aux(61) =< aux(175) it(32) =< aux(175) aux(39) =< aux(88) aux(39) =< aux(89) aux(55) =< aux(175) aux(52) =< aux(88) aux(62) =< aux(175)-1 aux(61) =< aux(39)+aux(39)+aux(174) it(32) =< aux(39)+aux(39)+aux(174) s(133) =< it(33)*aux(175) s(132) =< aux(39)+aux(39)+aux(174) s(155) =< aux(39)+aux(39)+aux(174) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(88) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=4,V>=4,V+V1>=9] * Chain [[32,33,34,35,36,44],40,49]: 18*it(32)+14*it(33)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4*s(174)+4 Such that:aux(177) =< V1 aux(178) =< V1+V aux(179) =< V s(174) =< aux(179) aux(61) =< aux(178) it(32) =< aux(178) it(33) =< aux(178) aux(55) =< aux(178) aux(52) =< aux(179) aux(62) =< aux(178)-1 aux(61) =< aux(179)+aux(179)+aux(177) it(32) =< aux(179)+aux(179)+aux(177) s(133) =< it(33)*aux(178) s(132) =< aux(179)+aux(179)+aux(177) s(155) =< aux(179)+aux(179)+aux(177) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(179) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],40,48,49]: 18*it(32)+14*it(33)+15*s(10)+13*s(22)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+8 Such that:aux(180) =< 1 aux(182) =< V1 aux(183) =< V1+V aux(184) =< V s(22) =< aux(184) s(10) =< aux(180) aux(61) =< aux(183) it(32) =< aux(183) it(33) =< aux(183) aux(55) =< aux(183) aux(52) =< aux(184) aux(62) =< aux(183)-1 aux(61) =< aux(184)+aux(184)+aux(182) it(32) =< aux(184)+aux(184)+aux(182) s(133) =< it(33)*aux(183) s(132) =< aux(184)+aux(184)+aux(182) s(155) =< aux(184)+aux(184)+aux(182) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(184) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3,V+V1>=7] * Chain [[32,33,34,35,36,44],40,46,49]: 18*it(32)+14*it(33)+1*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4*s(174)+8 Such that:s(34) =< 1 aux(186) =< V1 aux(187) =< V1+V aux(188) =< V s(174) =< aux(188) aux(61) =< aux(187) it(32) =< aux(187) it(33) =< aux(187) aux(55) =< aux(187) aux(52) =< aux(188) aux(62) =< aux(187)-1 aux(61) =< aux(188)+aux(188)+aux(186) it(32) =< aux(188)+aux(188)+aux(186) s(133) =< it(33)*aux(187) s(132) =< aux(188)+aux(188)+aux(186) s(155) =< aux(188)+aux(188)+aux(186) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(188) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3,V+V1>=7] * Chain [[32,33,34,35,36,44],39,[45,47],49]: 18*it(32)+21*it(33)+5*it(45)+1*s(8)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(179)+4 Such that:aux(189) =< 1 aux(191) =< V1 aux(192) =< V1+V aux(193) =< V s(179) =< aux(189) it(33) =< aux(192) aux(6) =< aux(192) it(45) =< aux(192) aux(6) =< aux(189)+aux(192) it(45) =< aux(189)+aux(192) s(8) =< aux(6) aux(61) =< aux(192) it(32) =< aux(192) aux(55) =< aux(192) aux(52) =< aux(193) aux(62) =< aux(192)-1 aux(61) =< aux(193)+aux(193)+aux(191) it(32) =< aux(193)+aux(193)+aux(191) s(133) =< it(33)*aux(192) s(132) =< aux(193)+aux(193)+aux(191) s(155) =< aux(193)+aux(193)+aux(191) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(193) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],39,[45,47],48,49]: 18*it(32)+30*it(33)+5*it(45)+1*s(8)+16*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+8 Such that:aux(194) =< 1 aux(196) =< V1 aux(197) =< V1+V aux(198) =< V s(10) =< aux(194) it(33) =< aux(197) aux(6) =< aux(197) it(45) =< aux(197) aux(6) =< aux(194)+aux(197) it(45) =< aux(194)+aux(197) s(8) =< aux(6) aux(61) =< aux(197) it(32) =< aux(197) aux(55) =< aux(197) aux(52) =< aux(198) aux(62) =< aux(197)-1 aux(61) =< aux(198)+aux(198)+aux(196) it(32) =< aux(198)+aux(198)+aux(196) s(133) =< it(33)*aux(197) s(132) =< aux(198)+aux(198)+aux(196) s(155) =< aux(198)+aux(198)+aux(196) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(198) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3,V+V1>=7] * Chain [[32,33,34,35,36,44],39,[45,47],46,49]: 18*it(32)+21*it(33)+5*it(45)+1*s(8)+2*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+8 Such that:aux(199) =< 1 aux(201) =< V1 aux(202) =< V1+V aux(203) =< V s(34) =< aux(199) it(33) =< aux(202) aux(6) =< aux(202) it(45) =< aux(202) aux(6) =< aux(199)+aux(202) it(45) =< aux(199)+aux(202) s(8) =< aux(6) aux(61) =< aux(202) it(32) =< aux(202) aux(55) =< aux(202) aux(52) =< aux(203) aux(62) =< aux(202)-1 aux(61) =< aux(203)+aux(203)+aux(201) it(32) =< aux(203)+aux(203)+aux(201) s(133) =< it(33)*aux(202) s(132) =< aux(203)+aux(203)+aux(201) s(155) =< aux(203)+aux(203)+aux(201) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(203) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3,V+V1>=7] * Chain [[32,33,34,35,36,44],39,49]: 18*it(32)+14*it(33)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(178)+1*s(179)+4 Such that:s(179) =< 1 aux(204) =< V1 aux(205) =< V1+V aux(206) =< V s(178) =< aux(206) aux(61) =< aux(205) it(32) =< aux(205) it(33) =< aux(205) aux(55) =< aux(205) aux(52) =< aux(206) aux(62) =< aux(205)-1 aux(61) =< aux(206)+aux(206)+aux(204) it(32) =< aux(206)+aux(206)+aux(204) s(133) =< it(33)*aux(205) s(132) =< aux(206)+aux(206)+aux(204) s(155) =< aux(206)+aux(206)+aux(204) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(206) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],39,48,49]: 18*it(32)+24*it(33)+16*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+8 Such that:aux(207) =< 1 aux(209) =< V1 aux(210) =< V1+V aux(211) =< V s(10) =< aux(207) it(33) =< aux(210) aux(61) =< aux(210) it(32) =< aux(210) aux(55) =< aux(210) aux(52) =< aux(211) aux(62) =< aux(210)-1 aux(61) =< aux(211)+aux(211)+aux(209) it(32) =< aux(211)+aux(211)+aux(209) s(133) =< it(33)*aux(210) s(132) =< aux(211)+aux(211)+aux(209) s(155) =< aux(211)+aux(211)+aux(209) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(211) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],39,46,49]: 18*it(32)+14*it(33)+2*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(178)+8 Such that:aux(212) =< 1 aux(213) =< V1 aux(214) =< V1+V aux(215) =< V s(178) =< aux(215) s(34) =< aux(212) aux(61) =< aux(214) it(32) =< aux(214) it(33) =< aux(214) aux(55) =< aux(214) aux(52) =< aux(215) aux(62) =< aux(214)-1 aux(61) =< aux(215)+aux(215)+aux(213) it(32) =< aux(215)+aux(215)+aux(213) s(133) =< it(33)*aux(214) s(132) =< aux(215)+aux(215)+aux(213) s(155) =< aux(215)+aux(215)+aux(213) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(215) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],38,[45,47],49]: 18*it(32)+10*it(33)+5*it(45)+10*it(47)+1*s(8)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(134)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+5 Such that:aux(15) =< 1 aux(88) =< V aux(89) =< V+1 aux(218) =< V1 aux(219) =< V1+V aux(220) =< V1+V+1 it(47) =< aux(220) aux(6) =< aux(220) it(45) =< aux(220) aux(6) =< aux(15)+aux(219) it(45) =< aux(15)+aux(219) s(8) =< aux(6) aux(61) =< aux(219) aux(64) =< aux(219) it(32) =< aux(219) it(33) =< aux(219) aux(61) =< aux(220) aux(64) =< aux(220) it(32) =< aux(220) it(33) =< aux(220) aux(39) =< aux(88) aux(39) =< aux(89) aux(55) =< aux(219) aux(52) =< aux(88) aux(62) =< aux(219)-1 aux(61) =< aux(39)+aux(39)+aux(218) it(32) =< aux(39)+aux(39)+aux(218) s(134) =< aux(64) s(133) =< it(33)*aux(219) s(132) =< aux(39)+aux(39)+aux(218) s(155) =< aux(39)+aux(39)+aux(218) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(88) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3] * Chain [[32,33,34,35,36,44],38,[45,47],48,49]: 18*it(32)+10*it(33)+5*it(45)+19*it(47)+1*s(8)+15*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(134)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(221) =< 1 aux(88) =< V aux(89) =< V+1 aux(223) =< V1 aux(224) =< V1+V aux(225) =< V1+V+1 it(47) =< aux(225) s(10) =< aux(221) aux(6) =< aux(225) it(45) =< aux(225) aux(6) =< aux(221)+aux(224) it(45) =< aux(221)+aux(224) s(8) =< aux(6) aux(61) =< aux(224) aux(64) =< aux(224) it(32) =< aux(224) it(33) =< aux(224) aux(61) =< aux(225) aux(64) =< aux(225) it(32) =< aux(225) it(33) =< aux(225) aux(39) =< aux(88) aux(39) =< aux(89) aux(55) =< aux(224) aux(52) =< aux(88) aux(62) =< aux(224)-1 aux(61) =< aux(39)+aux(39)+aux(223) it(32) =< aux(39)+aux(39)+aux(223) s(134) =< aux(64) s(133) =< it(33)*aux(224) s(132) =< aux(39)+aux(39)+aux(223) s(155) =< aux(39)+aux(39)+aux(223) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(88) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=4,V>=4] * Chain [[32,33,34,35,36,44],38,[45,47],46,49]: 18*it(32)+10*it(33)+5*it(45)+10*it(47)+1*s(8)+1*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(134)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(226) =< 1 aux(88) =< V aux(89) =< V+1 aux(228) =< V1 aux(229) =< V1+V aux(230) =< V1+V+1 it(47) =< aux(230) s(34) =< aux(226) aux(6) =< aux(230) it(45) =< aux(230) aux(6) =< aux(226)+aux(229) it(45) =< aux(226)+aux(229) s(8) =< aux(6) aux(61) =< aux(229) aux(64) =< aux(229) it(32) =< aux(229) it(33) =< aux(229) aux(61) =< aux(230) aux(64) =< aux(230) it(32) =< aux(230) it(33) =< aux(230) aux(39) =< aux(88) aux(39) =< aux(89) aux(55) =< aux(229) aux(52) =< aux(88) aux(62) =< aux(229)-1 aux(61) =< aux(39)+aux(39)+aux(228) it(32) =< aux(39)+aux(39)+aux(228) s(134) =< aux(64) s(133) =< it(33)*aux(229) s(132) =< aux(39)+aux(39)+aux(228) s(155) =< aux(39)+aux(39)+aux(228) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(88) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=4,V>=4] * Chain [[32,33,34,35,36,44],38,49]: 18*it(32)+14*it(33)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4*s(180)+5 Such that:aux(232) =< V1 aux(233) =< V1+V aux(234) =< V s(180) =< aux(232) aux(61) =< aux(233) it(32) =< aux(233) it(33) =< aux(233) aux(55) =< aux(233) aux(52) =< aux(234) aux(62) =< aux(233)-1 aux(61) =< aux(234)+aux(234)+aux(232) it(32) =< aux(234)+aux(234)+aux(232) s(133) =< it(33)*aux(233) s(132) =< aux(234)+aux(234)+aux(232) s(155) =< aux(234)+aux(234)+aux(232) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(234) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],38,48,49]: 18*it(32)+27*it(33)+15*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(235) =< 1 aux(237) =< V1 aux(238) =< V1+V aux(239) =< V it(33) =< aux(238) s(10) =< aux(235) aux(61) =< aux(238) it(32) =< aux(238) aux(55) =< aux(238) aux(52) =< aux(239) aux(62) =< aux(238)-1 aux(61) =< aux(239)+aux(239)+aux(237) it(32) =< aux(239)+aux(239)+aux(237) s(133) =< it(33)*aux(238) s(132) =< aux(239)+aux(239)+aux(237) s(155) =< aux(239)+aux(239)+aux(237) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(239) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3] * Chain [[32,33,34,35,36,44],38,46,49]: 18*it(32)+14*it(33)+1*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4*s(180)+9 Such that:s(34) =< 1 aux(241) =< V1 aux(242) =< V1+V aux(243) =< V s(180) =< aux(241) aux(61) =< aux(242) it(32) =< aux(242) it(33) =< aux(242) aux(55) =< aux(242) aux(52) =< aux(243) aux(62) =< aux(242)-1 aux(61) =< aux(243)+aux(243)+aux(241) it(32) =< aux(243)+aux(243)+aux(241) s(133) =< it(33)*aux(242) s(132) =< aux(243)+aux(243)+aux(241) s(155) =< aux(243)+aux(243)+aux(241) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(243) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3] * Chain [[32,33,34,35,36,44],37,[45,47],49]: 18*it(32)+10*it(33)+5*it(45)+10*it(47)+1*s(8)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(134)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+5 Such that:aux(15) =< 1 aux(246) =< V1 aux(247) =< V1+V aux(248) =< V1+V+1 aux(249) =< V it(47) =< aux(248) aux(6) =< aux(248) it(45) =< aux(248) aux(6) =< aux(15)+aux(247) it(45) =< aux(15)+aux(247) s(8) =< aux(6) aux(61) =< aux(247) aux(64) =< aux(247) it(32) =< aux(247) it(33) =< aux(247) aux(61) =< aux(248) aux(64) =< aux(248) it(32) =< aux(248) it(33) =< aux(248) aux(55) =< aux(247) aux(52) =< aux(249) aux(62) =< aux(247)-1 aux(61) =< aux(249)+aux(249)+aux(246) it(32) =< aux(249)+aux(249)+aux(246) s(134) =< aux(64) s(133) =< it(33)*aux(247) s(132) =< aux(249)+aux(249)+aux(246) s(155) =< aux(249)+aux(249)+aux(246) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(249) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=6] * Chain [[32,33,34,35,36,44],37,[45,47],48,49]: 18*it(32)+10*it(33)+5*it(45)+19*it(47)+1*s(8)+15*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(134)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(250) =< 1 aux(252) =< V1 aux(253) =< V1+V aux(254) =< V1+V+1 aux(255) =< V it(47) =< aux(254) s(10) =< aux(250) aux(6) =< aux(254) it(45) =< aux(254) aux(6) =< aux(250)+aux(253) it(45) =< aux(250)+aux(253) s(8) =< aux(6) aux(61) =< aux(253) aux(64) =< aux(253) it(32) =< aux(253) it(33) =< aux(253) aux(61) =< aux(254) aux(64) =< aux(254) it(32) =< aux(254) it(33) =< aux(254) aux(55) =< aux(253) aux(52) =< aux(255) aux(62) =< aux(253)-1 aux(61) =< aux(255)+aux(255)+aux(252) it(32) =< aux(255)+aux(255)+aux(252) s(134) =< aux(64) s(133) =< it(33)*aux(253) s(132) =< aux(255)+aux(255)+aux(252) s(155) =< aux(255)+aux(255)+aux(252) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(255) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=7] * Chain [[32,33,34,35,36,44],37,[45,47],46,49]: 18*it(32)+10*it(33)+5*it(45)+10*it(47)+1*s(8)+1*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(134)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(256) =< 1 aux(258) =< V1 aux(259) =< V1+V aux(260) =< V1+V+1 aux(261) =< V it(47) =< aux(260) s(34) =< aux(256) aux(6) =< aux(260) it(45) =< aux(260) aux(6) =< aux(256)+aux(259) it(45) =< aux(256)+aux(259) s(8) =< aux(6) aux(61) =< aux(259) aux(64) =< aux(259) it(32) =< aux(259) it(33) =< aux(259) aux(61) =< aux(260) aux(64) =< aux(260) it(32) =< aux(260) it(33) =< aux(260) aux(55) =< aux(259) aux(52) =< aux(261) aux(62) =< aux(259)-1 aux(61) =< aux(261)+aux(261)+aux(258) it(32) =< aux(261)+aux(261)+aux(258) s(134) =< aux(64) s(133) =< it(33)*aux(259) s(132) =< aux(261)+aux(261)+aux(258) s(155) =< aux(261)+aux(261)+aux(258) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(261) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=7] * Chain [[32,33,34,35,36,44],37,49]: 18*it(32)+14*it(33)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4*s(184)+5 Such that:aux(263) =< V1 aux(264) =< V1+V aux(265) =< V s(184) =< aux(265) aux(61) =< aux(264) it(32) =< aux(264) it(33) =< aux(264) aux(55) =< aux(264) aux(52) =< aux(265) aux(62) =< aux(264)-1 aux(61) =< aux(265)+aux(265)+aux(263) it(32) =< aux(265)+aux(265)+aux(263) s(133) =< it(33)*aux(264) s(132) =< aux(265)+aux(265)+aux(263) s(155) =< aux(265)+aux(265)+aux(263) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(265) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[32,33,34,35,36,44],37,48,49]: 18*it(32)+27*it(33)+15*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(266) =< 1 aux(268) =< V1 aux(269) =< V1+V aux(270) =< V it(33) =< aux(269) s(10) =< aux(266) aux(61) =< aux(269) it(32) =< aux(269) aux(55) =< aux(269) aux(52) =< aux(270) aux(62) =< aux(269)-1 aux(61) =< aux(270)+aux(270)+aux(268) it(32) =< aux(270)+aux(270)+aux(268) s(133) =< it(33)*aux(269) s(132) =< aux(270)+aux(270)+aux(268) s(155) =< aux(270)+aux(270)+aux(268) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(270) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=6] * Chain [[32,33,34,35,36,44],37,46,49]: 18*it(32)+14*it(33)+1*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4*s(184)+9 Such that:s(34) =< 1 aux(272) =< V1 aux(273) =< V1+V aux(274) =< V s(184) =< aux(274) aux(61) =< aux(273) it(32) =< aux(273) it(33) =< aux(273) aux(55) =< aux(273) aux(52) =< aux(274) aux(62) =< aux(273)-1 aux(61) =< aux(274)+aux(274)+aux(272) it(32) =< aux(274)+aux(274)+aux(272) s(133) =< it(33)*aux(273) s(132) =< aux(274)+aux(274)+aux(272) s(155) =< aux(274)+aux(274)+aux(272) s(136) =< it(33)*aux(55) s(142) =< it(33)*aux(55) s(141) =< it(32)*aux(55) s(131) =< it(32)*aux(52) s(155) =< it(32)*aux(55) s(128) =< it(32)*aux(52) s(139) =< aux(61) s(138) =< it(32)*aux(62) s(132) =< it(32)*aux(274) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=6] * Chain [49]: 0 with precondition: [Out=0,V1>=0,V>=0] * Chain [48,49]: 6*s(10)+9*s(14)+9*s(22)+4 Such that:aux(20) =< 1 aux(21) =< V1 aux(22) =< V s(10) =< aux(20) s(22) =< aux(21) s(14) =< aux(22) with precondition: [Out=0,V1>=1,V>=1] * Chain [46,49]: 1*s(34)+4 Such that:s(34) =< 1 with precondition: [V=1,Out=0,V1>=1] * Chain [43,49]: 9*s(160)+1*s(161)+4 Such that:s(161) =< 1 aux(108) =< V s(160) =< aux(108) with precondition: [Out=0,V>=2,V1>=V] * Chain [42,[45,47],49]: 5*it(45)+6*it(47)+1*s(8)+1*s(170)+1*s(171)+5 Such that:s(170) =< V aux(112) =< 1 aux(113) =< V1 s(171) =< aux(112) aux(6) =< aux(113) it(45) =< aux(113) it(47) =< aux(113) aux(6) =< aux(112)+aux(113) it(45) =< aux(112)+aux(113) s(8) =< aux(6) with precondition: [Out=0,V>=2,V1>=V] * Chain [42,[45,47],48,49]: 5*it(45)+15*it(47)+1*s(8)+16*s(10)+1*s(170)+9 Such that:s(170) =< V aux(117) =< 1 aux(118) =< V1 s(10) =< aux(117) it(47) =< aux(118) aux(6) =< aux(118) it(45) =< aux(118) aux(6) =< aux(117)+aux(118) it(45) =< aux(117)+aux(118) s(8) =< aux(6) with precondition: [Out=0,V1>=3,V>=2,V1>=V] * Chain [42,[45,47],46,49]: 5*it(45)+6*it(47)+1*s(8)+2*s(34)+1*s(170)+9 Such that:s(170) =< V aux(122) =< 1 aux(123) =< V1 s(34) =< aux(122) aux(6) =< aux(123) it(45) =< aux(123) it(47) =< aux(123) aux(6) =< aux(122)+aux(123) it(45) =< aux(122)+aux(123) s(8) =< aux(6) with precondition: [Out=0,V1>=3,V>=2,V1>=V] * Chain [42,49]: 1*s(170)+1*s(171)+5 Such that:s(171) =< 1 s(170) =< V with precondition: [Out=0,V>=2,V1>=V] * Chain [42,48,49]: 16*s(10)+9*s(22)+1*s(170)+9 Such that:aux(21) =< V1 s(170) =< V aux(130) =< 1 s(10) =< aux(130) s(22) =< aux(21) with precondition: [Out=0,V>=2,V1>=V] * Chain [42,46,49]: 2*s(34)+1*s(170)+9 Such that:s(170) =< V aux(134) =< 1 s(34) =< aux(134) with precondition: [Out=0,V>=2,V1>=V] * Chain [41,[45,47],49]: 5*it(45)+6*it(47)+1*s(8)+1*s(172)+1*s(173)+5 Such that:s(172) =< V1 aux(138) =< 1 aux(139) =< V s(173) =< aux(138) aux(6) =< aux(139) it(45) =< aux(139) it(47) =< aux(139) aux(6) =< aux(138)+aux(139) it(45) =< aux(138)+aux(139) s(8) =< aux(6) with precondition: [Out=0,V1>=2,V>=V1] * Chain [41,[45,47],48,49]: 5*it(45)+15*it(47)+1*s(8)+16*s(10)+1*s(172)+9 Such that:s(172) =< V1 aux(143) =< 1 aux(144) =< V s(10) =< aux(143) it(47) =< aux(144) aux(6) =< aux(144) it(45) =< aux(144) aux(6) =< aux(143)+aux(144) it(45) =< aux(143)+aux(144) s(8) =< aux(6) with precondition: [Out=0,V1>=2,V>=3,V>=V1] * Chain [41,[45,47],46,49]: 5*it(45)+6*it(47)+1*s(8)+2*s(34)+1*s(172)+9 Such that:s(172) =< V1 aux(148) =< 1 aux(149) =< V s(34) =< aux(148) aux(6) =< aux(149) it(45) =< aux(149) it(47) =< aux(149) aux(6) =< aux(148)+aux(149) it(45) =< aux(148)+aux(149) s(8) =< aux(6) with precondition: [Out=0,V1>=2,V>=3,V>=V1] * Chain [41,49]: 1*s(172)+1*s(173)+5 Such that:s(173) =< 1 s(172) =< V1 with precondition: [Out=0,V1>=2,V>=V1] * Chain [41,48,49]: 16*s(10)+9*s(22)+1*s(172)+9 Such that:s(172) =< V1 aux(21) =< V aux(156) =< 1 s(10) =< aux(156) s(22) =< aux(21) with precondition: [Out=0,V1>=2,V>=V1] * Chain [41,46,49]: 2*s(34)+1*s(172)+9 Such that:s(172) =< V1 aux(160) =< 1 s(34) =< aux(160) with precondition: [Out=0,V1>=2,V>=V1] * Chain [40,[45,47],49]: 5*it(45)+6*it(47)+1*s(8)+4*s(174)+4 Such that:aux(15) =< 1 aux(14) =< V+1 aux(165) =< V s(174) =< aux(165) aux(6) =< aux(14) it(45) =< aux(14) it(47) =< aux(14) aux(6) =< aux(15)+aux(165) it(45) =< aux(15)+aux(165) s(8) =< aux(6) with precondition: [Out=0,V1>=3,V>=3] * Chain [40,[45,47],48,49]: 5*it(45)+15*it(47)+1*s(8)+15*s(10)+4*s(174)+8 Such that:aux(25) =< V+1 aux(168) =< 1 aux(169) =< V s(174) =< aux(169) s(10) =< aux(168) it(47) =< aux(25) aux(6) =< aux(25) it(45) =< aux(25) aux(6) =< aux(168)+aux(169) it(45) =< aux(168)+aux(169) s(8) =< aux(6) with precondition: [Out=0,V1>=4,V>=4] * Chain [40,[45,47],46,49]: 5*it(45)+6*it(47)+1*s(8)+1*s(34)+4*s(174)+8 Such that:aux(28) =< V+1 aux(172) =< 1 aux(173) =< V s(34) =< aux(172) s(174) =< aux(173) aux(6) =< aux(28) it(45) =< aux(28) it(47) =< aux(28) aux(6) =< aux(172)+aux(173) it(45) =< aux(172)+aux(173) s(8) =< aux(6) with precondition: [Out=0,V1>=4,V>=4] * Chain [40,49]: 4*s(174)+4 Such that:aux(176) =< V s(174) =< aux(176) with precondition: [Out=0,V1>=2,V>=2] * Chain [40,48,49]: 15*s(10)+13*s(22)+8 Such that:aux(180) =< 1 aux(181) =< V s(22) =< aux(181) s(10) =< aux(180) with precondition: [Out=0,V1>=3,V>=3] * Chain [40,46,49]: 1*s(34)+4*s(174)+8 Such that:s(34) =< 1 aux(185) =< V s(174) =< aux(185) with precondition: [Out=0,V1>=3,V>=3] * Chain [39,[45,47],49]: 5*it(45)+7*it(47)+1*s(8)+1*s(179)+4 Such that:aux(189) =< 1 aux(190) =< V1 s(179) =< aux(189) it(47) =< aux(190) aux(6) =< aux(190) it(45) =< aux(190) aux(6) =< aux(189)+aux(190) it(45) =< aux(189)+aux(190) s(8) =< aux(6) with precondition: [Out=0,V1>=2,V>=2] * Chain [39,[45,47],48,49]: 5*it(45)+16*it(47)+1*s(8)+16*s(10)+8 Such that:aux(194) =< 1 aux(195) =< V1 s(10) =< aux(194) it(47) =< aux(195) aux(6) =< aux(195) it(45) =< aux(195) aux(6) =< aux(194)+aux(195) it(45) =< aux(194)+aux(195) s(8) =< aux(6) with precondition: [Out=0,V1>=3,V>=3] * Chain [39,[45,47],46,49]: 5*it(45)+7*it(47)+1*s(8)+2*s(34)+8 Such that:aux(199) =< 1 aux(200) =< V1 s(34) =< aux(199) it(47) =< aux(200) aux(6) =< aux(200) it(45) =< aux(200) aux(6) =< aux(199)+aux(200) it(45) =< aux(199)+aux(200) s(8) =< aux(6) with precondition: [Out=0,V1>=3,V>=3] * Chain [39,49]: 1*s(178)+1*s(179)+4 Such that:s(179) =< 1 s(178) =< V with precondition: [Out=0,V1>=2,V>=2] * Chain [39,48,49]: 16*s(10)+10*s(22)+8 Such that:aux(207) =< 1 aux(208) =< V1 s(10) =< aux(207) s(22) =< aux(208) with precondition: [Out=0,V1>=2,V>=2] * Chain [39,46,49]: 2*s(34)+1*s(178)+8 Such that:s(178) =< V aux(212) =< 1 s(34) =< aux(212) with precondition: [Out=0,V1>=2,V>=2] * Chain [38,[45,47],49]: 5*it(45)+9*it(47)+1*s(8)+1*s(180)+5 Such that:aux(15) =< 1 s(180) =< V1 aux(13) =< V aux(217) =< V+1 aux(6) =< aux(217) it(45) =< aux(217) it(47) =< aux(217) aux(6) =< aux(15)+aux(13) it(45) =< aux(15)+aux(13) s(8) =< aux(6) with precondition: [Out=0,V1>=2,V>=3,V>=V1] * Chain [38,[45,47],48,49]: 5*it(45)+18*it(47)+1*s(8)+15*s(10)+1*s(180)+9 Such that:s(180) =< V1 aux(24) =< V aux(221) =< 1 aux(222) =< V+1 s(10) =< aux(221) it(47) =< aux(222) aux(6) =< aux(222) it(45) =< aux(222) aux(6) =< aux(221)+aux(24) it(45) =< aux(221)+aux(24) s(8) =< aux(6) with precondition: [Out=0,V1>=2,V>=4,V>=V1] * Chain [38,[45,47],46,49]: 5*it(45)+9*it(47)+1*s(8)+1*s(34)+1*s(180)+9 Such that:s(180) =< V1 aux(27) =< V aux(226) =< 1 aux(227) =< V+1 s(34) =< aux(226) aux(6) =< aux(227) it(45) =< aux(227) it(47) =< aux(227) aux(6) =< aux(226)+aux(27) it(45) =< aux(226)+aux(27) s(8) =< aux(6) with precondition: [Out=0,V1>=2,V>=4,V>=V1] * Chain [38,49]: 4*s(180)+5 Such that:aux(231) =< V1 s(180) =< aux(231) with precondition: [Out=0,V1>=2,V>=V1] * Chain [38,48,49]: 15*s(10)+12*s(22)+1*s(180)+9 Such that:s(180) =< V1 aux(235) =< 1 aux(236) =< V s(10) =< aux(235) s(22) =< aux(236) with precondition: [Out=0,V1>=2,V>=3,V>=V1] * Chain [38,46,49]: 1*s(34)+4*s(180)+9 Such that:s(34) =< 1 aux(240) =< V1 s(180) =< aux(240) with precondition: [Out=0,V1>=2,V>=3,V>=V1] * Chain [37,[45,47],49]: 5*it(45)+9*it(47)+1*s(8)+1*s(184)+5 Such that:aux(15) =< 1 aux(13) =< V1 s(184) =< V aux(245) =< V1+1 aux(6) =< aux(245) it(45) =< aux(245) it(47) =< aux(245) aux(6) =< aux(15)+aux(13) it(45) =< aux(15)+aux(13) s(8) =< aux(6) with precondition: [Out=0,V1>=3,V>=2,V1>=V] * Chain [37,[45,47],48,49]: 5*it(45)+18*it(47)+1*s(8)+15*s(10)+1*s(184)+9 Such that:aux(24) =< V1 s(184) =< V aux(250) =< 1 aux(251) =< V1+1 s(10) =< aux(250) it(47) =< aux(251) aux(6) =< aux(251) it(45) =< aux(251) aux(6) =< aux(250)+aux(24) it(45) =< aux(250)+aux(24) s(8) =< aux(6) with precondition: [Out=0,V1>=4,V>=2,V1>=V] * Chain [37,[45,47],46,49]: 5*it(45)+9*it(47)+1*s(8)+1*s(34)+1*s(184)+9 Such that:aux(27) =< V1 s(184) =< V aux(256) =< 1 aux(257) =< V1+1 s(34) =< aux(256) aux(6) =< aux(257) it(45) =< aux(257) it(47) =< aux(257) aux(6) =< aux(256)+aux(27) it(45) =< aux(256)+aux(27) s(8) =< aux(6) with precondition: [Out=0,V1>=4,V>=2,V1>=V] * Chain [37,49]: 4*s(184)+5 Such that:aux(262) =< V s(184) =< aux(262) with precondition: [Out=0,V>=2,V1>=V] * Chain [37,48,49]: 15*s(10)+12*s(22)+1*s(184)+9 Such that:s(184) =< V aux(266) =< 1 aux(267) =< V1 s(10) =< aux(266) s(22) =< aux(267) with precondition: [Out=0,V1>=3,V>=2,V1>=V] * Chain [37,46,49]: 1*s(34)+4*s(184)+9 Such that:s(34) =< 1 aux(271) =< V s(184) =< aux(271) with precondition: [Out=0,V1>=3,V>=2,V1>=V] #### Cost of chains of encArg(V1,Out): * Chain [58]: 0 with precondition: [Out=0,V1>=0] * Chain [multiple([50,51,52,53,54,55,56,57],[[58]])]: 4*it(51)+478*it(55)+3*s(1790)+3*s(1792)+162*s(1795)+1147*s(1797)+135*s(1798)+27*s(1799)+30*s(1800)+6*s(1802)+648*s(1803)+42*s(1805)+42*s(1806)+72*s(1807)+216*s(1808)+36*s(1809)+1008*s(1810)+288*s(1811)+108*s(1812)+168*s(1813)+108*s(1814)+108*s(1817)+12*s(1818)+36*s(1819)+6*s(1820)+168*s(1821)+48*s(1822)+18*s(1823)+18*s(1824)+15*s(1825)+3*s(1826)+15*s(1827)+3*s(1828)+15*s(1829)+3*s(1830)+0 Such that:aux(302) =< V1 aux(303) =< V1/2 it(51) =< aux(302) it(55) =< aux(302) it(51) =< aux(303) aux(295) =< aux(302)+1 aux(297) =< aux(302) aux(287) =< aux(302)-1 s(1835) =< it(55)*aux(295) s(1832) =< it(55)*aux(297) s(1792) =< it(51)*aux(287) s(1791) =< it(51)*aux(287) s(1795) =< s(1832) s(1797) =< s(1835) s(1845) =< s(1835) s(1798) =< s(1835) s(1845) =< aux(302)+s(1835) s(1798) =< aux(302)+s(1835) s(1799) =< s(1845) s(1852) =< s(1835) s(1800) =< s(1835) s(1852) =< aux(302)+s(1832) s(1800) =< aux(302)+s(1832) s(1802) =< s(1852) s(1851) =< s(1835) s(1803) =< s(1835) s(1746) =< aux(295) s(1748) =< aux(295)-1 s(1851) =< s(1832)+s(1832)+s(1835) s(1803) =< s(1832)+s(1832)+s(1835) s(1805) =< s(1797)*aux(295) s(1846) =< s(1832)+s(1832)+s(1835) s(1848) =< s(1832)+s(1832)+s(1835) s(1847) =< s(1797)*s(1746) s(1806) =< s(1797)*s(1746) s(1850) =< s(1803)*s(1746) s(1849) =< s(1803)*aux(297) s(1848) =< s(1803)*s(1746) s(1807) =< s(1803)*aux(297) s(1808) =< s(1851) s(1809) =< s(1803)*s(1748) s(1846) =< s(1803)*aux(302) s(1810) =< s(1850) s(1811) =< s(1849) s(1812) =< s(1848) s(1813) =< s(1847) s(1814) =< s(1846) s(1842) =< s(1835) s(1817) =< s(1835) s(1843) =< s(1832) s(1843) =< s(1835) s(1842) =< s(1843)+s(1843)+s(1835) s(1817) =< s(1843)+s(1843)+s(1835) s(1838) =< s(1843)+s(1843)+s(1835) s(1839) =< s(1843)+s(1843)+s(1835) s(1841) =< s(1817)*s(1746) s(1840) =< s(1817)*aux(297) s(1839) =< s(1817)*s(1746) s(1818) =< s(1817)*aux(297) s(1819) =< s(1842) s(1820) =< s(1817)*s(1748) s(1838) =< s(1817)*aux(302) s(1821) =< s(1841) s(1822) =< s(1840) s(1823) =< s(1839) s(1824) =< s(1838) s(1837) =< s(1835) s(1825) =< s(1835) s(1837) =< s(1835)+s(1835) s(1825) =< s(1835)+s(1835) s(1826) =< s(1837) s(1834) =< s(1835) s(1827) =< s(1835) s(1834) =< s(1832)+s(1835) s(1827) =< s(1832)+s(1835) s(1828) =< s(1834) s(1831) =< s(1832) s(1829) =< s(1832) s(1831) =< aux(302)+s(1832) s(1829) =< aux(302)+s(1832) s(1830) =< s(1831) s(1790) =< s(1791) with precondition: [V1>=1,Out>=0,V1>=Out] #### Cost of chains of fun(V1,V,Out): * Chain [60]: 8*s(1856)+956*s(1857)+6*s(1863)+324*s(1865)+2294*s(1866)+270*s(1868)+54*s(1869)+60*s(1871)+12*s(1872)+1296*s(1874)+84*s(1877)+84*s(1881)+144*s(1884)+432*s(1885)+72*s(1886)+2016*s(1887)+576*s(1888)+216*s(1889)+336*s(1890)+216*s(1891)+216*s(1893)+24*s(1899)+72*s(1900)+12*s(1901)+336*s(1902)+96*s(1903)+36*s(1904)+36*s(1905)+30*s(1907)+6*s(1908)+30*s(1910)+6*s(1911)+30*s(1913)+6*s(1914)+6*s(1915)+8*s(1918)+956*s(1919)+6*s(1925)+324*s(1927)+2294*s(1928)+270*s(1930)+54*s(1931)+60*s(1933)+12*s(1934)+1296*s(1936)+84*s(1939)+84*s(1943)+144*s(1946)+432*s(1947)+72*s(1948)+2016*s(1949)+576*s(1950)+216*s(1951)+336*s(1952)+216*s(1953)+216*s(1955)+24*s(1961)+72*s(1962)+12*s(1963)+336*s(1964)+96*s(1965)+36*s(1966)+36*s(1967)+30*s(1969)+6*s(1970)+30*s(1972)+6*s(1973)+30*s(1975)+6*s(1976)+6*s(1977)+1 Such that:aux(304) =< V1 aux(305) =< V1/2 aux(306) =< V aux(307) =< V/2 s(1918) =< aux(304) s(1919) =< aux(304) s(1918) =< aux(305) s(1920) =< aux(304)+1 s(1921) =< aux(304) s(1922) =< aux(304)-1 s(1923) =< s(1919)*s(1920) s(1924) =< s(1919)*s(1921) s(1925) =< s(1918)*s(1922) s(1926) =< s(1918)*s(1922) s(1927) =< s(1924) s(1928) =< s(1923) s(1929) =< s(1923) s(1930) =< s(1923) s(1929) =< aux(304)+s(1923) s(1930) =< aux(304)+s(1923) s(1931) =< s(1929) s(1932) =< s(1923) s(1933) =< s(1923) s(1932) =< aux(304)+s(1924) s(1933) =< aux(304)+s(1924) s(1934) =< s(1932) s(1935) =< s(1923) s(1936) =< s(1923) s(1937) =< s(1920) s(1938) =< s(1920)-1 s(1935) =< s(1924)+s(1924)+s(1923) s(1936) =< s(1924)+s(1924)+s(1923) s(1939) =< s(1928)*s(1920) s(1940) =< s(1924)+s(1924)+s(1923) s(1941) =< s(1924)+s(1924)+s(1923) s(1942) =< s(1928)*s(1937) s(1943) =< s(1928)*s(1937) s(1944) =< s(1936)*s(1937) s(1945) =< s(1936)*s(1921) s(1941) =< s(1936)*s(1937) s(1946) =< s(1936)*s(1921) s(1947) =< s(1935) s(1948) =< s(1936)*s(1938) s(1940) =< s(1936)*aux(304) s(1949) =< s(1944) s(1950) =< s(1945) s(1951) =< s(1941) s(1952) =< s(1942) s(1953) =< s(1940) s(1954) =< s(1923) s(1955) =< s(1923) s(1956) =< s(1924) s(1956) =< s(1923) s(1954) =< s(1956)+s(1956)+s(1923) s(1955) =< s(1956)+s(1956)+s(1923) s(1957) =< s(1956)+s(1956)+s(1923) s(1958) =< s(1956)+s(1956)+s(1923) s(1959) =< s(1955)*s(1937) s(1960) =< s(1955)*s(1921) s(1958) =< s(1955)*s(1937) s(1961) =< s(1955)*s(1921) s(1962) =< s(1954) s(1963) =< s(1955)*s(1938) s(1957) =< s(1955)*aux(304) s(1964) =< s(1959) s(1965) =< s(1960) s(1966) =< s(1958) s(1967) =< s(1957) s(1968) =< s(1923) s(1969) =< s(1923) s(1968) =< s(1923)+s(1923) s(1969) =< s(1923)+s(1923) s(1970) =< s(1968) s(1971) =< s(1923) s(1972) =< s(1923) s(1971) =< s(1924)+s(1923) s(1972) =< s(1924)+s(1923) s(1973) =< s(1971) s(1974) =< s(1924) s(1975) =< s(1924) s(1974) =< aux(304)+s(1924) s(1975) =< aux(304)+s(1924) s(1976) =< s(1974) s(1977) =< s(1926) s(1856) =< aux(306) s(1857) =< aux(306) s(1856) =< aux(307) s(1858) =< aux(306)+1 s(1859) =< aux(306) s(1860) =< aux(306)-1 s(1861) =< s(1857)*s(1858) s(1862) =< s(1857)*s(1859) s(1863) =< s(1856)*s(1860) s(1864) =< s(1856)*s(1860) s(1865) =< s(1862) s(1866) =< s(1861) s(1867) =< s(1861) s(1868) =< s(1861) s(1867) =< aux(306)+s(1861) s(1868) =< aux(306)+s(1861) s(1869) =< s(1867) s(1870) =< s(1861) s(1871) =< s(1861) s(1870) =< aux(306)+s(1862) s(1871) =< aux(306)+s(1862) s(1872) =< s(1870) s(1873) =< s(1861) s(1874) =< s(1861) s(1875) =< s(1858) s(1876) =< s(1858)-1 s(1873) =< s(1862)+s(1862)+s(1861) s(1874) =< s(1862)+s(1862)+s(1861) s(1877) =< s(1866)*s(1858) s(1878) =< s(1862)+s(1862)+s(1861) s(1879) =< s(1862)+s(1862)+s(1861) s(1880) =< s(1866)*s(1875) s(1881) =< s(1866)*s(1875) s(1882) =< s(1874)*s(1875) s(1883) =< s(1874)*s(1859) s(1879) =< s(1874)*s(1875) s(1884) =< s(1874)*s(1859) s(1885) =< s(1873) s(1886) =< s(1874)*s(1876) s(1878) =< s(1874)*aux(306) s(1887) =< s(1882) s(1888) =< s(1883) s(1889) =< s(1879) s(1890) =< s(1880) s(1891) =< s(1878) s(1892) =< s(1861) s(1893) =< s(1861) s(1894) =< s(1862) s(1894) =< s(1861) s(1892) =< s(1894)+s(1894)+s(1861) s(1893) =< s(1894)+s(1894)+s(1861) s(1895) =< s(1894)+s(1894)+s(1861) s(1896) =< s(1894)+s(1894)+s(1861) s(1897) =< s(1893)*s(1875) s(1898) =< s(1893)*s(1859) s(1896) =< s(1893)*s(1875) s(1899) =< s(1893)*s(1859) s(1900) =< s(1892) s(1901) =< s(1893)*s(1876) s(1895) =< s(1893)*aux(306) s(1902) =< s(1897) s(1903) =< s(1898) s(1904) =< s(1896) s(1905) =< s(1895) s(1906) =< s(1861) s(1907) =< s(1861) s(1906) =< s(1861)+s(1861) s(1907) =< s(1861)+s(1861) s(1908) =< s(1906) s(1909) =< s(1861) s(1910) =< s(1861) s(1909) =< s(1862)+s(1861) s(1910) =< s(1862)+s(1861) s(1911) =< s(1909) s(1912) =< s(1862) s(1913) =< s(1862) s(1912) =< aux(306)+s(1862) s(1913) =< aux(306)+s(1862) s(1914) =< s(1912) s(1915) =< s(1864) with precondition: [Out=0,V1>=0,V>=0] * Chain [59]: 4*s(2104)+478*s(2105)+3*s(2111)+162*s(2113)+1147*s(2114)+135*s(2116)+27*s(2117)+30*s(2119)+6*s(2120)+648*s(2122)+42*s(2125)+42*s(2129)+72*s(2132)+216*s(2133)+36*s(2134)+1008*s(2135)+288*s(2136)+108*s(2137)+168*s(2138)+108*s(2139)+108*s(2141)+12*s(2147)+36*s(2148)+6*s(2149)+168*s(2150)+48*s(2151)+18*s(2152)+18*s(2153)+15*s(2155)+3*s(2156)+15*s(2158)+3*s(2159)+15*s(2161)+3*s(2162)+3*s(2163)+4*s(2166)+480*s(2167)+3*s(2173)+162*s(2175)+1147*s(2176)+135*s(2178)+27*s(2179)+30*s(2181)+6*s(2182)+648*s(2184)+42*s(2187)+42*s(2191)+72*s(2194)+216*s(2195)+36*s(2196)+1008*s(2197)+288*s(2198)+108*s(2199)+168*s(2200)+108*s(2201)+108*s(2203)+12*s(2209)+36*s(2210)+6*s(2211)+168*s(2212)+48*s(2213)+18*s(2214)+18*s(2215)+15*s(2217)+3*s(2218)+15*s(2220)+3*s(2221)+15*s(2223)+3*s(2224)+3*s(2225)+1 Such that:s(2102) =< V1 s(2103) =< V1/2 s(2165) =< V/2 aux(308) =< V s(2167) =< aux(308) s(2166) =< aux(308) s(2166) =< s(2165) s(2168) =< aux(308)+1 s(2169) =< aux(308) s(2170) =< aux(308)-1 s(2171) =< s(2167)*s(2168) s(2172) =< s(2167)*s(2169) s(2173) =< s(2166)*s(2170) s(2174) =< s(2166)*s(2170) s(2175) =< s(2172) s(2176) =< s(2171) s(2177) =< s(2171) s(2178) =< s(2171) s(2177) =< aux(308)+s(2171) s(2178) =< aux(308)+s(2171) s(2179) =< s(2177) s(2180) =< s(2171) s(2181) =< s(2171) s(2180) =< aux(308)+s(2172) s(2181) =< aux(308)+s(2172) s(2182) =< s(2180) s(2183) =< s(2171) s(2184) =< s(2171) s(2185) =< s(2168) s(2186) =< s(2168)-1 s(2183) =< s(2172)+s(2172)+s(2171) s(2184) =< s(2172)+s(2172)+s(2171) s(2187) =< s(2176)*s(2168) s(2188) =< s(2172)+s(2172)+s(2171) s(2189) =< s(2172)+s(2172)+s(2171) s(2190) =< s(2176)*s(2185) s(2191) =< s(2176)*s(2185) s(2192) =< s(2184)*s(2185) s(2193) =< s(2184)*s(2169) s(2189) =< s(2184)*s(2185) s(2194) =< s(2184)*s(2169) s(2195) =< s(2183) s(2196) =< s(2184)*s(2186) s(2188) =< s(2184)*aux(308) s(2197) =< s(2192) s(2198) =< s(2193) s(2199) =< s(2189) s(2200) =< s(2190) s(2201) =< s(2188) s(2202) =< s(2171) s(2203) =< s(2171) s(2204) =< s(2172) s(2204) =< s(2171) s(2202) =< s(2204)+s(2204)+s(2171) s(2203) =< s(2204)+s(2204)+s(2171) s(2205) =< s(2204)+s(2204)+s(2171) s(2206) =< s(2204)+s(2204)+s(2171) s(2207) =< s(2203)*s(2185) s(2208) =< s(2203)*s(2169) s(2206) =< s(2203)*s(2185) s(2209) =< s(2203)*s(2169) s(2210) =< s(2202) s(2211) =< s(2203)*s(2186) s(2205) =< s(2203)*aux(308) s(2212) =< s(2207) s(2213) =< s(2208) s(2214) =< s(2206) s(2215) =< s(2205) s(2216) =< s(2171) s(2217) =< s(2171) s(2216) =< s(2171)+s(2171) s(2217) =< s(2171)+s(2171) s(2218) =< s(2216) s(2219) =< s(2171) s(2220) =< s(2171) s(2219) =< s(2172)+s(2171) s(2220) =< s(2172)+s(2171) s(2221) =< s(2219) s(2222) =< s(2172) s(2223) =< s(2172) s(2222) =< aux(308)+s(2172) s(2223) =< aux(308)+s(2172) s(2224) =< s(2222) s(2225) =< s(2174) s(2104) =< s(2102) s(2105) =< s(2102) s(2104) =< s(2103) s(2106) =< s(2102)+1 s(2107) =< s(2102) s(2108) =< s(2102)-1 s(2109) =< s(2105)*s(2106) s(2110) =< s(2105)*s(2107) s(2111) =< s(2104)*s(2108) s(2112) =< s(2104)*s(2108) s(2113) =< s(2110) s(2114) =< s(2109) s(2115) =< s(2109) s(2116) =< s(2109) s(2115) =< s(2102)+s(2109) s(2116) =< s(2102)+s(2109) s(2117) =< s(2115) s(2118) =< s(2109) s(2119) =< s(2109) s(2118) =< s(2102)+s(2110) s(2119) =< s(2102)+s(2110) s(2120) =< s(2118) s(2121) =< s(2109) s(2122) =< s(2109) s(2123) =< s(2106) s(2124) =< s(2106)-1 s(2121) =< s(2110)+s(2110)+s(2109) s(2122) =< s(2110)+s(2110)+s(2109) s(2125) =< s(2114)*s(2106) s(2126) =< s(2110)+s(2110)+s(2109) s(2127) =< s(2110)+s(2110)+s(2109) s(2128) =< s(2114)*s(2123) s(2129) =< s(2114)*s(2123) s(2130) =< s(2122)*s(2123) s(2131) =< s(2122)*s(2107) s(2127) =< s(2122)*s(2123) s(2132) =< s(2122)*s(2107) s(2133) =< s(2121) s(2134) =< s(2122)*s(2124) s(2126) =< s(2122)*s(2102) s(2135) =< s(2130) s(2136) =< s(2131) s(2137) =< s(2127) s(2138) =< s(2128) s(2139) =< s(2126) s(2140) =< s(2109) s(2141) =< s(2109) s(2142) =< s(2110) s(2142) =< s(2109) s(2140) =< s(2142)+s(2142)+s(2109) s(2141) =< s(2142)+s(2142)+s(2109) s(2143) =< s(2142)+s(2142)+s(2109) s(2144) =< s(2142)+s(2142)+s(2109) s(2145) =< s(2141)*s(2123) s(2146) =< s(2141)*s(2107) s(2144) =< s(2141)*s(2123) s(2147) =< s(2141)*s(2107) s(2148) =< s(2140) s(2149) =< s(2141)*s(2124) s(2143) =< s(2141)*s(2102) s(2150) =< s(2145) s(2151) =< s(2146) s(2152) =< s(2144) s(2153) =< s(2143) s(2154) =< s(2109) s(2155) =< s(2109) s(2154) =< s(2109)+s(2109) s(2155) =< s(2109)+s(2109) s(2156) =< s(2154) s(2157) =< s(2109) s(2158) =< s(2109) s(2157) =< s(2110)+s(2109) s(2158) =< s(2110)+s(2109) s(2159) =< s(2157) s(2160) =< s(2110) s(2161) =< s(2110) s(2160) =< s(2102)+s(2110) s(2161) =< s(2102)+s(2110) s(2162) =< s(2160) s(2163) =< s(2112) with precondition: [Out>=1,V1>=Out,V>=Out] #### Cost of chains of fun2(V1,Out): * Chain [63]: 0 with precondition: [Out=0,V1>=0] * Chain [62]: 0 with precondition: [Out=1,V1>=0] * Chain [61]: 4*s(2230)+478*s(2231)+3*s(2237)+162*s(2239)+1147*s(2240)+135*s(2242)+27*s(2243)+30*s(2245)+6*s(2246)+648*s(2248)+42*s(2251)+42*s(2255)+72*s(2258)+216*s(2259)+36*s(2260)+1008*s(2261)+288*s(2262)+108*s(2263)+168*s(2264)+108*s(2265)+108*s(2267)+12*s(2273)+36*s(2274)+6*s(2275)+168*s(2276)+48*s(2277)+18*s(2278)+18*s(2279)+15*s(2281)+3*s(2282)+15*s(2284)+3*s(2285)+15*s(2287)+3*s(2288)+3*s(2289)+0 Such that:s(2228) =< V1 s(2229) =< V1/2 s(2230) =< s(2228) s(2231) =< s(2228) s(2230) =< s(2229) s(2232) =< s(2228)+1 s(2233) =< s(2228) s(2234) =< s(2228)-1 s(2235) =< s(2231)*s(2232) s(2236) =< s(2231)*s(2233) s(2237) =< s(2230)*s(2234) s(2238) =< s(2230)*s(2234) s(2239) =< s(2236) s(2240) =< s(2235) s(2241) =< s(2235) s(2242) =< s(2235) s(2241) =< s(2228)+s(2235) s(2242) =< s(2228)+s(2235) s(2243) =< s(2241) s(2244) =< s(2235) s(2245) =< s(2235) s(2244) =< s(2228)+s(2236) s(2245) =< s(2228)+s(2236) s(2246) =< s(2244) s(2247) =< s(2235) s(2248) =< s(2235) s(2249) =< s(2232) s(2250) =< s(2232)-1 s(2247) =< s(2236)+s(2236)+s(2235) s(2248) =< s(2236)+s(2236)+s(2235) s(2251) =< s(2240)*s(2232) s(2252) =< s(2236)+s(2236)+s(2235) s(2253) =< s(2236)+s(2236)+s(2235) s(2254) =< s(2240)*s(2249) s(2255) =< s(2240)*s(2249) s(2256) =< s(2248)*s(2249) s(2257) =< s(2248)*s(2233) s(2253) =< s(2248)*s(2249) s(2258) =< s(2248)*s(2233) s(2259) =< s(2247) s(2260) =< s(2248)*s(2250) s(2252) =< s(2248)*s(2228) s(2261) =< s(2256) s(2262) =< s(2257) s(2263) =< s(2253) s(2264) =< s(2254) s(2265) =< s(2252) s(2266) =< s(2235) s(2267) =< s(2235) s(2268) =< s(2236) s(2268) =< s(2235) s(2266) =< s(2268)+s(2268)+s(2235) s(2267) =< s(2268)+s(2268)+s(2235) s(2269) =< s(2268)+s(2268)+s(2235) s(2270) =< s(2268)+s(2268)+s(2235) s(2271) =< s(2267)*s(2249) s(2272) =< s(2267)*s(2233) s(2270) =< s(2267)*s(2249) s(2273) =< s(2267)*s(2233) s(2274) =< s(2266) s(2275) =< s(2267)*s(2250) s(2269) =< s(2267)*s(2228) s(2276) =< s(2271) s(2277) =< s(2272) s(2278) =< s(2270) s(2279) =< s(2269) s(2280) =< s(2235) s(2281) =< s(2235) s(2280) =< s(2235)+s(2235) s(2281) =< s(2235)+s(2235) s(2282) =< s(2280) s(2283) =< s(2235) s(2284) =< s(2235) s(2283) =< s(2236)+s(2235) s(2284) =< s(2236)+s(2235) s(2285) =< s(2283) s(2286) =< s(2236) s(2287) =< s(2236) s(2286) =< s(2228)+s(2236) s(2287) =< s(2228)+s(2236) s(2288) =< s(2286) s(2289) =< s(2238) with precondition: [V1>=1,Out>=1,V1+1>=Out] #### Cost of chains of fun3(V1,V,Out): * Chain [66]: 12*s(2292)+1434*s(2293)+9*s(2299)+486*s(2301)+3441*s(2302)+405*s(2304)+81*s(2305)+90*s(2307)+18*s(2308)+1944*s(2310)+126*s(2313)+126*s(2317)+216*s(2320)+648*s(2321)+108*s(2322)+3024*s(2323)+864*s(2324)+324*s(2325)+504*s(2326)+324*s(2327)+324*s(2329)+36*s(2335)+108*s(2336)+18*s(2337)+504*s(2338)+144*s(2339)+54*s(2340)+54*s(2341)+45*s(2343)+9*s(2344)+45*s(2346)+9*s(2347)+45*s(2349)+9*s(2350)+9*s(2351)+12*s(2416)+1434*s(2417)+9*s(2423)+486*s(2425)+3441*s(2426)+405*s(2428)+81*s(2429)+90*s(2431)+18*s(2432)+1944*s(2434)+126*s(2437)+126*s(2441)+216*s(2444)+648*s(2445)+108*s(2446)+3024*s(2447)+864*s(2448)+324*s(2449)+504*s(2450)+324*s(2451)+324*s(2453)+36*s(2459)+108*s(2460)+18*s(2461)+504*s(2462)+144*s(2463)+54*s(2464)+54*s(2465)+45*s(2467)+9*s(2468)+45*s(2470)+9*s(2471)+45*s(2473)+9*s(2474)+9*s(2475)+1 Such that:aux(309) =< V1 aux(310) =< V1/2 aux(311) =< V aux(312) =< V/2 s(2416) =< aux(309) s(2417) =< aux(309) s(2416) =< aux(310) s(2418) =< aux(309)+1 s(2419) =< aux(309) s(2420) =< aux(309)-1 s(2421) =< s(2417)*s(2418) s(2422) =< s(2417)*s(2419) s(2423) =< s(2416)*s(2420) s(2424) =< s(2416)*s(2420) s(2425) =< s(2422) s(2426) =< s(2421) s(2427) =< s(2421) s(2428) =< s(2421) s(2427) =< aux(309)+s(2421) s(2428) =< aux(309)+s(2421) s(2429) =< s(2427) s(2430) =< s(2421) s(2431) =< s(2421) s(2430) =< aux(309)+s(2422) s(2431) =< aux(309)+s(2422) s(2432) =< s(2430) s(2433) =< s(2421) s(2434) =< s(2421) s(2435) =< s(2418) s(2436) =< s(2418)-1 s(2433) =< s(2422)+s(2422)+s(2421) s(2434) =< s(2422)+s(2422)+s(2421) s(2437) =< s(2426)*s(2418) s(2438) =< s(2422)+s(2422)+s(2421) s(2439) =< s(2422)+s(2422)+s(2421) s(2440) =< s(2426)*s(2435) s(2441) =< s(2426)*s(2435) s(2442) =< s(2434)*s(2435) s(2443) =< s(2434)*s(2419) s(2439) =< s(2434)*s(2435) s(2444) =< s(2434)*s(2419) s(2445) =< s(2433) s(2446) =< s(2434)*s(2436) s(2438) =< s(2434)*aux(309) s(2447) =< s(2442) s(2448) =< s(2443) s(2449) =< s(2439) s(2450) =< s(2440) s(2451) =< s(2438) s(2452) =< s(2421) s(2453) =< s(2421) s(2454) =< s(2422) s(2454) =< s(2421) s(2452) =< s(2454)+s(2454)+s(2421) s(2453) =< s(2454)+s(2454)+s(2421) s(2455) =< s(2454)+s(2454)+s(2421) s(2456) =< s(2454)+s(2454)+s(2421) s(2457) =< s(2453)*s(2435) s(2458) =< s(2453)*s(2419) s(2456) =< s(2453)*s(2435) s(2459) =< s(2453)*s(2419) s(2460) =< s(2452) s(2461) =< s(2453)*s(2436) s(2455) =< s(2453)*aux(309) s(2462) =< s(2457) s(2463) =< s(2458) s(2464) =< s(2456) s(2465) =< s(2455) s(2466) =< s(2421) s(2467) =< s(2421) s(2466) =< s(2421)+s(2421) s(2467) =< s(2421)+s(2421) s(2468) =< s(2466) s(2469) =< s(2421) s(2470) =< s(2421) s(2469) =< s(2422)+s(2421) s(2470) =< s(2422)+s(2421) s(2471) =< s(2469) s(2472) =< s(2422) s(2473) =< s(2422) s(2472) =< aux(309)+s(2422) s(2473) =< aux(309)+s(2422) s(2474) =< s(2472) s(2475) =< s(2424) s(2292) =< aux(311) s(2293) =< aux(311) s(2292) =< aux(312) s(2294) =< aux(311)+1 s(2295) =< aux(311) s(2296) =< aux(311)-1 s(2297) =< s(2293)*s(2294) s(2298) =< s(2293)*s(2295) s(2299) =< s(2292)*s(2296) s(2300) =< s(2292)*s(2296) s(2301) =< s(2298) s(2302) =< s(2297) s(2303) =< s(2297) s(2304) =< s(2297) s(2303) =< aux(311)+s(2297) s(2304) =< aux(311)+s(2297) s(2305) =< s(2303) s(2306) =< s(2297) s(2307) =< s(2297) s(2306) =< aux(311)+s(2298) s(2307) =< aux(311)+s(2298) s(2308) =< s(2306) s(2309) =< s(2297) s(2310) =< s(2297) s(2311) =< s(2294) s(2312) =< s(2294)-1 s(2309) =< s(2298)+s(2298)+s(2297) s(2310) =< s(2298)+s(2298)+s(2297) s(2313) =< s(2302)*s(2294) s(2314) =< s(2298)+s(2298)+s(2297) s(2315) =< s(2298)+s(2298)+s(2297) s(2316) =< s(2302)*s(2311) s(2317) =< s(2302)*s(2311) s(2318) =< s(2310)*s(2311) s(2319) =< s(2310)*s(2295) s(2315) =< s(2310)*s(2311) s(2320) =< s(2310)*s(2295) s(2321) =< s(2309) s(2322) =< s(2310)*s(2312) s(2314) =< s(2310)*aux(311) s(2323) =< s(2318) s(2324) =< s(2319) s(2325) =< s(2315) s(2326) =< s(2316) s(2327) =< s(2314) s(2328) =< s(2297) s(2329) =< s(2297) s(2330) =< s(2298) s(2330) =< s(2297) s(2328) =< s(2330)+s(2330)+s(2297) s(2329) =< s(2330)+s(2330)+s(2297) s(2331) =< s(2330)+s(2330)+s(2297) s(2332) =< s(2330)+s(2330)+s(2297) s(2333) =< s(2329)*s(2311) s(2334) =< s(2329)*s(2295) s(2332) =< s(2329)*s(2311) s(2335) =< s(2329)*s(2295) s(2336) =< s(2328) s(2337) =< s(2329)*s(2312) s(2331) =< s(2329)*aux(311) s(2338) =< s(2333) s(2339) =< s(2334) s(2340) =< s(2332) s(2341) =< s(2331) s(2342) =< s(2297) s(2343) =< s(2297) s(2342) =< s(2297)+s(2297) s(2343) =< s(2297)+s(2297) s(2344) =< s(2342) s(2345) =< s(2297) s(2346) =< s(2297) s(2345) =< s(2298)+s(2297) s(2346) =< s(2298)+s(2297) s(2347) =< s(2345) s(2348) =< s(2298) s(2349) =< s(2298) s(2348) =< aux(311)+s(2298) s(2349) =< aux(311)+s(2298) s(2350) =< s(2348) s(2351) =< s(2300) with precondition: [Out=0,V1>=0,V>=0] * Chain [65]: 16*s(2664)+1914*s(2665)+12*s(2671)+648*s(2673)+4588*s(2674)+540*s(2676)+108*s(2677)+120*s(2679)+24*s(2680)+2592*s(2682)+168*s(2685)+168*s(2689)+288*s(2692)+864*s(2693)+144*s(2694)+4032*s(2695)+1152*s(2696)+432*s(2697)+672*s(2698)+432*s(2699)+432*s(2701)+48*s(2707)+144*s(2708)+24*s(2709)+672*s(2710)+192*s(2711)+72*s(2712)+72*s(2713)+60*s(2715)+12*s(2716)+60*s(2718)+12*s(2719)+60*s(2721)+12*s(2722)+12*s(2723)+12*s(2726)+1434*s(2727)+9*s(2733)+486*s(2735)+3441*s(2736)+405*s(2738)+81*s(2739)+90*s(2741)+18*s(2742)+1944*s(2744)+126*s(2747)+126*s(2751)+216*s(2754)+648*s(2755)+108*s(2756)+3024*s(2757)+864*s(2758)+324*s(2759)+504*s(2760)+324*s(2761)+324*s(2763)+36*s(2769)+108*s(2770)+18*s(2771)+504*s(2772)+144*s(2773)+54*s(2774)+54*s(2775)+45*s(2777)+9*s(2778)+45*s(2780)+9*s(2781)+45*s(2783)+9*s(2784)+9*s(2785)+1 Such that:aux(315) =< V1 aux(316) =< V1/2 aux(317) =< V aux(318) =< V/2 s(2664) =< aux(317) s(2665) =< aux(317) s(2664) =< aux(318) s(2666) =< aux(317)+1 s(2667) =< aux(317) s(2668) =< aux(317)-1 s(2669) =< s(2665)*s(2666) s(2670) =< s(2665)*s(2667) s(2671) =< s(2664)*s(2668) s(2672) =< s(2664)*s(2668) s(2673) =< s(2670) s(2674) =< s(2669) s(2675) =< s(2669) s(2676) =< s(2669) s(2675) =< aux(317)+s(2669) s(2676) =< aux(317)+s(2669) s(2677) =< s(2675) s(2678) =< s(2669) s(2679) =< s(2669) s(2678) =< aux(317)+s(2670) s(2679) =< aux(317)+s(2670) s(2680) =< s(2678) s(2681) =< s(2669) s(2682) =< s(2669) s(2683) =< s(2666) s(2684) =< s(2666)-1 s(2681) =< s(2670)+s(2670)+s(2669) s(2682) =< s(2670)+s(2670)+s(2669) s(2685) =< s(2674)*s(2666) s(2686) =< s(2670)+s(2670)+s(2669) s(2687) =< s(2670)+s(2670)+s(2669) s(2688) =< s(2674)*s(2683) s(2689) =< s(2674)*s(2683) s(2690) =< s(2682)*s(2683) s(2691) =< s(2682)*s(2667) s(2687) =< s(2682)*s(2683) s(2692) =< s(2682)*s(2667) s(2693) =< s(2681) s(2694) =< s(2682)*s(2684) s(2686) =< s(2682)*aux(317) s(2695) =< s(2690) s(2696) =< s(2691) s(2697) =< s(2687) s(2698) =< s(2688) s(2699) =< s(2686) s(2700) =< s(2669) s(2701) =< s(2669) s(2702) =< s(2670) s(2702) =< s(2669) s(2700) =< s(2702)+s(2702)+s(2669) s(2701) =< s(2702)+s(2702)+s(2669) s(2703) =< s(2702)+s(2702)+s(2669) s(2704) =< s(2702)+s(2702)+s(2669) s(2705) =< s(2701)*s(2683) s(2706) =< s(2701)*s(2667) s(2704) =< s(2701)*s(2683) s(2707) =< s(2701)*s(2667) s(2708) =< s(2700) s(2709) =< s(2701)*s(2684) s(2703) =< s(2701)*aux(317) s(2710) =< s(2705) s(2711) =< s(2706) s(2712) =< s(2704) s(2713) =< s(2703) s(2714) =< s(2669) s(2715) =< s(2669) s(2714) =< s(2669)+s(2669) s(2715) =< s(2669)+s(2669) s(2716) =< s(2714) s(2717) =< s(2669) s(2718) =< s(2669) s(2717) =< s(2670)+s(2669) s(2718) =< s(2670)+s(2669) s(2719) =< s(2717) s(2720) =< s(2670) s(2721) =< s(2670) s(2720) =< aux(317)+s(2670) s(2721) =< aux(317)+s(2670) s(2722) =< s(2720) s(2723) =< s(2672) s(2726) =< aux(315) s(2727) =< aux(315) s(2726) =< aux(316) s(2728) =< aux(315)+1 s(2729) =< aux(315) s(2730) =< aux(315)-1 s(2731) =< s(2727)*s(2728) s(2732) =< s(2727)*s(2729) s(2733) =< s(2726)*s(2730) s(2734) =< s(2726)*s(2730) s(2735) =< s(2732) s(2736) =< s(2731) s(2737) =< s(2731) s(2738) =< s(2731) s(2737) =< aux(315)+s(2731) s(2738) =< aux(315)+s(2731) s(2739) =< s(2737) s(2740) =< s(2731) s(2741) =< s(2731) s(2740) =< aux(315)+s(2732) s(2741) =< aux(315)+s(2732) s(2742) =< s(2740) s(2743) =< s(2731) s(2744) =< s(2731) s(2745) =< s(2728) s(2746) =< s(2728)-1 s(2743) =< s(2732)+s(2732)+s(2731) s(2744) =< s(2732)+s(2732)+s(2731) s(2747) =< s(2736)*s(2728) s(2748) =< s(2732)+s(2732)+s(2731) s(2749) =< s(2732)+s(2732)+s(2731) s(2750) =< s(2736)*s(2745) s(2751) =< s(2736)*s(2745) s(2752) =< s(2744)*s(2745) s(2753) =< s(2744)*s(2729) s(2749) =< s(2744)*s(2745) s(2754) =< s(2744)*s(2729) s(2755) =< s(2743) s(2756) =< s(2744)*s(2746) s(2748) =< s(2744)*aux(315) s(2757) =< s(2752) s(2758) =< s(2753) s(2759) =< s(2749) s(2760) =< s(2750) s(2761) =< s(2748) s(2762) =< s(2731) s(2763) =< s(2731) s(2764) =< s(2732) s(2764) =< s(2731) s(2762) =< s(2764)+s(2764)+s(2731) s(2763) =< s(2764)+s(2764)+s(2731) s(2765) =< s(2764)+s(2764)+s(2731) s(2766) =< s(2764)+s(2764)+s(2731) s(2767) =< s(2763)*s(2745) s(2768) =< s(2763)*s(2729) s(2766) =< s(2763)*s(2745) s(2769) =< s(2763)*s(2729) s(2770) =< s(2762) s(2771) =< s(2763)*s(2746) s(2765) =< s(2763)*aux(315) s(2772) =< s(2767) s(2773) =< s(2768) s(2774) =< s(2766) s(2775) =< s(2765) s(2776) =< s(2731) s(2777) =< s(2731) s(2776) =< s(2731)+s(2731) s(2777) =< s(2731)+s(2731) s(2778) =< s(2776) s(2779) =< s(2731) s(2780) =< s(2731) s(2779) =< s(2732)+s(2731) s(2780) =< s(2732)+s(2731) s(2781) =< s(2779) s(2782) =< s(2732) s(2783) =< s(2732) s(2782) =< aux(315)+s(2732) s(2783) =< aux(315)+s(2732) s(2784) =< s(2782) s(2785) =< s(2734) with precondition: [V1>=0,V>=1,Out>=0,V>=Out] * Chain [64]: 12*s(3100)+1434*s(3101)+9*s(3107)+486*s(3109)+3441*s(3110)+405*s(3112)+81*s(3113)+90*s(3115)+18*s(3116)+1944*s(3118)+126*s(3121)+126*s(3125)+216*s(3128)+648*s(3129)+108*s(3130)+3024*s(3131)+864*s(3132)+324*s(3133)+504*s(3134)+324*s(3135)+324*s(3137)+36*s(3143)+108*s(3144)+18*s(3145)+504*s(3146)+144*s(3147)+54*s(3148)+54*s(3149)+45*s(3151)+9*s(3152)+45*s(3154)+9*s(3155)+45*s(3157)+9*s(3158)+9*s(3159)+8*s(3224)+957*s(3225)+6*s(3231)+324*s(3233)+2294*s(3234)+270*s(3236)+54*s(3237)+60*s(3239)+12*s(3240)+1296*s(3242)+84*s(3245)+84*s(3249)+144*s(3252)+432*s(3253)+72*s(3254)+2016*s(3255)+576*s(3256)+216*s(3257)+336*s(3258)+216*s(3259)+216*s(3261)+24*s(3267)+72*s(3268)+12*s(3269)+336*s(3270)+96*s(3271)+36*s(3272)+36*s(3273)+30*s(3275)+6*s(3276)+30*s(3278)+6*s(3279)+30*s(3281)+6*s(3282)+6*s(3283)+1 Such that:aux(320) =< V1 aux(321) =< V1/2 aux(322) =< V aux(323) =< V/2 s(3100) =< aux(320) s(3101) =< aux(320) s(3100) =< aux(321) s(3102) =< aux(320)+1 s(3103) =< aux(320) s(3104) =< aux(320)-1 s(3105) =< s(3101)*s(3102) s(3106) =< s(3101)*s(3103) s(3107) =< s(3100)*s(3104) s(3108) =< s(3100)*s(3104) s(3109) =< s(3106) s(3110) =< s(3105) s(3111) =< s(3105) s(3112) =< s(3105) s(3111) =< aux(320)+s(3105) s(3112) =< aux(320)+s(3105) s(3113) =< s(3111) s(3114) =< s(3105) s(3115) =< s(3105) s(3114) =< aux(320)+s(3106) s(3115) =< aux(320)+s(3106) s(3116) =< s(3114) s(3117) =< s(3105) s(3118) =< s(3105) s(3119) =< s(3102) s(3120) =< s(3102)-1 s(3117) =< s(3106)+s(3106)+s(3105) s(3118) =< s(3106)+s(3106)+s(3105) s(3121) =< s(3110)*s(3102) s(3122) =< s(3106)+s(3106)+s(3105) s(3123) =< s(3106)+s(3106)+s(3105) s(3124) =< s(3110)*s(3119) s(3125) =< s(3110)*s(3119) s(3126) =< s(3118)*s(3119) s(3127) =< s(3118)*s(3103) s(3123) =< s(3118)*s(3119) s(3128) =< s(3118)*s(3103) s(3129) =< s(3117) s(3130) =< s(3118)*s(3120) s(3122) =< s(3118)*aux(320) s(3131) =< s(3126) s(3132) =< s(3127) s(3133) =< s(3123) s(3134) =< s(3124) s(3135) =< s(3122) s(3136) =< s(3105) s(3137) =< s(3105) s(3138) =< s(3106) s(3138) =< s(3105) s(3136) =< s(3138)+s(3138)+s(3105) s(3137) =< s(3138)+s(3138)+s(3105) s(3139) =< s(3138)+s(3138)+s(3105) s(3140) =< s(3138)+s(3138)+s(3105) s(3141) =< s(3137)*s(3119) s(3142) =< s(3137)*s(3103) s(3140) =< s(3137)*s(3119) s(3143) =< s(3137)*s(3103) s(3144) =< s(3136) s(3145) =< s(3137)*s(3120) s(3139) =< s(3137)*aux(320) s(3146) =< s(3141) s(3147) =< s(3142) s(3148) =< s(3140) s(3149) =< s(3139) s(3150) =< s(3105) s(3151) =< s(3105) s(3150) =< s(3105)+s(3105) s(3151) =< s(3105)+s(3105) s(3152) =< s(3150) s(3153) =< s(3105) s(3154) =< s(3105) s(3153) =< s(3106)+s(3105) s(3154) =< s(3106)+s(3105) s(3155) =< s(3153) s(3156) =< s(3106) s(3157) =< s(3106) s(3156) =< aux(320)+s(3106) s(3157) =< aux(320)+s(3106) s(3158) =< s(3156) s(3159) =< s(3108) s(3224) =< aux(322) s(3225) =< aux(322) s(3224) =< aux(323) s(3226) =< aux(322)+1 s(3227) =< aux(322) s(3228) =< aux(322)-1 s(3229) =< s(3225)*s(3226) s(3230) =< s(3225)*s(3227) s(3231) =< s(3224)*s(3228) s(3232) =< s(3224)*s(3228) s(3233) =< s(3230) s(3234) =< s(3229) s(3235) =< s(3229) s(3236) =< s(3229) s(3235) =< aux(322)+s(3229) s(3236) =< aux(322)+s(3229) s(3237) =< s(3235) s(3238) =< s(3229) s(3239) =< s(3229) s(3238) =< aux(322)+s(3230) s(3239) =< aux(322)+s(3230) s(3240) =< s(3238) s(3241) =< s(3229) s(3242) =< s(3229) s(3243) =< s(3226) s(3244) =< s(3226)-1 s(3241) =< s(3230)+s(3230)+s(3229) s(3242) =< s(3230)+s(3230)+s(3229) s(3245) =< s(3234)*s(3226) s(3246) =< s(3230)+s(3230)+s(3229) s(3247) =< s(3230)+s(3230)+s(3229) s(3248) =< s(3234)*s(3243) s(3249) =< s(3234)*s(3243) s(3250) =< s(3242)*s(3243) s(3251) =< s(3242)*s(3227) s(3247) =< s(3242)*s(3243) s(3252) =< s(3242)*s(3227) s(3253) =< s(3241) s(3254) =< s(3242)*s(3244) s(3246) =< s(3242)*aux(322) s(3255) =< s(3250) s(3256) =< s(3251) s(3257) =< s(3247) s(3258) =< s(3248) s(3259) =< s(3246) s(3260) =< s(3229) s(3261) =< s(3229) s(3262) =< s(3230) s(3262) =< s(3229) s(3260) =< s(3262)+s(3262)+s(3229) s(3261) =< s(3262)+s(3262)+s(3229) s(3263) =< s(3262)+s(3262)+s(3229) s(3264) =< s(3262)+s(3262)+s(3229) s(3265) =< s(3261)*s(3243) s(3266) =< s(3261)*s(3227) s(3264) =< s(3261)*s(3243) s(3267) =< s(3261)*s(3227) s(3268) =< s(3260) s(3269) =< s(3261)*s(3244) s(3263) =< s(3261)*aux(322) s(3270) =< s(3265) s(3271) =< s(3266) s(3272) =< s(3264) s(3273) =< s(3263) s(3274) =< s(3229) s(3275) =< s(3229) s(3274) =< s(3229)+s(3229) s(3275) =< s(3229)+s(3229) s(3276) =< s(3274) s(3277) =< s(3229) s(3278) =< s(3229) s(3277) =< s(3230)+s(3229) s(3278) =< s(3230)+s(3229) s(3279) =< s(3277) s(3280) =< s(3230) s(3281) =< s(3230) s(3280) =< aux(322)+s(3230) s(3281) =< aux(322)+s(3230) s(3282) =< s(3280) s(3283) =< s(3232) with precondition: [V1>=1,V>=0,Out>=0,V1>=Out] #### Cost of chains of fun4(V1,V,Out): * Chain [68]: 12*s(3412)+1436*s(3413)+9*s(3419)+486*s(3421)+3441*s(3422)+405*s(3424)+81*s(3425)+90*s(3427)+18*s(3428)+1944*s(3430)+126*s(3433)+126*s(3437)+216*s(3440)+648*s(3441)+108*s(3442)+3024*s(3443)+864*s(3444)+324*s(3445)+504*s(3446)+324*s(3447)+324*s(3449)+36*s(3455)+108*s(3456)+18*s(3457)+504*s(3458)+144*s(3459)+54*s(3460)+54*s(3461)+45*s(3463)+9*s(3464)+45*s(3466)+9*s(3467)+45*s(3469)+9*s(3470)+9*s(3471)+8*s(3537)+956*s(3538)+6*s(3544)+324*s(3546)+2294*s(3547)+270*s(3549)+54*s(3550)+60*s(3552)+12*s(3553)+1296*s(3555)+84*s(3558)+84*s(3562)+144*s(3565)+432*s(3566)+72*s(3567)+2016*s(3568)+576*s(3569)+216*s(3570)+336*s(3571)+216*s(3572)+216*s(3574)+24*s(3580)+72*s(3581)+12*s(3582)+336*s(3583)+96*s(3584)+36*s(3585)+36*s(3586)+30*s(3588)+6*s(3589)+30*s(3591)+6*s(3592)+30*s(3594)+6*s(3595)+6*s(3596)+1 Such that:aux(326) =< V1 aux(327) =< V1/2 aux(328) =< V aux(329) =< V/2 s(3537) =< aux(326) s(3538) =< aux(326) s(3537) =< aux(327) s(3539) =< aux(326)+1 s(3540) =< aux(326) s(3541) =< aux(326)-1 s(3542) =< s(3538)*s(3539) s(3543) =< s(3538)*s(3540) s(3544) =< s(3537)*s(3541) s(3545) =< s(3537)*s(3541) s(3546) =< s(3543) s(3547) =< s(3542) s(3548) =< s(3542) s(3549) =< s(3542) s(3548) =< aux(326)+s(3542) s(3549) =< aux(326)+s(3542) s(3550) =< s(3548) s(3551) =< s(3542) s(3552) =< s(3542) s(3551) =< aux(326)+s(3543) s(3552) =< aux(326)+s(3543) s(3553) =< s(3551) s(3554) =< s(3542) s(3555) =< s(3542) s(3556) =< s(3539) s(3557) =< s(3539)-1 s(3554) =< s(3543)+s(3543)+s(3542) s(3555) =< s(3543)+s(3543)+s(3542) s(3558) =< s(3547)*s(3539) s(3559) =< s(3543)+s(3543)+s(3542) s(3560) =< s(3543)+s(3543)+s(3542) s(3561) =< s(3547)*s(3556) s(3562) =< s(3547)*s(3556) s(3563) =< s(3555)*s(3556) s(3564) =< s(3555)*s(3540) s(3560) =< s(3555)*s(3556) s(3565) =< s(3555)*s(3540) s(3566) =< s(3554) s(3567) =< s(3555)*s(3557) s(3559) =< s(3555)*aux(326) s(3568) =< s(3563) s(3569) =< s(3564) s(3570) =< s(3560) s(3571) =< s(3561) s(3572) =< s(3559) s(3573) =< s(3542) s(3574) =< s(3542) s(3575) =< s(3543) s(3575) =< s(3542) s(3573) =< s(3575)+s(3575)+s(3542) s(3574) =< s(3575)+s(3575)+s(3542) s(3576) =< s(3575)+s(3575)+s(3542) s(3577) =< s(3575)+s(3575)+s(3542) s(3578) =< s(3574)*s(3556) s(3579) =< s(3574)*s(3540) s(3577) =< s(3574)*s(3556) s(3580) =< s(3574)*s(3540) s(3581) =< s(3573) s(3582) =< s(3574)*s(3557) s(3576) =< s(3574)*aux(326) s(3583) =< s(3578) s(3584) =< s(3579) s(3585) =< s(3577) s(3586) =< s(3576) s(3587) =< s(3542) s(3588) =< s(3542) s(3587) =< s(3542)+s(3542) s(3588) =< s(3542)+s(3542) s(3589) =< s(3587) s(3590) =< s(3542) s(3591) =< s(3542) s(3590) =< s(3543)+s(3542) s(3591) =< s(3543)+s(3542) s(3592) =< s(3590) s(3593) =< s(3543) s(3594) =< s(3543) s(3593) =< aux(326)+s(3543) s(3594) =< aux(326)+s(3543) s(3595) =< s(3593) s(3596) =< s(3545) s(3413) =< aux(328) s(3412) =< aux(328) s(3412) =< aux(329) s(3414) =< aux(328)+1 s(3415) =< aux(328) s(3416) =< aux(328)-1 s(3417) =< s(3413)*s(3414) s(3418) =< s(3413)*s(3415) s(3419) =< s(3412)*s(3416) s(3420) =< s(3412)*s(3416) s(3421) =< s(3418) s(3422) =< s(3417) s(3423) =< s(3417) s(3424) =< s(3417) s(3423) =< aux(328)+s(3417) s(3424) =< aux(328)+s(3417) s(3425) =< s(3423) s(3426) =< s(3417) s(3427) =< s(3417) s(3426) =< aux(328)+s(3418) s(3427) =< aux(328)+s(3418) s(3428) =< s(3426) s(3429) =< s(3417) s(3430) =< s(3417) s(3431) =< s(3414) s(3432) =< s(3414)-1 s(3429) =< s(3418)+s(3418)+s(3417) s(3430) =< s(3418)+s(3418)+s(3417) s(3433) =< s(3422)*s(3414) s(3434) =< s(3418)+s(3418)+s(3417) s(3435) =< s(3418)+s(3418)+s(3417) s(3436) =< s(3422)*s(3431) s(3437) =< s(3422)*s(3431) s(3438) =< s(3430)*s(3431) s(3439) =< s(3430)*s(3415) s(3435) =< s(3430)*s(3431) s(3440) =< s(3430)*s(3415) s(3441) =< s(3429) s(3442) =< s(3430)*s(3432) s(3434) =< s(3430)*aux(328) s(3443) =< s(3438) s(3444) =< s(3439) s(3445) =< s(3435) s(3446) =< s(3436) s(3447) =< s(3434) s(3448) =< s(3417) s(3449) =< s(3417) s(3450) =< s(3418) s(3450) =< s(3417) s(3448) =< s(3450)+s(3450)+s(3417) s(3449) =< s(3450)+s(3450)+s(3417) s(3451) =< s(3450)+s(3450)+s(3417) s(3452) =< s(3450)+s(3450)+s(3417) s(3453) =< s(3449)*s(3431) s(3454) =< s(3449)*s(3415) s(3452) =< s(3449)*s(3431) s(3455) =< s(3449)*s(3415) s(3456) =< s(3448) s(3457) =< s(3449)*s(3432) s(3451) =< s(3449)*aux(328) s(3458) =< s(3453) s(3459) =< s(3454) s(3460) =< s(3452) s(3461) =< s(3451) s(3462) =< s(3417) s(3463) =< s(3417) s(3462) =< s(3417)+s(3417) s(3463) =< s(3417)+s(3417) s(3464) =< s(3462) s(3465) =< s(3417) s(3466) =< s(3417) s(3465) =< s(3418)+s(3417) s(3466) =< s(3418)+s(3417) s(3467) =< s(3465) s(3468) =< s(3418) s(3469) =< s(3418) s(3468) =< aux(328)+s(3418) s(3469) =< aux(328)+s(3418) s(3470) =< s(3468) s(3471) =< s(3420) with precondition: [Out=0,V1>=0,V>=0] * Chain [67]: 12*s(3725)+1434*s(3726)+9*s(3732)+486*s(3734)+3441*s(3735)+405*s(3737)+81*s(3738)+90*s(3740)+18*s(3741)+1944*s(3743)+126*s(3746)+126*s(3750)+216*s(3753)+648*s(3754)+108*s(3755)+3024*s(3756)+864*s(3757)+324*s(3758)+504*s(3759)+324*s(3760)+324*s(3762)+36*s(3768)+108*s(3769)+18*s(3770)+504*s(3771)+144*s(3772)+54*s(3773)+54*s(3774)+45*s(3776)+9*s(3777)+45*s(3779)+9*s(3780)+45*s(3782)+9*s(3783)+9*s(3784)+8*s(3849)+957*s(3850)+6*s(3856)+324*s(3858)+2294*s(3859)+270*s(3861)+54*s(3862)+60*s(3864)+12*s(3865)+1296*s(3867)+84*s(3870)+84*s(3874)+144*s(3877)+432*s(3878)+72*s(3879)+2016*s(3880)+576*s(3881)+216*s(3882)+336*s(3883)+216*s(3884)+216*s(3886)+24*s(3892)+72*s(3893)+12*s(3894)+336*s(3895)+96*s(3896)+36*s(3897)+36*s(3898)+30*s(3900)+6*s(3901)+30*s(3903)+6*s(3904)+30*s(3906)+6*s(3907)+6*s(3908)+1 Such that:aux(331) =< V1 aux(332) =< V1/2 aux(333) =< V aux(334) =< V/2 s(3725) =< aux(331) s(3726) =< aux(331) s(3725) =< aux(332) s(3727) =< aux(331)+1 s(3728) =< aux(331) s(3729) =< aux(331)-1 s(3730) =< s(3726)*s(3727) s(3731) =< s(3726)*s(3728) s(3732) =< s(3725)*s(3729) s(3733) =< s(3725)*s(3729) s(3734) =< s(3731) s(3735) =< s(3730) s(3736) =< s(3730) s(3737) =< s(3730) s(3736) =< aux(331)+s(3730) s(3737) =< aux(331)+s(3730) s(3738) =< s(3736) s(3739) =< s(3730) s(3740) =< s(3730) s(3739) =< aux(331)+s(3731) s(3740) =< aux(331)+s(3731) s(3741) =< s(3739) s(3742) =< s(3730) s(3743) =< s(3730) s(3744) =< s(3727) s(3745) =< s(3727)-1 s(3742) =< s(3731)+s(3731)+s(3730) s(3743) =< s(3731)+s(3731)+s(3730) s(3746) =< s(3735)*s(3727) s(3747) =< s(3731)+s(3731)+s(3730) s(3748) =< s(3731)+s(3731)+s(3730) s(3749) =< s(3735)*s(3744) s(3750) =< s(3735)*s(3744) s(3751) =< s(3743)*s(3744) s(3752) =< s(3743)*s(3728) s(3748) =< s(3743)*s(3744) s(3753) =< s(3743)*s(3728) s(3754) =< s(3742) s(3755) =< s(3743)*s(3745) s(3747) =< s(3743)*aux(331) s(3756) =< s(3751) s(3757) =< s(3752) s(3758) =< s(3748) s(3759) =< s(3749) s(3760) =< s(3747) s(3761) =< s(3730) s(3762) =< s(3730) s(3763) =< s(3731) s(3763) =< s(3730) s(3761) =< s(3763)+s(3763)+s(3730) s(3762) =< s(3763)+s(3763)+s(3730) s(3764) =< s(3763)+s(3763)+s(3730) s(3765) =< s(3763)+s(3763)+s(3730) s(3766) =< s(3762)*s(3744) s(3767) =< s(3762)*s(3728) s(3765) =< s(3762)*s(3744) s(3768) =< s(3762)*s(3728) s(3769) =< s(3761) s(3770) =< s(3762)*s(3745) s(3764) =< s(3762)*aux(331) s(3771) =< s(3766) s(3772) =< s(3767) s(3773) =< s(3765) s(3774) =< s(3764) s(3775) =< s(3730) s(3776) =< s(3730) s(3775) =< s(3730)+s(3730) s(3776) =< s(3730)+s(3730) s(3777) =< s(3775) s(3778) =< s(3730) s(3779) =< s(3730) s(3778) =< s(3731)+s(3730) s(3779) =< s(3731)+s(3730) s(3780) =< s(3778) s(3781) =< s(3731) s(3782) =< s(3731) s(3781) =< aux(331)+s(3731) s(3782) =< aux(331)+s(3731) s(3783) =< s(3781) s(3784) =< s(3733) s(3849) =< aux(333) s(3850) =< aux(333) s(3849) =< aux(334) s(3851) =< aux(333)+1 s(3852) =< aux(333) s(3853) =< aux(333)-1 s(3854) =< s(3850)*s(3851) s(3855) =< s(3850)*s(3852) s(3856) =< s(3849)*s(3853) s(3857) =< s(3849)*s(3853) s(3858) =< s(3855) s(3859) =< s(3854) s(3860) =< s(3854) s(3861) =< s(3854) s(3860) =< aux(333)+s(3854) s(3861) =< aux(333)+s(3854) s(3862) =< s(3860) s(3863) =< s(3854) s(3864) =< s(3854) s(3863) =< aux(333)+s(3855) s(3864) =< aux(333)+s(3855) s(3865) =< s(3863) s(3866) =< s(3854) s(3867) =< s(3854) s(3868) =< s(3851) s(3869) =< s(3851)-1 s(3866) =< s(3855)+s(3855)+s(3854) s(3867) =< s(3855)+s(3855)+s(3854) s(3870) =< s(3859)*s(3851) s(3871) =< s(3855)+s(3855)+s(3854) s(3872) =< s(3855)+s(3855)+s(3854) s(3873) =< s(3859)*s(3868) s(3874) =< s(3859)*s(3868) s(3875) =< s(3867)*s(3868) s(3876) =< s(3867)*s(3852) s(3872) =< s(3867)*s(3868) s(3877) =< s(3867)*s(3852) s(3878) =< s(3866) s(3879) =< s(3867)*s(3869) s(3871) =< s(3867)*aux(333) s(3880) =< s(3875) s(3881) =< s(3876) s(3882) =< s(3872) s(3883) =< s(3873) s(3884) =< s(3871) s(3885) =< s(3854) s(3886) =< s(3854) s(3887) =< s(3855) s(3887) =< s(3854) s(3885) =< s(3887)+s(3887)+s(3854) s(3886) =< s(3887)+s(3887)+s(3854) s(3888) =< s(3887)+s(3887)+s(3854) s(3889) =< s(3887)+s(3887)+s(3854) s(3890) =< s(3886)*s(3868) s(3891) =< s(3886)*s(3852) s(3889) =< s(3886)*s(3868) s(3892) =< s(3886)*s(3852) s(3893) =< s(3885) s(3894) =< s(3886)*s(3869) s(3888) =< s(3886)*aux(333) s(3895) =< s(3890) s(3896) =< s(3891) s(3897) =< s(3889) s(3898) =< s(3888) s(3899) =< s(3854) s(3900) =< s(3854) s(3899) =< s(3854)+s(3854) s(3900) =< s(3854)+s(3854) s(3901) =< s(3899) s(3902) =< s(3854) s(3903) =< s(3854) s(3902) =< s(3855)+s(3854) s(3903) =< s(3855)+s(3854) s(3904) =< s(3902) s(3905) =< s(3855) s(3906) =< s(3855) s(3905) =< aux(333)+s(3855) s(3906) =< aux(333)+s(3855) s(3907) =< s(3905) s(3908) =< s(3857) with precondition: [V1>=1,V>=0,Out>=0,V1>=Out] #### Cost of chains of fun5(V1,V,Out): * Chain [69]: 2288*s(4041)+8*s(4141)+2057*s(4142)+6*s(4148)+468*s(4150)+2294*s(4151)+270*s(4153)+54*s(4154)+60*s(4156)+12*s(4157)+1296*s(4159)+84*s(4162)+84*s(4166)+144*s(4169)+432*s(4170)+72*s(4171)+2016*s(4172)+576*s(4173)+216*s(4174)+336*s(4175)+216*s(4176)+216*s(4178)+24*s(4184)+72*s(4185)+12*s(4186)+336*s(4187)+96*s(4188)+36*s(4189)+36*s(4190)+30*s(4192)+6*s(4193)+30*s(4195)+6*s(4196)+30*s(4198)+6*s(4199)+6*s(4200)+90*s(4216)+204*s(4217)+18*s(4218)+609*s(4223)+36*s(4228)+36*s(4232)+66*s(4235)+201*s(4236)+33*s(4237)+1188*s(4238)+99*s(4240)+99*s(4242)+54*s(4249)+60*s(4250)+24*s(4251)+6*s(4252)+6*s(4256)+6*s(4259)+18*s(4260)+3*s(4261)+108*s(4262)+9*s(4264)+24*s(4265)+9*s(4266)+54*s(4268)+6*s(4274)+18*s(4275)+3*s(4276)+108*s(4277)+9*s(4279)+9*s(4280)+90*s(4282)+18*s(4283)+54*s(4285)+6*s(4290)+18*s(4291)+3*s(4292)+108*s(4293)+9*s(4295)+9*s(4296)+8*s(4308)+2849*s(4309)+6*s(4315)+1314*s(4317)+2294*s(4318)+270*s(4320)+54*s(4321)+30*s(4323)+6*s(4324)+648*s(4326)+84*s(4329)+84*s(4333)+72*s(4336)+216*s(4337)+36*s(4338)+1008*s(4339)+288*s(4340)+108*s(4341)+336*s(4342)+108*s(4343)+108*s(4345)+12*s(4351)+36*s(4352)+6*s(4353)+168*s(4354)+48*s(4355)+18*s(4356)+18*s(4357)+30*s(4359)+6*s(4360)+15*s(4362)+3*s(4363)+15*s(4365)+3*s(4366)+6*s(4367)+60*s(4379)+150*s(4380)+12*s(4381)+120*s(4387)+24*s(4388)+36*s(4395)+36*s(4399)+36*s(4404)+108*s(4407)+168*s(4416)+60*s(4418)+6*s(4419)+6*s(4423)+6*s(4428)+192*s(4429)+18*s(4431)+15*s(4465)+3*s(4466)+162*s(4484)+30*s(4490)+6*s(4491)+648*s(4493)+72*s(4503)+216*s(4504)+36*s(4505)+1008*s(4506)+288*s(4507)+108*s(4508)+108*s(4510)+108*s(4512)+12*s(4518)+36*s(4519)+6*s(4520)+168*s(4521)+48*s(4522)+18*s(4523)+18*s(4524)+15*s(4529)+3*s(4530)+15*s(4532)+3*s(4533)+594*s(4619)+761*s(4620)+36*s(4624)+36*s(4628)+66*s(4631)+198*s(4632)+33*s(4633)+924*s(4634)+264*s(4635)+99*s(4636)+144*s(4637)+99*s(4638)+78*s(4639)+30*s(4641)+6*s(4642)+54*s(4645)+60*s(4646)+24*s(4647)+6*s(4648)+6*s(4652)+6*s(4655)+18*s(4656)+3*s(4657)+84*s(4658)+24*s(4659)+9*s(4660)+24*s(4661)+9*s(4662)+54*s(4664)+6*s(4670)+18*s(4671)+3*s(4672)+84*s(4673)+24*s(4674)+9*s(4675)+9*s(4676)+60*s(4678)+12*s(4679)+54*s(4681)+6*s(4686)+18*s(4687)+3*s(4688)+84*s(4689)+24*s(4690)+9*s(4691)+9*s(4692)+15*s(4694)+3*s(4695)+15*s(4697)+3*s(4698)+9 Such that:s(4600) =< V1+V s(4601) =< V1+V+1 aux(345) =< 1 aux(346) =< V1 aux(347) =< V1+1 aux(348) =< V1/2 aux(349) =< V aux(350) =< V+1 aux(351) =< V/2 s(4041) =< aux(345) s(4309) =< aux(346) s(4142) =< aux(349) s(4378) =< aux(347) s(4379) =< aux(347) s(4380) =< aux(347) s(4378) =< aux(345)+aux(346) s(4379) =< aux(345)+aux(346) s(4381) =< s(4378) s(4215) =< aux(350) s(4216) =< aux(350) s(4217) =< aux(350) s(4215) =< aux(345)+aux(349) s(4216) =< aux(345)+aux(349) s(4218) =< s(4215) s(4386) =< aux(346) s(4387) =< aux(346) s(4386) =< aux(345)+aux(346) s(4387) =< aux(345)+aux(346) s(4388) =< s(4386) s(4618) =< s(4600) s(4619) =< s(4600) s(4620) =< s(4600) s(4621) =< s(4600) s(4144) =< aux(349) s(4623) =< s(4600)-1 s(4618) =< aux(349)+aux(349)+aux(346) s(4619) =< aux(349)+aux(349)+aux(346) s(4624) =< s(4620)*s(4600) s(4625) =< aux(349)+aux(349)+aux(346) s(4626) =< aux(349)+aux(349)+aux(346) s(4627) =< s(4620)*s(4621) s(4628) =< s(4620)*s(4621) s(4629) =< s(4619)*s(4621) s(4630) =< s(4619)*s(4144) s(4626) =< s(4619)*s(4621) s(4631) =< s(4619)*s(4144) s(4632) =< s(4618) s(4633) =< s(4619)*s(4623) s(4625) =< s(4619)*aux(349) s(4634) =< s(4629) s(4635) =< s(4630) s(4636) =< s(4626) s(4637) =< s(4627) s(4638) =< s(4625) s(4639) =< s(4601) s(4640) =< s(4601) s(4641) =< s(4601) s(4640) =< aux(345)+s(4600) s(4641) =< aux(345)+s(4600) s(4642) =< s(4640) s(4643) =< s(4600) s(4644) =< s(4600) s(4645) =< s(4600) s(4646) =< s(4600) s(4643) =< s(4601) s(4644) =< s(4601) s(4645) =< s(4601) s(4646) =< s(4601) s(4643) =< aux(349)+aux(349)+aux(346) s(4645) =< aux(349)+aux(349)+aux(346) s(4647) =< s(4644) s(4648) =< s(4646)*s(4600) s(4649) =< aux(349)+aux(349)+aux(346) s(4650) =< aux(349)+aux(349)+aux(346) s(4651) =< s(4646)*s(4621) s(4652) =< s(4646)*s(4621) s(4653) =< s(4645)*s(4621) s(4654) =< s(4645)*s(4144) s(4650) =< s(4645)*s(4621) s(4655) =< s(4645)*s(4144) s(4656) =< s(4643) s(4657) =< s(4645)*s(4623) s(4649) =< s(4645)*aux(349) s(4658) =< s(4653) s(4659) =< s(4654) s(4660) =< s(4650) s(4661) =< s(4651) s(4662) =< s(4649) s(4663) =< s(4600) s(4664) =< s(4600) s(4663) =< s(4601) s(4664) =< s(4601) s(4248) =< aux(349) s(4248) =< aux(350) s(4663) =< s(4248)+s(4248)+aux(346) s(4664) =< s(4248)+s(4248)+aux(346) s(4666) =< s(4248)+s(4248)+aux(346) s(4667) =< s(4248)+s(4248)+aux(346) s(4668) =< s(4664)*s(4621) s(4669) =< s(4664)*s(4144) s(4667) =< s(4664)*s(4621) s(4670) =< s(4664)*s(4144) s(4671) =< s(4663) s(4672) =< s(4664)*s(4623) s(4666) =< s(4664)*aux(349) s(4673) =< s(4668) s(4674) =< s(4669) s(4675) =< s(4667) s(4676) =< s(4666) s(4677) =< s(4600) s(4678) =< s(4600) s(4677) =< aux(345)+s(4600) s(4678) =< aux(345)+s(4600) s(4679) =< s(4677) s(4680) =< s(4600) s(4681) =< s(4600) s(4680) =< s(4248)+s(4248)+aux(346) s(4681) =< s(4248)+s(4248)+aux(346) s(4682) =< s(4248)+s(4248)+aux(346) s(4683) =< s(4248)+s(4248)+aux(346) s(4684) =< s(4681)*s(4621) s(4685) =< s(4681)*s(4144) s(4683) =< s(4681)*s(4621) s(4686) =< s(4681)*s(4144) s(4687) =< s(4680) s(4688) =< s(4681)*s(4623) s(4682) =< s(4681)*aux(349) s(4689) =< s(4684) s(4690) =< s(4685) s(4691) =< s(4683) s(4692) =< s(4682) s(4693) =< s(4600) s(4694) =< s(4600) s(4693) =< s(4600)+s(4600) s(4694) =< s(4600)+s(4600) s(4695) =< s(4693) s(4696) =< s(4600) s(4697) =< s(4600) s(4696) =< aux(349)+aux(346) s(4697) =< aux(349)+aux(346) s(4698) =< s(4696) s(4281) =< aux(349) s(4282) =< aux(349) s(4281) =< aux(345)+aux(349) s(4282) =< aux(345)+aux(349) s(4283) =< s(4281) s(4141) =< aux(349) s(4141) =< aux(351) s(4143) =< aux(349)+1 s(4145) =< aux(349)-1 s(4146) =< s(4142)*s(4143) s(4147) =< s(4142)*s(4144) s(4148) =< s(4141)*s(4145) s(4149) =< s(4141)*s(4145) s(4150) =< s(4147) s(4151) =< s(4146) s(4152) =< s(4146) s(4153) =< s(4146) s(4152) =< aux(349)+s(4146) s(4153) =< aux(349)+s(4146) s(4154) =< s(4152) s(4155) =< s(4146) s(4156) =< s(4146) s(4155) =< aux(349)+s(4147) s(4156) =< aux(349)+s(4147) s(4157) =< s(4155) s(4158) =< s(4146) s(4159) =< s(4146) s(4160) =< s(4143) s(4161) =< s(4143)-1 s(4158) =< s(4147)+s(4147)+s(4146) s(4159) =< s(4147)+s(4147)+s(4146) s(4162) =< s(4151)*s(4143) s(4163) =< s(4147)+s(4147)+s(4146) s(4164) =< s(4147)+s(4147)+s(4146) s(4165) =< s(4151)*s(4160) s(4166) =< s(4151)*s(4160) s(4167) =< s(4159)*s(4160) s(4168) =< s(4159)*s(4144) s(4164) =< s(4159)*s(4160) s(4169) =< s(4159)*s(4144) s(4170) =< s(4158) s(4171) =< s(4159)*s(4161) s(4163) =< s(4159)*aux(349) s(4172) =< s(4167) s(4173) =< s(4168) s(4174) =< s(4164) s(4175) =< s(4165) s(4176) =< s(4163) s(4177) =< s(4146) s(4178) =< s(4146) s(4179) =< s(4147) s(4179) =< s(4146) s(4177) =< s(4179)+s(4179)+s(4146) s(4178) =< s(4179)+s(4179)+s(4146) s(4180) =< s(4179)+s(4179)+s(4146) s(4181) =< s(4179)+s(4179)+s(4146) s(4182) =< s(4178)*s(4160) s(4183) =< s(4178)*s(4144) s(4181) =< s(4178)*s(4160) s(4184) =< s(4178)*s(4144) s(4185) =< s(4177) s(4186) =< s(4178)*s(4161) s(4180) =< s(4178)*aux(349) s(4187) =< s(4182) s(4188) =< s(4183) s(4189) =< s(4181) s(4190) =< s(4180) s(4191) =< s(4146) s(4192) =< s(4146) s(4191) =< s(4146)+s(4146) s(4192) =< s(4146)+s(4146) s(4193) =< s(4191) s(4194) =< s(4146) s(4195) =< s(4146) s(4194) =< s(4147)+s(4146) s(4195) =< s(4147)+s(4146) s(4196) =< s(4194) s(4197) =< s(4147) s(4198) =< s(4147) s(4197) =< aux(349)+s(4147) s(4198) =< aux(349)+s(4147) s(4199) =< s(4197) s(4200) =< s(4149) s(4308) =< aux(346) s(4308) =< aux(348) s(4310) =< aux(346)+1 s(4311) =< aux(346) s(4312) =< aux(346)-1 s(4313) =< s(4309)*s(4310) s(4481) =< s(4309)*s(4311) s(4315) =< s(4308)*s(4312) s(4316) =< s(4308)*s(4312) s(4484) =< s(4481) s(4318) =< s(4313) s(4319) =< s(4313) s(4320) =< s(4313) s(4319) =< aux(346)+s(4313) s(4320) =< aux(346)+s(4313) s(4321) =< s(4319) s(4489) =< s(4313) s(4490) =< s(4313) s(4489) =< aux(346)+s(4481) s(4490) =< aux(346)+s(4481) s(4491) =< s(4489) s(4492) =< s(4313) s(4493) =< s(4313) s(4327) =< s(4310) s(4328) =< s(4310)-1 s(4492) =< s(4481)+s(4481)+s(4313) s(4493) =< s(4481)+s(4481)+s(4313) s(4329) =< s(4318)*s(4310) s(4497) =< s(4481)+s(4481)+s(4313) s(4498) =< s(4481)+s(4481)+s(4313) s(4332) =< s(4318)*s(4327) s(4333) =< s(4318)*s(4327) s(4501) =< s(4493)*s(4327) s(4502) =< s(4493)*s(4311) s(4498) =< s(4493)*s(4327) s(4503) =< s(4493)*s(4311) s(4504) =< s(4492) s(4505) =< s(4493)*s(4328) s(4497) =< s(4493)*aux(346) s(4506) =< s(4501) s(4507) =< s(4502) s(4508) =< s(4498) s(4342) =< s(4332) s(4510) =< s(4497) s(4511) =< s(4313) s(4512) =< s(4313) s(4513) =< s(4481) s(4513) =< s(4313) s(4511) =< s(4513)+s(4513)+s(4313) s(4512) =< s(4513)+s(4513)+s(4313) s(4514) =< s(4513)+s(4513)+s(4313) s(4515) =< s(4513)+s(4513)+s(4313) s(4516) =< s(4512)*s(4327) s(4517) =< s(4512)*s(4311) s(4515) =< s(4512)*s(4327) s(4518) =< s(4512)*s(4311) s(4519) =< s(4511) s(4520) =< s(4512)*s(4328) s(4514) =< s(4512)*aux(346) s(4521) =< s(4516) s(4522) =< s(4517) s(4523) =< s(4515) s(4524) =< s(4514) s(4358) =< s(4313) s(4359) =< s(4313) s(4358) =< s(4313)+s(4313) s(4359) =< s(4313)+s(4313) s(4360) =< s(4358) s(4528) =< s(4313) s(4529) =< s(4313) s(4528) =< s(4481)+s(4313) s(4529) =< s(4481)+s(4313) s(4530) =< s(4528) s(4531) =< s(4481) s(4532) =< s(4481) s(4531) =< aux(346)+s(4481) s(4532) =< aux(346)+s(4481) s(4533) =< s(4531) s(4367) =< s(4316) s(4395) =< s(4309)*aux(346) s(4397) =< aux(346) s(4314) =< s(4309)*s(4311) s(4399) =< s(4309)*s(4311) s(4397) =< s(4309)*s(4311) s(4404) =< s(4309)*s(4312) s(4317) =< s(4314) s(4407) =< s(4397) s(4414) =< aux(346) s(4416) =< aux(346) s(4414) =< aux(347) s(4416) =< aux(347) s(4418) =< s(4414) s(4419) =< s(4416)*aux(346) s(4421) =< aux(346) s(4422) =< s(4416)*s(4311) s(4423) =< s(4416)*s(4311) s(4421) =< s(4416)*s(4311) s(4428) =< s(4416)*s(4312) s(4429) =< s(4422) s(4431) =< s(4421) s(4464) =< aux(346) s(4465) =< aux(346) s(4464) =< aux(346)+aux(346) s(4465) =< aux(346)+aux(346) s(4466) =< s(4464) s(4322) =< s(4313) s(4323) =< s(4313) s(4322) =< aux(346)+s(4314) s(4323) =< aux(346)+s(4314) s(4324) =< s(4322) s(4325) =< s(4313) s(4326) =< s(4313) s(4325) =< s(4314)+s(4314)+s(4313) s(4326) =< s(4314)+s(4314)+s(4313) s(4330) =< s(4314)+s(4314)+s(4313) s(4331) =< s(4314)+s(4314)+s(4313) s(4334) =< s(4326)*s(4327) s(4335) =< s(4326)*s(4311) s(4331) =< s(4326)*s(4327) s(4336) =< s(4326)*s(4311) s(4337) =< s(4325) s(4338) =< s(4326)*s(4328) s(4330) =< s(4326)*aux(346) s(4339) =< s(4334) s(4340) =< s(4335) s(4341) =< s(4331) s(4343) =< s(4330) s(4344) =< s(4313) s(4345) =< s(4313) s(4346) =< s(4314) s(4346) =< s(4313) s(4344) =< s(4346)+s(4346)+s(4313) s(4345) =< s(4346)+s(4346)+s(4313) s(4347) =< s(4346)+s(4346)+s(4313) s(4348) =< s(4346)+s(4346)+s(4313) s(4349) =< s(4345)*s(4327) s(4350) =< s(4345)*s(4311) s(4348) =< s(4345)*s(4327) s(4351) =< s(4345)*s(4311) s(4352) =< s(4344) s(4353) =< s(4345)*s(4328) s(4347) =< s(4345)*aux(346) s(4354) =< s(4349) s(4355) =< s(4350) s(4356) =< s(4348) s(4357) =< s(4347) s(4361) =< s(4313) s(4362) =< s(4313) s(4361) =< s(4314)+s(4313) s(4362) =< s(4314)+s(4313) s(4363) =< s(4361) s(4364) =< s(4314) s(4365) =< s(4314) s(4364) =< aux(346)+s(4314) s(4365) =< aux(346)+s(4314) s(4366) =< s(4364) s(4222) =< aux(349) s(4223) =< aux(349) s(4222) =< aux(349)+aux(349) s(4223) =< aux(349)+aux(349) s(4228) =< s(4142)*aux(349) s(4229) =< aux(349)+aux(349) s(4230) =< aux(349)+aux(349) s(4232) =< s(4142)*s(4144) s(4233) =< s(4223)*s(4144) s(4230) =< s(4223)*s(4144) s(4235) =< s(4223)*s(4144) s(4236) =< s(4222) s(4237) =< s(4223)*s(4145) s(4229) =< s(4223)*aux(349) s(4238) =< s(4233) s(4240) =< s(4230) s(4242) =< s(4229) s(4247) =< aux(349) s(4249) =< aux(349) s(4250) =< aux(349) s(4247) =< aux(350) s(4249) =< aux(350) s(4250) =< aux(350) s(4247) =< aux(349)+aux(349) s(4249) =< aux(349)+aux(349) s(4251) =< s(4248) s(4252) =< s(4250)*aux(349) s(4253) =< aux(349)+aux(349) s(4254) =< aux(349)+aux(349) s(4255) =< s(4250)*s(4144) s(4256) =< s(4250)*s(4144) s(4257) =< s(4249)*s(4144) s(4254) =< s(4249)*s(4144) s(4259) =< s(4249)*s(4144) s(4260) =< s(4247) s(4261) =< s(4249)*s(4145) s(4253) =< s(4249)*aux(349) s(4262) =< s(4257) s(4264) =< s(4254) s(4265) =< s(4255) s(4266) =< s(4253) s(4267) =< aux(349) s(4268) =< aux(349) s(4267) =< aux(350) s(4268) =< aux(350) s(4267) =< s(4248)+s(4248) s(4268) =< s(4248)+s(4248) s(4270) =< s(4248)+s(4248) s(4271) =< s(4248)+s(4248) s(4272) =< s(4268)*s(4144) s(4271) =< s(4268)*s(4144) s(4274) =< s(4268)*s(4144) s(4275) =< s(4267) s(4276) =< s(4268)*s(4145) s(4270) =< s(4268)*aux(349) s(4277) =< s(4272) s(4279) =< s(4271) s(4280) =< s(4270) s(4284) =< aux(349) s(4285) =< aux(349) s(4284) =< s(4248)+s(4248) s(4285) =< s(4248)+s(4248) s(4286) =< s(4248)+s(4248) s(4287) =< s(4248)+s(4248) s(4288) =< s(4285)*s(4144) s(4287) =< s(4285)*s(4144) s(4290) =< s(4285)*s(4144) s(4291) =< s(4284) s(4292) =< s(4285)*s(4145) s(4286) =< s(4285)*aux(349) s(4293) =< s(4288) s(4295) =< s(4287) s(4296) =< s(4286) with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of start(V1,V): * Chain [70]: 10358*s(4703)+12057*s(4705)+2755*s(4716)+75*s(4720)+186*s(4721)+15*s(4722)+120*s(4724)+267*s(4725)+24*s(4726)+150*s(4728)+30*s(4729)+1188*s(4731)+1522*s(4732)+72*s(4736)+72*s(4740)+132*s(4743)+396*s(4744)+66*s(4745)+1848*s(4746)+528*s(4747)+198*s(4748)+288*s(4749)+198*s(4750)+156*s(4751)+60*s(4753)+12*s(4754)+108*s(4757)+120*s(4758)+48*s(4759)+12*s(4760)+12*s(4764)+12*s(4767)+36*s(4768)+6*s(4769)+168*s(4770)+48*s(4771)+18*s(4772)+48*s(4773)+18*s(4774)+108*s(4776)+12*s(4782)+36*s(4783)+6*s(4784)+168*s(4785)+48*s(4786)+18*s(4787)+18*s(4788)+120*s(4790)+24*s(4791)+108*s(4793)+12*s(4798)+36*s(4799)+6*s(4800)+168*s(4801)+48*s(4802)+18*s(4803)+18*s(4804)+30*s(4806)+6*s(4807)+30*s(4809)+6*s(4810)+105*s(4812)+21*s(4813)+84*s(4816)+63*s(4823)+4554*s(4825)+24087*s(4826)+2835*s(4828)+567*s(4829)+630*s(4831)+126*s(4832)+13608*s(4834)+882*s(4837)+882*s(4841)+1512*s(4844)+4536*s(4845)+756*s(4846)+21168*s(4847)+6048*s(4848)+2268*s(4849)+3528*s(4850)+2268*s(4851)+2268*s(4853)+252*s(4859)+756*s(4860)+126*s(4861)+3528*s(4862)+1008*s(4863)+378*s(4864)+378*s(4865)+315*s(4867)+63*s(4868)+315*s(4870)+63*s(4871)+315*s(4873)+63*s(4874)+63*s(4875)+76*s(4940)+57*s(4947)+3222*s(4949)+21793*s(4950)+2565*s(4952)+513*s(4953)+570*s(4955)+114*s(4956)+12312*s(4958)+798*s(4961)+798*s(4965)+1368*s(4968)+4104*s(4969)+684*s(4970)+19152*s(4971)+5472*s(4972)+2052*s(4973)+3192*s(4974)+2052*s(4975)+2052*s(4977)+228*s(4983)+684*s(4984)+114*s(4985)+3192*s(4986)+912*s(4987)+342*s(4988)+342*s(4989)+285*s(4991)+57*s(4992)+285*s(4994)+57*s(4995)+285*s(4997)+57*s(4998)+57*s(4999)+36*s(6030)+36*s(6033)+36*s(6034)+108*s(6036)+168*s(6038)+60*s(6039)+6*s(6040)+6*s(6043)+6*s(6044)+192*s(6045)+18*s(6046)+15*s(6048)+3*s(6049)+609*s(6087)+36*s(6088)+36*s(6091)+66*s(6093)+201*s(6094)+33*s(6095)+1188*s(6096)+99*s(6097)+99*s(6098)+54*s(6100)+60*s(6101)+24*s(6102)+6*s(6103)+6*s(6107)+6*s(6109)+18*s(6110)+3*s(6111)+108*s(6112)+9*s(6113)+24*s(6114)+9*s(6115)+54*s(6117)+6*s(6121)+18*s(6122)+3*s(6123)+108*s(6124)+9*s(6125)+9*s(6126)+54*s(6128)+6*s(6132)+18*s(6133)+3*s(6134)+108*s(6135)+9*s(6136)+9*s(6137)+9 Such that:aux(352) =< 1 aux(353) =< V1 aux(354) =< V1+1 aux(355) =< V1+V aux(356) =< V1+V+1 aux(357) =< V1/2 aux(358) =< V aux(359) =< V+1 aux(360) =< V/2 s(4705) =< aux(353) s(4703) =< aux(358) s(4716) =< aux(352) s(4719) =< aux(354) s(4720) =< aux(354) s(4721) =< aux(354) s(4719) =< aux(352)+aux(353) s(4720) =< aux(352)+aux(353) s(4722) =< s(4719) s(4723) =< aux(359) s(4724) =< aux(359) s(4725) =< aux(359) s(4723) =< aux(352)+aux(358) s(4724) =< aux(352)+aux(358) s(4726) =< s(4723) s(4727) =< aux(353) s(4728) =< aux(353) s(4727) =< aux(352)+aux(353) s(4728) =< aux(352)+aux(353) s(4729) =< s(4727) s(4730) =< aux(355) s(4731) =< aux(355) s(4732) =< aux(355) s(4733) =< aux(355) s(4734) =< aux(358) s(4735) =< aux(355)-1 s(4730) =< aux(358)+aux(358)+aux(353) s(4731) =< aux(358)+aux(358)+aux(353) s(4736) =< s(4732)*aux(355) s(4737) =< aux(358)+aux(358)+aux(353) s(4738) =< aux(358)+aux(358)+aux(353) s(4739) =< s(4732)*s(4733) s(4740) =< s(4732)*s(4733) s(4741) =< s(4731)*s(4733) s(4742) =< s(4731)*s(4734) s(4738) =< s(4731)*s(4733) s(4743) =< s(4731)*s(4734) s(4744) =< s(4730) s(4745) =< s(4731)*s(4735) s(4737) =< s(4731)*aux(358) s(4746) =< s(4741) s(4747) =< s(4742) s(4748) =< s(4738) s(4749) =< s(4739) s(4750) =< s(4737) s(4751) =< aux(356) s(4752) =< aux(356) s(4753) =< aux(356) s(4752) =< aux(352)+aux(355) s(4753) =< aux(352)+aux(355) s(4754) =< s(4752) s(4755) =< aux(355) s(4756) =< aux(355) s(4757) =< aux(355) s(4758) =< aux(355) s(4755) =< aux(356) s(4756) =< aux(356) s(4757) =< aux(356) s(4758) =< aux(356) s(4755) =< aux(358)+aux(358)+aux(353) s(4757) =< aux(358)+aux(358)+aux(353) s(4759) =< s(4756) s(4760) =< s(4758)*aux(355) s(4761) =< aux(358)+aux(358)+aux(353) s(4762) =< aux(358)+aux(358)+aux(353) s(4763) =< s(4758)*s(4733) s(4764) =< s(4758)*s(4733) s(4765) =< s(4757)*s(4733) s(4766) =< s(4757)*s(4734) s(4762) =< s(4757)*s(4733) s(4767) =< s(4757)*s(4734) s(4768) =< s(4755) s(4769) =< s(4757)*s(4735) s(4761) =< s(4757)*aux(358) s(4770) =< s(4765) s(4771) =< s(4766) s(4772) =< s(4762) s(4773) =< s(4763) s(4774) =< s(4761) s(4775) =< aux(355) s(4776) =< aux(355) s(4775) =< aux(356) s(4776) =< aux(356) s(4777) =< aux(358) s(4777) =< aux(359) s(4775) =< s(4777)+s(4777)+aux(353) s(4776) =< s(4777)+s(4777)+aux(353) s(4778) =< s(4777)+s(4777)+aux(353) s(4779) =< s(4777)+s(4777)+aux(353) s(4780) =< s(4776)*s(4733) s(4781) =< s(4776)*s(4734) s(4779) =< s(4776)*s(4733) s(4782) =< s(4776)*s(4734) s(4783) =< s(4775) s(4784) =< s(4776)*s(4735) s(4778) =< s(4776)*aux(358) s(4785) =< s(4780) s(4786) =< s(4781) s(4787) =< s(4779) s(4788) =< s(4778) s(4789) =< aux(355) s(4790) =< aux(355) s(4789) =< aux(352)+aux(355) s(4790) =< aux(352)+aux(355) s(4791) =< s(4789) s(4792) =< aux(355) s(4793) =< aux(355) s(4792) =< s(4777)+s(4777)+aux(353) s(4793) =< s(4777)+s(4777)+aux(353) s(4794) =< s(4777)+s(4777)+aux(353) s(4795) =< s(4777)+s(4777)+aux(353) s(4796) =< s(4793)*s(4733) s(4797) =< s(4793)*s(4734) s(4795) =< s(4793)*s(4733) s(4798) =< s(4793)*s(4734) s(4799) =< s(4792) s(4800) =< s(4793)*s(4735) s(4794) =< s(4793)*aux(358) s(4801) =< s(4796) s(4802) =< s(4797) s(4803) =< s(4795) s(4804) =< s(4794) s(4805) =< aux(355) s(4806) =< aux(355) s(4805) =< aux(355)+aux(355) s(4806) =< aux(355)+aux(355) s(4807) =< s(4805) s(4808) =< aux(355) s(4809) =< aux(355) s(4808) =< aux(358)+aux(353) s(4809) =< aux(358)+aux(353) s(4810) =< s(4808) s(4811) =< aux(358) s(4812) =< aux(358) s(4811) =< aux(352)+aux(358) s(4812) =< aux(352)+aux(358) s(4813) =< s(4811) s(4940) =< aux(358) s(4940) =< aux(360) s(4942) =< aux(358)+1 s(4944) =< aux(358)-1 s(4945) =< s(4703)*s(4942) s(4946) =< s(4703)*s(4734) s(4947) =< s(4940)*s(4944) s(4948) =< s(4940)*s(4944) s(4949) =< s(4946) s(4950) =< s(4945) s(4951) =< s(4945) s(4952) =< s(4945) s(4951) =< aux(358)+s(4945) s(4952) =< aux(358)+s(4945) s(4953) =< s(4951) s(4954) =< s(4945) s(4955) =< s(4945) s(4954) =< aux(358)+s(4946) s(4955) =< aux(358)+s(4946) s(4956) =< s(4954) s(4957) =< s(4945) s(4958) =< s(4945) s(4959) =< s(4942) s(4960) =< s(4942)-1 s(4957) =< s(4946)+s(4946)+s(4945) s(4958) =< s(4946)+s(4946)+s(4945) s(4961) =< s(4950)*s(4942) s(4962) =< s(4946)+s(4946)+s(4945) s(4963) =< s(4946)+s(4946)+s(4945) s(4964) =< s(4950)*s(4959) s(4965) =< s(4950)*s(4959) s(4966) =< s(4958)*s(4959) s(4967) =< s(4958)*s(4734) s(4963) =< s(4958)*s(4959) s(4968) =< s(4958)*s(4734) s(4969) =< s(4957) s(4970) =< s(4958)*s(4960) s(4962) =< s(4958)*aux(358) s(4971) =< s(4966) s(4972) =< s(4967) s(4973) =< s(4963) s(4974) =< s(4964) s(4975) =< s(4962) s(4976) =< s(4945) s(4977) =< s(4945) s(4978) =< s(4946) s(4978) =< s(4945) s(4976) =< s(4978)+s(4978)+s(4945) s(4977) =< s(4978)+s(4978)+s(4945) s(4979) =< s(4978)+s(4978)+s(4945) s(4980) =< s(4978)+s(4978)+s(4945) s(4981) =< s(4977)*s(4959) s(4982) =< s(4977)*s(4734) s(4980) =< s(4977)*s(4959) s(4983) =< s(4977)*s(4734) s(4984) =< s(4976) s(4985) =< s(4977)*s(4960) s(4979) =< s(4977)*aux(358) s(4986) =< s(4981) s(4987) =< s(4982) s(4988) =< s(4980) s(4989) =< s(4979) s(4990) =< s(4945) s(4991) =< s(4945) s(4990) =< s(4945)+s(4945) s(4991) =< s(4945)+s(4945) s(4992) =< s(4990) s(4993) =< s(4945) s(4994) =< s(4945) s(4993) =< s(4946)+s(4945) s(4994) =< s(4946)+s(4945) s(4995) =< s(4993) s(4996) =< s(4946) s(4997) =< s(4946) s(4996) =< aux(358)+s(4946) s(4997) =< aux(358)+s(4946) s(4998) =< s(4996) s(4999) =< s(4948) s(4816) =< aux(353) s(4816) =< aux(357) s(4818) =< aux(353)+1 s(4819) =< aux(353) s(4820) =< aux(353)-1 s(4821) =< s(4705)*s(4818) s(4822) =< s(4705)*s(4819) s(4823) =< s(4816)*s(4820) s(4824) =< s(4816)*s(4820) s(4825) =< s(4822) s(4826) =< s(4821) s(4827) =< s(4821) s(4828) =< s(4821) s(4827) =< aux(353)+s(4821) s(4828) =< aux(353)+s(4821) s(4829) =< s(4827) s(4830) =< s(4821) s(4831) =< s(4821) s(4830) =< aux(353)+s(4822) s(4831) =< aux(353)+s(4822) s(4832) =< s(4830) s(4833) =< s(4821) s(4834) =< s(4821) s(4835) =< s(4818) s(4836) =< s(4818)-1 s(4833) =< s(4822)+s(4822)+s(4821) s(4834) =< s(4822)+s(4822)+s(4821) s(4837) =< s(4826)*s(4818) s(4838) =< s(4822)+s(4822)+s(4821) s(4839) =< s(4822)+s(4822)+s(4821) s(4840) =< s(4826)*s(4835) s(4841) =< s(4826)*s(4835) s(4842) =< s(4834)*s(4835) s(4843) =< s(4834)*s(4819) s(4839) =< s(4834)*s(4835) s(4844) =< s(4834)*s(4819) s(4845) =< s(4833) s(4846) =< s(4834)*s(4836) s(4838) =< s(4834)*aux(353) s(4847) =< s(4842) s(4848) =< s(4843) s(4849) =< s(4839) s(4850) =< s(4840) s(4851) =< s(4838) s(4852) =< s(4821) s(4853) =< s(4821) s(4854) =< s(4822) s(4854) =< s(4821) s(4852) =< s(4854)+s(4854)+s(4821) s(4853) =< s(4854)+s(4854)+s(4821) s(4855) =< s(4854)+s(4854)+s(4821) s(4856) =< s(4854)+s(4854)+s(4821) s(4857) =< s(4853)*s(4835) s(4858) =< s(4853)*s(4819) s(4856) =< s(4853)*s(4835) s(4859) =< s(4853)*s(4819) s(4860) =< s(4852) s(4861) =< s(4853)*s(4836) s(4855) =< s(4853)*aux(353) s(4862) =< s(4857) s(4863) =< s(4858) s(4864) =< s(4856) s(4865) =< s(4855) s(4866) =< s(4821) s(4867) =< s(4821) s(4866) =< s(4821)+s(4821) s(4867) =< s(4821)+s(4821) s(4868) =< s(4866) s(4869) =< s(4821) s(4870) =< s(4821) s(4869) =< s(4822)+s(4821) s(4870) =< s(4822)+s(4821) s(4871) =< s(4869) s(4872) =< s(4822) s(4873) =< s(4822) s(4872) =< aux(353)+s(4822) s(4873) =< aux(353)+s(4822) s(4874) =< s(4872) s(4875) =< s(4824) s(6030) =< s(4705)*aux(353) s(6031) =< aux(353) s(6033) =< s(4705)*s(4819) s(6031) =< s(4705)*s(4819) s(6034) =< s(4705)*s(4820) s(6036) =< s(6031) s(6037) =< aux(353) s(6038) =< aux(353) s(6037) =< aux(354) s(6038) =< aux(354) s(6039) =< s(6037) s(6040) =< s(6038)*aux(353) s(6041) =< aux(353) s(6042) =< s(6038)*s(4819) s(6043) =< s(6038)*s(4819) s(6041) =< s(6038)*s(4819) s(6044) =< s(6038)*s(4820) s(6045) =< s(6042) s(6046) =< s(6041) s(6047) =< aux(353) s(6048) =< aux(353) s(6047) =< aux(353)+aux(353) s(6048) =< aux(353)+aux(353) s(6049) =< s(6047) s(6086) =< aux(358) s(6087) =< aux(358) s(6086) =< aux(358)+aux(358) s(6087) =< aux(358)+aux(358) s(6088) =< s(4703)*aux(358) s(6089) =< aux(358)+aux(358) s(6090) =< aux(358)+aux(358) s(6091) =< s(4703)*s(4734) s(6092) =< s(6087)*s(4734) s(6090) =< s(6087)*s(4734) s(6093) =< s(6087)*s(4734) s(6094) =< s(6086) s(6095) =< s(6087)*s(4944) s(6089) =< s(6087)*aux(358) s(6096) =< s(6092) s(6097) =< s(6090) s(6098) =< s(6089) s(6099) =< aux(358) s(6100) =< aux(358) s(6101) =< aux(358) s(6099) =< aux(359) s(6100) =< aux(359) s(6101) =< aux(359) s(6099) =< aux(358)+aux(358) s(6100) =< aux(358)+aux(358) s(6102) =< s(4777) s(6103) =< s(6101)*aux(358) s(6104) =< aux(358)+aux(358) s(6105) =< aux(358)+aux(358) s(6106) =< s(6101)*s(4734) s(6107) =< s(6101)*s(4734) s(6108) =< s(6100)*s(4734) s(6105) =< s(6100)*s(4734) s(6109) =< s(6100)*s(4734) s(6110) =< s(6099) s(6111) =< s(6100)*s(4944) s(6104) =< s(6100)*aux(358) s(6112) =< s(6108) s(6113) =< s(6105) s(6114) =< s(6106) s(6115) =< s(6104) s(6116) =< aux(358) s(6117) =< aux(358) s(6116) =< aux(359) s(6117) =< aux(359) s(6116) =< s(4777)+s(4777) s(6117) =< s(4777)+s(4777) s(6118) =< s(4777)+s(4777) s(6119) =< s(4777)+s(4777) s(6120) =< s(6117)*s(4734) s(6119) =< s(6117)*s(4734) s(6121) =< s(6117)*s(4734) s(6122) =< s(6116) s(6123) =< s(6117)*s(4944) s(6118) =< s(6117)*aux(358) s(6124) =< s(6120) s(6125) =< s(6119) s(6126) =< s(6118) s(6127) =< aux(358) s(6128) =< aux(358) s(6127) =< s(4777)+s(4777) s(6128) =< s(4777)+s(4777) s(6129) =< s(4777)+s(4777) s(6130) =< s(4777)+s(4777) s(6131) =< s(6128)*s(4734) s(6130) =< s(6128)*s(4734) s(6132) =< s(6128)*s(4734) s(6133) =< s(6127) s(6134) =< s(6128)*s(4944) s(6129) =< s(6128)*aux(358) s(6135) =< s(6131) s(6136) =< s(6130) s(6137) =< s(6129) with precondition: [] Closed-form bounds of start(V1,V): ------------------------------------- * Chain [70] with precondition: [] - Upper bound: nat(V1)*98646+2764+nat(V1)*140931*nat(V1)+nat(V1)*39690*nat(V1)*nat(V1)+nat(V1)*168*nat(nat(V1)+ -1)+nat(V)*90493+nat(V)*128065*nat(V)+nat(V)*35910*nat(V)*nat(V)+nat(V)*156*nat(nat(V)+ -1)+nat(V)*840*nat(V1+V)+nat(nat(V1+V)+ -1)*84*nat(V1+V)+nat(V1+V)*3922+nat(V1+V)*2856*nat(V1+V)+nat(V1+1)*276+nat(V+1)*411+nat(V1+V+1)*228 - Complexity: n^3 ### Maximum cost of start(V1,V): nat(V1)*98646+2764+nat(V1)*140931*nat(V1)+nat(V1)*39690*nat(V1)*nat(V1)+nat(V1)*168*nat(nat(V1)+ -1)+nat(V)*90493+nat(V)*128065*nat(V)+nat(V)*35910*nat(V)*nat(V)+nat(V)*156*nat(nat(V)+ -1)+nat(V)*840*nat(V1+V)+nat(nat(V1+V)+ -1)*84*nat(V1+V)+nat(V1+V)*3922+nat(V1+V)*2856*nat(V1+V)+nat(V1+1)*276+nat(V+1)*411+nat(V1+V+1)*228 Asymptotic class: n^3 * Total analysis performed in 31071 ms. ---------------------------------------- (16) BOUNDS(1, n^3) ---------------------------------------- (17) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (18) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: min(x, 0') -> 0' min(0', y) -> 0' min(s(x), s(y)) -> s(min(x, y)) max(x, 0') -> x max(0', y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0') -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) The (relative) TRS S consists of the following rules: encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_max(x_1, x_2)) -> max(encArg(x_1), encArg(x_2)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_max(x_1, x_2) -> max(encArg(x_1), encArg(x_2)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (19) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (20) Obligation: Innermost TRS: Rules: min(x, 0') -> 0' min(0', y) -> 0' min(s(x), s(y)) -> s(min(x, y)) max(x, 0') -> x max(0', y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0') -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_max(x_1, x_2)) -> max(encArg(x_1), encArg(x_2)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_max(x_1, x_2) -> max(encArg(x_1), encArg(x_2)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) Types: min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd 0' :: 0':s:cons_min:cons_max:cons_-:cons_gcd s :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd - :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encArg :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_- :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_0 :: 0':s:cons_min:cons_max:cons_-:cons_gcd encode_s :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_- :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd hole_0':s:cons_min:cons_max:cons_-:cons_gcd1_3 :: 0':s:cons_min:cons_max:cons_-:cons_gcd gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3 :: Nat -> 0':s:cons_min:cons_max:cons_-:cons_gcd ---------------------------------------- (21) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: min, max, -, gcd, encArg They will be analysed ascendingly in the following order: min < gcd min < encArg max < gcd max < encArg - < gcd - < encArg gcd < encArg ---------------------------------------- (22) Obligation: Innermost TRS: Rules: min(x, 0') -> 0' min(0', y) -> 0' min(s(x), s(y)) -> s(min(x, y)) max(x, 0') -> x max(0', y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0') -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_max(x_1, x_2)) -> max(encArg(x_1), encArg(x_2)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_max(x_1, x_2) -> max(encArg(x_1), encArg(x_2)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) Types: min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd 0' :: 0':s:cons_min:cons_max:cons_-:cons_gcd s :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd - :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encArg :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_- :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_0 :: 0':s:cons_min:cons_max:cons_-:cons_gcd encode_s :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_- :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd hole_0':s:cons_min:cons_max:cons_-:cons_gcd1_3 :: 0':s:cons_min:cons_max:cons_-:cons_gcd gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3 :: Nat -> 0':s:cons_min:cons_max:cons_-:cons_gcd Generator Equations: gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0) <=> 0' gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(+(x, 1)) <=> s(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(x)) The following defined symbols remain to be analysed: min, max, -, gcd, encArg They will be analysed ascendingly in the following order: min < gcd min < encArg max < gcd max < encArg - < gcd - < encArg gcd < encArg ---------------------------------------- (23) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: min(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n4_3), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n4_3)) -> gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n4_3), rt in Omega(1 + n4_3) Induction Base: min(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0)) ->_R^Omega(1) 0' Induction Step: min(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(+(n4_3, 1)), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(+(n4_3, 1))) ->_R^Omega(1) s(min(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n4_3), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n4_3))) ->_IH s(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(c5_3)) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (24) Complex Obligation (BEST) ---------------------------------------- (25) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: min(x, 0') -> 0' min(0', y) -> 0' min(s(x), s(y)) -> s(min(x, y)) max(x, 0') -> x max(0', y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0') -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_max(x_1, x_2)) -> max(encArg(x_1), encArg(x_2)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_max(x_1, x_2) -> max(encArg(x_1), encArg(x_2)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) Types: min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd 0' :: 0':s:cons_min:cons_max:cons_-:cons_gcd s :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd - :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encArg :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_- :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_0 :: 0':s:cons_min:cons_max:cons_-:cons_gcd encode_s :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_- :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd hole_0':s:cons_min:cons_max:cons_-:cons_gcd1_3 :: 0':s:cons_min:cons_max:cons_-:cons_gcd gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3 :: Nat -> 0':s:cons_min:cons_max:cons_-:cons_gcd Generator Equations: gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0) <=> 0' gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(+(x, 1)) <=> s(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(x)) The following defined symbols remain to be analysed: min, max, -, gcd, encArg They will be analysed ascendingly in the following order: min < gcd min < encArg max < gcd max < encArg - < gcd - < encArg gcd < encArg ---------------------------------------- (26) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (27) BOUNDS(n^1, INF) ---------------------------------------- (28) Obligation: Innermost TRS: Rules: min(x, 0') -> 0' min(0', y) -> 0' min(s(x), s(y)) -> s(min(x, y)) max(x, 0') -> x max(0', y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0') -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_max(x_1, x_2)) -> max(encArg(x_1), encArg(x_2)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_max(x_1, x_2) -> max(encArg(x_1), encArg(x_2)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) Types: min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd 0' :: 0':s:cons_min:cons_max:cons_-:cons_gcd s :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd - :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encArg :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_- :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_0 :: 0':s:cons_min:cons_max:cons_-:cons_gcd encode_s :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_- :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd hole_0':s:cons_min:cons_max:cons_-:cons_gcd1_3 :: 0':s:cons_min:cons_max:cons_-:cons_gcd gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3 :: Nat -> 0':s:cons_min:cons_max:cons_-:cons_gcd Lemmas: min(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n4_3), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n4_3)) -> gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n4_3), rt in Omega(1 + n4_3) Generator Equations: gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0) <=> 0' gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(+(x, 1)) <=> s(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(x)) The following defined symbols remain to be analysed: max, -, gcd, encArg They will be analysed ascendingly in the following order: max < gcd max < encArg - < gcd - < encArg gcd < encArg ---------------------------------------- (29) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: max(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n517_3), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n517_3)) -> gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n517_3), rt in Omega(1 + n517_3) Induction Base: max(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0)) ->_R^Omega(1) gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0) Induction Step: max(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(+(n517_3, 1)), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(+(n517_3, 1))) ->_R^Omega(1) s(max(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n517_3), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n517_3))) ->_IH s(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(c518_3)) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (30) Obligation: Innermost TRS: Rules: min(x, 0') -> 0' min(0', y) -> 0' min(s(x), s(y)) -> s(min(x, y)) max(x, 0') -> x max(0', y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0') -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_max(x_1, x_2)) -> max(encArg(x_1), encArg(x_2)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_max(x_1, x_2) -> max(encArg(x_1), encArg(x_2)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) Types: min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd 0' :: 0':s:cons_min:cons_max:cons_-:cons_gcd s :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd - :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encArg :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_- :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_0 :: 0':s:cons_min:cons_max:cons_-:cons_gcd encode_s :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_- :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd hole_0':s:cons_min:cons_max:cons_-:cons_gcd1_3 :: 0':s:cons_min:cons_max:cons_-:cons_gcd gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3 :: Nat -> 0':s:cons_min:cons_max:cons_-:cons_gcd Lemmas: min(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n4_3), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n4_3)) -> gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n4_3), rt in Omega(1 + n4_3) max(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n517_3), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n517_3)) -> gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n517_3), rt in Omega(1 + n517_3) Generator Equations: gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0) <=> 0' gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(+(x, 1)) <=> s(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(x)) The following defined symbols remain to be analysed: -, gcd, encArg They will be analysed ascendingly in the following order: - < gcd - < encArg gcd < encArg ---------------------------------------- (31) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: -(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n1172_3), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n1172_3)) -> gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0), rt in Omega(1 + n1172_3) Induction Base: -(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0)) ->_R^Omega(1) gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0) Induction Step: -(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(+(n1172_3, 1)), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(+(n1172_3, 1))) ->_R^Omega(1) -(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n1172_3), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n1172_3)) ->_IH gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (32) Obligation: Innermost TRS: Rules: min(x, 0') -> 0' min(0', y) -> 0' min(s(x), s(y)) -> s(min(x, y)) max(x, 0') -> x max(0', y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0') -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_min(x_1, x_2)) -> min(encArg(x_1), encArg(x_2)) encArg(cons_max(x_1, x_2)) -> max(encArg(x_1), encArg(x_2)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) encode_min(x_1, x_2) -> min(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_max(x_1, x_2) -> max(encArg(x_1), encArg(x_2)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) Types: min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd 0' :: 0':s:cons_min:cons_max:cons_-:cons_gcd s :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd - :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encArg :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_- :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd cons_gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_min :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_0 :: 0':s:cons_min:cons_max:cons_-:cons_gcd encode_s :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_max :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_- :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd encode_gcd :: 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd -> 0':s:cons_min:cons_max:cons_-:cons_gcd hole_0':s:cons_min:cons_max:cons_-:cons_gcd1_3 :: 0':s:cons_min:cons_max:cons_-:cons_gcd gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3 :: Nat -> 0':s:cons_min:cons_max:cons_-:cons_gcd Lemmas: min(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n4_3), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n4_3)) -> gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n4_3), rt in Omega(1 + n4_3) max(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n517_3), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n517_3)) -> gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n517_3), rt in Omega(1 + n517_3) -(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n1172_3), gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n1172_3)) -> gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0), rt in Omega(1 + n1172_3) Generator Equations: gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0) <=> 0' gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(+(x, 1)) <=> s(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(x)) The following defined symbols remain to be analysed: gcd, encArg They will be analysed ascendingly in the following order: gcd < encArg ---------------------------------------- (33) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n1805_3)) -> gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n1805_3), rt in Omega(0) Induction Base: encArg(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(0)) ->_R^Omega(0) 0' Induction Step: encArg(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(+(n1805_3, 1))) ->_R^Omega(0) s(encArg(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(n1805_3))) ->_IH s(gen_0':s:cons_min:cons_max:cons_-:cons_gcd2_3(c1806_3)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (34) BOUNDS(1, INF)