/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3).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), 191 ms] (4) CpxRelTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 43.0 s] (14) BOUNDS(1, n^3) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRelTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 5 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 512 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 110 ms] (28) 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: minus(x, y) -> cond(gt(x, y), x, y) cond(false, x, y) -> 0 cond(true, x, y) -> s(minus(x, s(y))) gt(0, v) -> false gt(s(u), 0) -> true gt(s(u), s(v)) -> gt(u, v) 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(false) -> false encArg(0) -> 0 encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gt(x_1, x_2)) -> gt(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gt(x_1, x_2) -> gt(encArg(x_1), encArg(x_2)) encode_false -> false encode_0 -> 0 encode_true -> true encode_s(x_1) -> s(encArg(x_1)) ---------------------------------------- (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: minus(x, y) -> cond(gt(x, y), x, y) cond(false, x, y) -> 0 cond(true, x, y) -> s(minus(x, s(y))) gt(0, v) -> false gt(s(u), 0) -> true gt(s(u), s(v)) -> gt(u, v) The (relative) TRS S consists of the following rules: encArg(false) -> false encArg(0) -> 0 encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gt(x_1, x_2)) -> gt(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gt(x_1, x_2) -> gt(encArg(x_1), encArg(x_2)) encode_false -> false encode_0 -> 0 encode_true -> true encode_s(x_1) -> s(encArg(x_1)) 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: minus(x, y) -> cond(gt(x, y), x, y) cond(false, x, y) -> 0 cond(true, x, y) -> s(minus(x, s(y))) gt(0, v) -> false gt(s(u), 0) -> true gt(s(u), s(v)) -> gt(u, v) The (relative) TRS S consists of the following rules: encArg(false) -> false encArg(0) -> 0 encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gt(x_1, x_2)) -> gt(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gt(x_1, x_2) -> gt(encArg(x_1), encArg(x_2)) encode_false -> false encode_0 -> 0 encode_true -> true encode_s(x_1) -> s(encArg(x_1)) 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: minus(x, y) -> cond(gt(x, y), x, y) [1] cond(false, x, y) -> 0 [1] cond(true, x, y) -> s(minus(x, s(y))) [1] gt(0, v) -> false [1] gt(s(u), 0) -> true [1] gt(s(u), s(v)) -> gt(u, v) [1] encArg(false) -> false [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_gt(x_1, x_2)) -> gt(encArg(x_1), encArg(x_2)) [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_gt(x_1, x_2) -> gt(encArg(x_1), encArg(x_2)) [0] encode_false -> false [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s(x_1) -> s(encArg(x_1)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: minus(x, y) -> cond(gt(x, y), x, y) [1] cond(false, x, y) -> 0 [1] cond(true, x, y) -> s(minus(x, s(y))) [1] gt(0, v) -> false [1] gt(s(u), 0) -> true [1] gt(s(u), s(v)) -> gt(u, v) [1] encArg(false) -> false [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_gt(x_1, x_2)) -> gt(encArg(x_1), encArg(x_2)) [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_gt(x_1, x_2) -> gt(encArg(x_1), encArg(x_2)) [0] encode_false -> false [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s(x_1) -> s(encArg(x_1)) [0] The TRS has the following type information: minus :: false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt cond :: false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt gt :: false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt false :: false:0:true:s:cons_minus:cons_cond:cons_gt 0 :: false:0:true:s:cons_minus:cons_cond:cons_gt true :: false:0:true:s:cons_minus:cons_cond:cons_gt s :: false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt encArg :: false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt cons_minus :: false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt cons_cond :: false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt cons_gt :: false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt encode_minus :: false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt encode_cond :: false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt encode_gt :: false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt encode_false :: false:0:true:s:cons_minus:cons_cond:cons_gt encode_0 :: false:0:true:s:cons_minus:cons_cond:cons_gt encode_true :: false:0:true:s:cons_minus:cons_cond:cons_gt encode_s :: false:0:true:s:cons_minus:cons_cond:cons_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt Rewrite Strategy: INNERMOST ---------------------------------------- (9) 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_minus(v0, v1) -> null_encode_minus [0] encode_cond(v0, v1, v2) -> null_encode_cond [0] encode_gt(v0, v1) -> null_encode_gt [0] encode_false -> null_encode_false [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s(v0) -> null_encode_s [0] cond(v0, v1, v2) -> null_cond [0] gt(v0, v1) -> null_gt [0] And the following fresh constants: null_encArg, null_encode_minus, null_encode_cond, null_encode_gt, null_encode_false, null_encode_0, null_encode_true, null_encode_s, null_cond, null_gt ---------------------------------------- (10) 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: minus(x, y) -> cond(gt(x, y), x, y) [1] cond(false, x, y) -> 0 [1] cond(true, x, y) -> s(minus(x, s(y))) [1] gt(0, v) -> false [1] gt(s(u), 0) -> true [1] gt(s(u), s(v)) -> gt(u, v) [1] encArg(false) -> false [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_gt(x_1, x_2)) -> gt(encArg(x_1), encArg(x_2)) [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_gt(x_1, x_2) -> gt(encArg(x_1), encArg(x_2)) [0] encode_false -> false [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s(x_1) -> s(encArg(x_1)) [0] encArg(v0) -> null_encArg [0] encode_minus(v0, v1) -> null_encode_minus [0] encode_cond(v0, v1, v2) -> null_encode_cond [0] encode_gt(v0, v1) -> null_encode_gt [0] encode_false -> null_encode_false [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s(v0) -> null_encode_s [0] cond(v0, v1, v2) -> null_cond [0] gt(v0, v1) -> null_gt [0] The TRS has the following type information: minus :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt cond :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt gt :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt false :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt 0 :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt true :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt s :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt encArg :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt cons_minus :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt cons_cond :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt cons_gt :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt encode_minus :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt encode_cond :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt encode_gt :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt encode_false :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt encode_0 :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt encode_true :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt encode_s :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt -> false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt null_encArg :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt null_encode_minus :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt null_encode_cond :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt null_encode_gt :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt null_encode_false :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt null_encode_0 :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt null_encode_true :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt null_encode_s :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt null_cond :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt null_gt :: false:0:true:s:cons_minus:cons_cond:cons_gt:null_encArg:null_encode_minus:null_encode_cond:null_encode_gt:null_encode_false:null_encode_0:null_encode_true:null_encode_s:null_cond:null_gt Rewrite Strategy: INNERMOST ---------------------------------------- (11) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: false => 1 0 => 0 true => 2 null_encArg => 0 null_encode_minus => 0 null_encode_cond => 0 null_encode_gt => 0 null_encode_false => 0 null_encode_0 => 0 null_encode_true => 0 null_encode_s => 0 null_cond => 0 null_gt => 0 ---------------------------------------- (12) Obligation: Complexity RNTS consisting of the following rules: cond(z, z', z'') -{ 1 }-> 0 :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0 cond(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 cond(z, z', z'') -{ 1 }-> 1 + minus(x, 1 + y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0 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 }-> gt(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> cond(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encArg(z) -{ 0 }-> 2 :|: z = 2 encArg(z) -{ 0 }-> 1 :|: z = 1 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_0 -{ 0 }-> 0 :|: encode_cond(z, z', z'') -{ 0 }-> cond(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3 encode_cond(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_false -{ 0 }-> 1 :|: encode_false -{ 0 }-> 0 :|: encode_gt(z, z') -{ 0 }-> gt(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_gt(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_minus(z, z') -{ 0 }-> minus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_minus(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 encode_true -{ 0 }-> 2 :|: encode_true -{ 0 }-> 0 :|: gt(z, z') -{ 1 }-> gt(u, v) :|: v >= 0, z' = 1 + v, z = 1 + u, u >= 0 gt(z, z') -{ 1 }-> 2 :|: z = 1 + u, z' = 0, u >= 0 gt(z, z') -{ 1 }-> 1 :|: v >= 0, z' = v, z = 0 gt(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 minus(z, z') -{ 1 }-> cond(gt(x, y), x, y) :|: x >= 0, y >= 0, z = x, z' = y Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (13) CompleteCoflocoProof (FINISHED) Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: eq(start(V1, V, V5),0,[minus(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V5),0,[cond(V1, V, V5, Out)],[V1 >= 0,V >= 0,V5 >= 0]). eq(start(V1, V, V5),0,[gt(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V5),0,[encArg(V1, Out)],[V1 >= 0]). eq(start(V1, V, V5),0,[fun(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V5),0,[fun1(V1, V, V5, Out)],[V1 >= 0,V >= 0,V5 >= 0]). eq(start(V1, V, V5),0,[fun2(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V5),0,[fun3(Out)],[]). eq(start(V1, V, V5),0,[fun4(Out)],[]). eq(start(V1, V, V5),0,[fun5(Out)],[]). eq(start(V1, V, V5),0,[fun6(V1, Out)],[V1 >= 0]). eq(minus(V1, V, Out),1,[gt(V3, V2, Ret0),cond(Ret0, V3, V2, Ret)],[Out = Ret,V3 >= 0,V2 >= 0,V1 = V3,V = V2]). eq(cond(V1, V, V5, Out),1,[],[Out = 0,V = V4,V5 = V6,V1 = 1,V4 >= 0,V6 >= 0]). eq(cond(V1, V, V5, Out),1,[minus(V8, 1 + V7, Ret1)],[Out = 1 + Ret1,V1 = 2,V = V8,V5 = V7,V8 >= 0,V7 >= 0]). eq(gt(V1, V, Out),1,[],[Out = 1,V9 >= 0,V = V9,V1 = 0]). eq(gt(V1, V, Out),1,[],[Out = 2,V1 = 1 + V10,V = 0,V10 >= 0]). eq(gt(V1, V, Out),1,[gt(V11, V12, Ret2)],[Out = Ret2,V12 >= 0,V = 1 + V12,V1 = 1 + V11,V11 >= 0]). eq(encArg(V1, Out),0,[],[Out = 1,V1 = 1]). eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]). eq(encArg(V1, Out),0,[],[Out = 2,V1 = 2]). eq(encArg(V1, Out),0,[encArg(V13, Ret11)],[Out = 1 + Ret11,V1 = 1 + V13,V13 >= 0]). eq(encArg(V1, Out),0,[encArg(V14, Ret01),encArg(V15, Ret12),minus(Ret01, Ret12, Ret3)],[Out = Ret3,V14 >= 0,V1 = 1 + V14 + V15,V15 >= 0]). eq(encArg(V1, Out),0,[encArg(V17, Ret02),encArg(V18, Ret13),encArg(V16, Ret21),cond(Ret02, Ret13, Ret21, Ret4)],[Out = Ret4,V17 >= 0,V1 = 1 + V16 + V17 + V18,V16 >= 0,V18 >= 0]). eq(encArg(V1, Out),0,[encArg(V20, Ret03),encArg(V19, Ret14),gt(Ret03, Ret14, Ret5)],[Out = Ret5,V20 >= 0,V1 = 1 + V19 + V20,V19 >= 0]). eq(fun(V1, V, Out),0,[encArg(V22, Ret04),encArg(V21, Ret15),minus(Ret04, Ret15, Ret6)],[Out = Ret6,V22 >= 0,V21 >= 0,V1 = V22,V = V21]). eq(fun1(V1, V, V5, Out),0,[encArg(V24, Ret05),encArg(V25, Ret16),encArg(V23, Ret22),cond(Ret05, Ret16, Ret22, Ret7)],[Out = Ret7,V24 >= 0,V23 >= 0,V25 >= 0,V1 = V24,V = V25,V5 = V23]). eq(fun2(V1, V, Out),0,[encArg(V26, Ret06),encArg(V27, Ret17),gt(Ret06, Ret17, Ret8)],[Out = Ret8,V26 >= 0,V27 >= 0,V1 = V26,V = V27]). eq(fun3(Out),0,[],[Out = 1]). eq(fun4(Out),0,[],[Out = 0]). eq(fun5(Out),0,[],[Out = 2]). eq(fun6(V1, Out),0,[encArg(V28, Ret18)],[Out = 1 + Ret18,V28 >= 0,V1 = V28]). eq(encArg(V1, Out),0,[],[Out = 0,V29 >= 0,V1 = V29]). eq(fun(V1, V, Out),0,[],[Out = 0,V31 >= 0,V30 >= 0,V1 = V31,V = V30]). eq(fun1(V1, V, V5, Out),0,[],[Out = 0,V33 >= 0,V5 = V34,V32 >= 0,V1 = V33,V = V32,V34 >= 0]). eq(fun2(V1, V, Out),0,[],[Out = 0,V35 >= 0,V36 >= 0,V1 = V35,V = V36]). eq(fun3(Out),0,[],[Out = 0]). eq(fun5(Out),0,[],[Out = 0]). eq(fun6(V1, Out),0,[],[Out = 0,V37 >= 0,V1 = V37]). eq(cond(V1, V, V5, Out),0,[],[Out = 0,V38 >= 0,V5 = V39,V40 >= 0,V1 = V38,V = V40,V39 >= 0]). eq(gt(V1, V, Out),0,[],[Out = 0,V42 >= 0,V41 >= 0,V1 = V42,V = V41]). input_output_vars(minus(V1,V,Out),[V1,V],[Out]). input_output_vars(cond(V1,V,V5,Out),[V1,V,V5],[Out]). input_output_vars(gt(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(V1,V,V5,Out),[V1,V,V5],[Out]). input_output_vars(fun2(V1,V,Out),[V1,V],[Out]). input_output_vars(fun3(Out),[],[Out]). input_output_vars(fun4(Out),[],[Out]). input_output_vars(fun5(Out),[],[Out]). input_output_vars(fun6(V1,Out),[V1],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [gt/3] 1. recursive : [cond/4,minus/3] 2. recursive [non_tail,multiple] : [encArg/2] 3. non_recursive : [fun/3] 4. non_recursive : [fun1/4] 5. non_recursive : [fun2/3] 6. non_recursive : [fun3/1] 7. non_recursive : [fun4/1] 8. non_recursive : [fun5/1] 9. non_recursive : [fun6/2] 10. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into gt/3 1. SCC is partially evaluated into minus/3 2. SCC is partially evaluated into encArg/2 3. SCC is partially evaluated into fun/3 4. SCC is partially evaluated into fun1/4 5. SCC is partially evaluated into fun2/3 6. SCC is partially evaluated into fun3/1 7. SCC is completely evaluated into other SCCs 8. SCC is partially evaluated into fun5/1 9. SCC is partially evaluated into fun6/2 10. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations gt/3 * CE 19 is refined into CE [43] * CE 17 is refined into CE [44] * CE 16 is refined into CE [45] * CE 18 is refined into CE [46] ### Cost equations --> "Loop" of gt/3 * CEs [46] --> Loop 23 * CEs [43] --> Loop 24 * CEs [44] --> Loop 25 * CEs [45] --> Loop 26 ### Ranking functions of CR gt(V1,V,Out) * RF of phase [23]: [V,V1] #### Partial ranking functions of CR gt(V1,V,Out) * Partial RF of phase [23]: - RF of loop [23:1]: V V1 ### Specialization of cost equations minus/3 * CE 13 is refined into CE [47,48,49,50,51] * CE 15 is refined into CE [52,53] * CE 14 is refined into CE [54,55] ### Cost equations --> "Loop" of minus/3 * CEs [55] --> Loop 27 * CEs [54] --> Loop 28 * CEs [48] --> Loop 29 * CEs [47,49,50,51,52,53] --> Loop 30 ### Ranking functions of CR minus(V1,V,Out) * RF of phase [27]: [V1-V] #### Partial ranking functions of CR minus(V1,V,Out) * Partial RF of phase [27]: - RF of loop [27:1]: V1-V ### Specialization of cost equations encArg/2 * CE 24 is refined into CE [56] * CE 25 is refined into CE [57] * CE 23 is refined into CE [58] * CE 27 is refined into CE [59,60,61,62] * CE 28 is refined into CE [63,64,65,66,67] * CE 26 is refined into CE [68] * CE 21 is refined into CE [69,70] * CE 20 is refined into CE [71] * CE 22 is refined into CE [72] ### Cost equations --> "Loop" of encArg/2 * CEs [70] --> Loop 31 * CEs [69] --> Loop 32 * CEs [71,72] --> Loop 33 * CEs [68] --> Loop 34 * CEs [62] --> Loop 35 * CEs [61] --> Loop 36 * CEs [67] --> Loop 37 * CEs [64] --> Loop 38 * CEs [66] --> Loop 39 * CEs [60] --> Loop 40 * CEs [63] --> Loop 41 * CEs [59,65] --> Loop 42 * CEs [56] --> Loop 43 * CEs [57] --> Loop 44 * CEs [58] --> Loop 45 ### Ranking functions of CR encArg(V1,Out) * RF of phase [31,32,33,34,35,36,37,38,39,40,41,42]: [V1] #### Partial ranking functions of CR encArg(V1,Out) * Partial RF of phase [31,32,33,34,35,36,37,38,39,40,41,42]: - RF of loop [31:1,31:2,31:3,32:1,32:2,32:3,33:1,33:2,33:3,34:1,35:1,35:2,36:1,36:2,37:1,37:2,38:1,38:2,39:1,39:2,40:1,40:2,41:1,41:2,42:1,42:2]: V1 ### Specialization of cost equations fun/3 * CE 29 is refined into CE [73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92] * CE 30 is refined into CE [93] ### Cost equations --> "Loop" of fun/3 * CEs [76,78] --> Loop 46 * CEs [77,91] --> Loop 47 * CEs [75,81,84,89] --> Loop 48 * CEs [74,80,83,85,88] --> Loop 49 * CEs [73,79,82,86,87,90,92,93] --> Loop 50 ### Ranking functions of CR fun(V1,V,Out) #### Partial ranking functions of CR fun(V1,V,Out) ### Specialization of cost equations fun1/4 * CE 31 is refined into CE [94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120] * CE 32 is refined into CE [121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148] * CE 33 is refined into CE [149,150,151,152,153,154,155,156,157] * CE 34 is refined into CE [158] ### Cost equations --> "Loop" of fun1/4 * CEs [128,131] --> Loop 51 * CEs [127,129,130] --> Loop 52 * CEs [97,98,99,115,116,117,152,153,154] --> Loop 53 * CEs [124,138] --> Loop 54 * CEs [123,133,137,147] --> Loop 55 * CEs [95,101,104,110,113,119,150,156] --> Loop 56 * CEs [122,126,136,140,142,145] --> Loop 57 * CEs [121,125,132,134,135,139,141,143,144,146,148] --> Loop 58 * CEs [94,96,100,102,103,105,106,107,108,109,111,112,114,118,120,149,151,155,157,158] --> Loop 59 ### Ranking functions of CR fun1(V1,V,V5,Out) #### Partial ranking functions of CR fun1(V1,V,V5,Out) ### Specialization of cost equations fun2/3 * CE 35 is refined into CE [159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184] * CE 36 is refined into CE [185] ### Cost equations --> "Loop" of fun2/3 * CEs [167] --> Loop 60 * CEs [164,166,181] --> Loop 61 * CEs [165,182] --> Loop 62 * CEs [160,163,169,171,174,177] --> Loop 63 * CEs [159,162,168,173,176,179,183] --> Loop 64 * CEs [161,170,172,175,178,180,184,185] --> Loop 65 ### Ranking functions of CR fun2(V1,V,Out) #### Partial ranking functions of CR fun2(V1,V,Out) ### Specialization of cost equations fun3/1 * CE 37 is refined into CE [186] * CE 38 is refined into CE [187] ### Cost equations --> "Loop" of fun3/1 * CEs [186] --> Loop 66 * CEs [187] --> Loop 67 ### Ranking functions of CR fun3(Out) #### Partial ranking functions of CR fun3(Out) ### Specialization of cost equations fun5/1 * CE 39 is refined into CE [188] * CE 40 is refined into CE [189] ### Cost equations --> "Loop" of fun5/1 * CEs [188] --> Loop 68 * CEs [189] --> Loop 69 ### Ranking functions of CR fun5(Out) #### Partial ranking functions of CR fun5(Out) ### Specialization of cost equations fun6/2 * CE 41 is refined into CE [190,191,192] * CE 42 is refined into CE [193] ### Cost equations --> "Loop" of fun6/2 * CEs [192] --> Loop 70 * CEs [193] --> Loop 71 * CEs [190,191] --> Loop 72 ### Ranking functions of CR fun6(V1,Out) #### Partial ranking functions of CR fun6(V1,Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [194] * CE 2 is refined into CE [195,196] * CE 3 is refined into CE [197] * CE 4 is refined into CE [198,199,200,201] * CE 5 is refined into CE [202,203,204,205,206] * CE 6 is refined into CE [207,208,209] * CE 7 is refined into CE [210,211,212,213] * CE 8 is refined into CE [214,215,216,217,218,219] * CE 9 is refined into CE [220,221,222] * CE 10 is refined into CE [223,224] * CE 11 is refined into CE [225,226] * CE 12 is refined into CE [227,228,229] ### Cost equations --> "Loop" of start/3 * CEs [194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229] --> Loop 73 ### Ranking functions of CR start(V1,V,V5) #### Partial ranking functions of CR start(V1,V,V5) Computing Bounds ===================================== #### Cost of chains of gt(V1,V,Out): * Chain [[23],26]: 1*it(23)+1 Such that:it(23) =< V1 with precondition: [Out=1,V1>=1,V>=V1] * Chain [[23],25]: 1*it(23)+1 Such that:it(23) =< V with precondition: [Out=2,V>=1,V1>=V+1] * Chain [[23],24]: 1*it(23)+0 Such that:it(23) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [26]: 1 with precondition: [V1=0,Out=1,V>=0] * Chain [25]: 1 with precondition: [V=0,Out=2,V1>=1] * Chain [24]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of minus(V1,V,Out): * Chain [[27],30]: 3*it(27)+2*s(2)+2*s(3)+1*s(8)+3 Such that:aux(2) =< V+Out it(27) =< Out aux(4) =< V1 s(3) =< aux(4) s(2) =< aux(2) s(8) =< it(27)*aux(4) with precondition: [V>=1,Out>=1,V1>=Out+V] * Chain [30]: 2*s(2)+2*s(3)+3 Such that:aux(1) =< V1 aux(2) =< V s(3) =< aux(1) s(2) =< aux(2) with precondition: [Out=0,V1>=0,V>=0] * Chain [29]: 2 with precondition: [V=0,Out=0,V1>=1] * Chain [28,[27],30]: 5*it(27)+2*s(3)+1*s(8)+6 Such that:aux(4) =< V1 aux(5) =< Out it(27) =< aux(5) s(3) =< aux(4) s(8) =< it(27)*aux(4) with precondition: [V=0,Out>=2,V1>=Out] * Chain [28,30]: 2*s(2)+2*s(3)+6 Such that:aux(2) =< 1 aux(1) =< V1 s(3) =< aux(1) s(2) =< aux(2) with precondition: [V=0,Out=1,V1>=1] #### Cost of chains of encArg(V1,Out): * Chain [45]: 0 with precondition: [V1=1,Out=1] * Chain [44]: 0 with precondition: [V1=2,Out=2] * Chain [43]: 0 with precondition: [Out=0,V1>=0] * Chain [multiple([31,32,33,34,35,36,37,38,39,40,41,42],[[45],[44],[43]])]: 4*it(31)+4*it(32)+1*it(33)+3*it(35)+6*it(36)+1*it(37)+7*it(38)+1*it(39)+4*it(41)+7*s(69)+1*s(70)+2*s(72)+2*s(73)+7*s(76)+1*s(77)+7*s(79)+1*s(80)+1*s(82)+1*s(83)+2*s(84)+2*s(85)+2*s(88)+2*s(89)+1*s(90)+0 Such that:it([45]) =< 2/3*V1+1/3 aux(29) =< V1 aux(30) =< 2*V1+1 aux(31) =< V1/2 aux(32) =< 2/3*V1 aux(33) =< 2/5*V1 aux(34) =< 3/7*V1 aux(35) =< 3/11*V1 it(33) =< aux(29) it(35) =< aux(29) it(36) =< aux(29) it(37) =< aux(29) it(38) =< aux(29) it(39) =< aux(29) it(41) =< aux(29) it([45]) =< aux(29) it([43]) =< aux(30) it([45]) =< aux(30) it(36) =< aux(31) it(37) =< aux(31) it(39) =< aux(31) aux(24) =< aux(32) it(38) =< aux(32) it(39) =< aux(32) it(35) =< aux(33) it(37) =< aux(33) it(32) =< aux(34) it(31) =< aux(35) aux(15) =< aux(29)+1 aux(17) =< aux(29)+2 aux(10) =< aux(29) aux(12) =< aux(29)-1 aux(24) =< it([43])*(1/3)+aux(32) it(38) =< it([43])*(1/3)+aux(32) it(39) =< it([43])*(1/3)+aux(32) it(41) =< it([43])*(1/3)+aux(32) it(36) =< it([43])*(1/2)+aux(31) it(37) =< it([43])*(1/2)+aux(31) it(38) =< it([43])*(1/2)+aux(31) it(39) =< it([43])*(1/2)+aux(31) it(41) =< it([43])*(1/2)+aux(31) it(35) =< it([43])*(3/5)+it([45])*(1/5)+aux(33) it(36) =< it([43])*(3/5)+it([45])*(1/5)+aux(33) it(37) =< it([43])*(3/5)+it([45])*(1/5)+aux(33) it(38) =< it([43])*(3/5)+it([45])*(1/5)+aux(33) it(39) =< it([43])*(3/5)+it([45])*(1/5)+aux(33) it(41) =< it([43])*(3/5)+it([45])*(1/5)+aux(33) it(32) =< it([43])*(2/7)+aux(34) it(33) =< it([43])*(2/7)+aux(34) it(31) =< it([43])*(4/11)+it([45])*(1/11)+aux(35) it(32) =< it([43])*(4/11)+it([45])*(1/11)+aux(35) it(33) =< it([43])*(4/11)+it([45])*(1/11)+aux(35) s(90) =< it(41)*aux(15) s(92) =< it(41)*aux(15) s(91) =< it(41)*aux(17) s(87) =< it(38)*aux(17) s(83) =< it(39)*aux(10) s(82) =< it(37)*aux(12) s(81) =< it(36)*aux(17) s(78) =< it(35)*aux(15) s(74) =< it(32)*aux(10) s(75) =< it(32)*aux(12) s(71) =< it(31)*aux(10) s(88) =< s(92) s(89) =< s(91) s(84) =< s(87) s(85) =< aux(24) s(79) =< s(81) s(80) =< s(79)*aux(17) s(76) =< s(78) s(77) =< s(76)*aux(15) s(72) =< s(75) s(73) =< s(74) s(69) =< s(71) s(70) =< s(69)*aux(29) with precondition: [V1>=1,Out>=0,V1>=Out] #### Cost of chains of fun(V1,V,Out): * Chain [50]: 2*s(147)+6*s(148)+12*s(149)+2*s(150)+14*s(151)+2*s(152)+8*s(153)+8*s(155)+8*s(156)+2*s(161)+2*s(165)+2*s(166)+4*s(172)+4*s(173)+4*s(174)+4*s(175)+14*s(176)+2*s(177)+14*s(178)+2*s(179)+4*s(180)+4*s(181)+14*s(182)+2*s(183)+3*s(192)+9*s(193)+18*s(194)+3*s(195)+21*s(196)+3*s(197)+12*s(198)+12*s(200)+12*s(201)+3*s(206)+3*s(210)+3*s(211)+6*s(217)+6*s(218)+6*s(219)+6*s(220)+21*s(221)+3*s(222)+21*s(223)+3*s(224)+6*s(225)+6*s(226)+21*s(227)+3*s(228)+4*s(231)+6*s(232)+8*s(329)+3 Such that:aux(43) =< 2 aux(44) =< V1 aux(45) =< 2*V1+1 aux(46) =< V1/2 aux(47) =< 2/3*V1 aux(48) =< 2/3*V1+1/3 aux(49) =< 2/5*V1 aux(50) =< 3/7*V1 aux(51) =< 3/11*V1 aux(52) =< V aux(53) =< 2*V+1 aux(54) =< V/2 aux(55) =< 2/3*V aux(56) =< 2/3*V+1/3 aux(57) =< 2/5*V aux(58) =< 3/7*V aux(59) =< 3/11*V s(143) =< aux(48) s(188) =< aux(56) s(329) =< aux(43) s(232) =< aux(52) s(192) =< aux(52) s(193) =< aux(52) s(194) =< aux(52) s(195) =< aux(52) s(196) =< aux(52) s(197) =< aux(52) s(198) =< aux(52) s(188) =< aux(52) s(188) =< aux(53) s(194) =< aux(54) s(195) =< aux(54) s(197) =< aux(54) s(199) =< aux(55) s(196) =< aux(55) s(197) =< aux(55) s(193) =< aux(57) s(195) =< aux(57) s(200) =< aux(58) s(201) =< aux(59) s(202) =< aux(52)+1 s(203) =< aux(52)+2 s(204) =< aux(52) s(205) =< aux(52)-1 s(199) =< aux(53)*(1/3)+aux(55) s(196) =< aux(53)*(1/3)+aux(55) s(197) =< aux(53)*(1/3)+aux(55) s(198) =< aux(53)*(1/3)+aux(55) s(194) =< aux(53)*(1/2)+aux(54) s(195) =< aux(53)*(1/2)+aux(54) s(196) =< aux(53)*(1/2)+aux(54) s(197) =< aux(53)*(1/2)+aux(54) s(198) =< aux(53)*(1/2)+aux(54) s(193) =< aux(53)*(3/5)+s(188)*(1/5)+aux(57) s(194) =< aux(53)*(3/5)+s(188)*(1/5)+aux(57) s(195) =< aux(53)*(3/5)+s(188)*(1/5)+aux(57) s(196) =< aux(53)*(3/5)+s(188)*(1/5)+aux(57) s(197) =< aux(53)*(3/5)+s(188)*(1/5)+aux(57) s(198) =< aux(53)*(3/5)+s(188)*(1/5)+aux(57) s(200) =< aux(53)*(2/7)+aux(58) s(192) =< aux(53)*(2/7)+aux(58) s(201) =< aux(53)*(4/11)+s(188)*(1/11)+aux(59) s(200) =< aux(53)*(4/11)+s(188)*(1/11)+aux(59) s(192) =< aux(53)*(4/11)+s(188)*(1/11)+aux(59) s(206) =< s(198)*s(202) s(207) =< s(198)*s(202) s(208) =< s(198)*s(203) s(209) =< s(196)*s(203) s(210) =< s(197)*s(204) s(211) =< s(195)*s(205) s(212) =< s(194)*s(203) s(213) =< s(193)*s(202) s(214) =< s(200)*s(204) s(215) =< s(200)*s(205) s(216) =< s(201)*s(204) s(217) =< s(207) s(218) =< s(208) s(219) =< s(209) s(220) =< s(199) s(221) =< s(212) s(222) =< s(221)*s(203) s(223) =< s(213) s(224) =< s(223)*s(202) s(225) =< s(215) s(226) =< s(214) s(227) =< s(216) s(228) =< s(227)*aux(52) s(231) =< aux(44) s(147) =< aux(44) s(148) =< aux(44) s(149) =< aux(44) s(150) =< aux(44) s(151) =< aux(44) s(152) =< aux(44) s(153) =< aux(44) s(143) =< aux(44) s(143) =< aux(45) s(149) =< aux(46) s(150) =< aux(46) s(152) =< aux(46) s(154) =< aux(47) s(151) =< aux(47) s(152) =< aux(47) s(148) =< aux(49) s(150) =< aux(49) s(155) =< aux(50) s(156) =< aux(51) s(157) =< aux(44)+1 s(158) =< aux(44)+2 s(159) =< aux(44) s(160) =< aux(44)-1 s(154) =< aux(45)*(1/3)+aux(47) s(151) =< aux(45)*(1/3)+aux(47) s(152) =< aux(45)*(1/3)+aux(47) s(153) =< aux(45)*(1/3)+aux(47) s(149) =< aux(45)*(1/2)+aux(46) s(150) =< aux(45)*(1/2)+aux(46) s(151) =< aux(45)*(1/2)+aux(46) s(152) =< aux(45)*(1/2)+aux(46) s(153) =< aux(45)*(1/2)+aux(46) s(148) =< aux(45)*(3/5)+s(143)*(1/5)+aux(49) s(149) =< aux(45)*(3/5)+s(143)*(1/5)+aux(49) s(150) =< aux(45)*(3/5)+s(143)*(1/5)+aux(49) s(151) =< aux(45)*(3/5)+s(143)*(1/5)+aux(49) s(152) =< aux(45)*(3/5)+s(143)*(1/5)+aux(49) s(153) =< aux(45)*(3/5)+s(143)*(1/5)+aux(49) s(155) =< aux(45)*(2/7)+aux(50) s(147) =< aux(45)*(2/7)+aux(50) s(156) =< aux(45)*(4/11)+s(143)*(1/11)+aux(51) s(155) =< aux(45)*(4/11)+s(143)*(1/11)+aux(51) s(147) =< aux(45)*(4/11)+s(143)*(1/11)+aux(51) s(161) =< s(153)*s(157) s(162) =< s(153)*s(157) s(163) =< s(153)*s(158) s(164) =< s(151)*s(158) s(165) =< s(152)*s(159) s(166) =< s(150)*s(160) s(167) =< s(149)*s(158) s(168) =< s(148)*s(157) s(169) =< s(155)*s(159) s(170) =< s(155)*s(160) s(171) =< s(156)*s(159) s(172) =< s(162) s(173) =< s(163) s(174) =< s(164) s(175) =< s(154) s(176) =< s(167) s(177) =< s(176)*s(158) s(178) =< s(168) s(179) =< s(178)*s(157) s(180) =< s(170) s(181) =< s(169) s(182) =< s(171) s(183) =< s(182)*aux(44) with precondition: [Out=0,V1>=0,V>=0] * Chain [49]: 2*s(400)+6*s(401)+12*s(402)+2*s(403)+14*s(404)+2*s(405)+8*s(406)+8*s(408)+8*s(409)+2*s(414)+2*s(418)+2*s(419)+4*s(425)+4*s(426)+4*s(427)+4*s(428)+14*s(429)+2*s(430)+14*s(431)+2*s(432)+4*s(433)+4*s(434)+14*s(435)+2*s(436)+3*s(445)+9*s(446)+18*s(447)+3*s(448)+21*s(449)+3*s(450)+12*s(451)+12*s(453)+12*s(454)+3*s(459)+3*s(463)+3*s(464)+6*s(470)+6*s(471)+6*s(472)+6*s(473)+21*s(474)+3*s(475)+21*s(476)+3*s(477)+6*s(478)+6*s(479)+21*s(480)+3*s(481)+4*s(484)+11*s(485)+8*s(582)+1*s(634)+6 Such that:aux(63) =< 1 aux(64) =< 2 aux(65) =< V1 aux(66) =< 2*V1+1 aux(67) =< V1/2 aux(68) =< 2/3*V1 aux(69) =< 2/3*V1+1/3 aux(70) =< 2/5*V1 aux(71) =< 3/7*V1 aux(72) =< 3/11*V1 aux(73) =< V aux(74) =< 2*V+1 aux(75) =< V/2 aux(76) =< 2/3*V aux(77) =< 2/3*V+1/3 aux(78) =< 2/5*V aux(79) =< 3/7*V aux(80) =< 3/11*V s(485) =< aux(63) s(396) =< aux(69) s(441) =< aux(77) s(484) =< aux(65) s(445) =< aux(73) s(446) =< aux(73) s(447) =< aux(73) s(448) =< aux(73) s(449) =< aux(73) s(450) =< aux(73) s(451) =< aux(73) s(441) =< aux(73) s(441) =< aux(74) s(447) =< aux(75) s(448) =< aux(75) s(450) =< aux(75) s(452) =< aux(76) s(449) =< aux(76) s(450) =< aux(76) s(446) =< aux(78) s(448) =< aux(78) s(453) =< aux(79) s(454) =< aux(80) s(455) =< aux(73)+1 s(456) =< aux(73)+2 s(457) =< aux(73) s(458) =< aux(73)-1 s(452) =< aux(74)*(1/3)+aux(76) s(449) =< aux(74)*(1/3)+aux(76) s(450) =< aux(74)*(1/3)+aux(76) s(451) =< aux(74)*(1/3)+aux(76) s(447) =< aux(74)*(1/2)+aux(75) s(448) =< aux(74)*(1/2)+aux(75) s(449) =< aux(74)*(1/2)+aux(75) s(450) =< aux(74)*(1/2)+aux(75) s(451) =< aux(74)*(1/2)+aux(75) s(446) =< aux(74)*(3/5)+s(441)*(1/5)+aux(78) s(447) =< aux(74)*(3/5)+s(441)*(1/5)+aux(78) s(448) =< aux(74)*(3/5)+s(441)*(1/5)+aux(78) s(449) =< aux(74)*(3/5)+s(441)*(1/5)+aux(78) s(450) =< aux(74)*(3/5)+s(441)*(1/5)+aux(78) s(451) =< aux(74)*(3/5)+s(441)*(1/5)+aux(78) s(453) =< aux(74)*(2/7)+aux(79) s(445) =< aux(74)*(2/7)+aux(79) s(454) =< aux(74)*(4/11)+s(441)*(1/11)+aux(80) s(453) =< aux(74)*(4/11)+s(441)*(1/11)+aux(80) s(445) =< aux(74)*(4/11)+s(441)*(1/11)+aux(80) s(459) =< s(451)*s(455) s(460) =< s(451)*s(455) s(461) =< s(451)*s(456) s(462) =< s(449)*s(456) s(463) =< s(450)*s(457) s(464) =< s(448)*s(458) s(465) =< s(447)*s(456) s(466) =< s(446)*s(455) s(467) =< s(453)*s(457) s(468) =< s(453)*s(458) s(469) =< s(454)*s(457) s(470) =< s(460) s(471) =< s(461) s(472) =< s(462) s(473) =< s(452) s(474) =< s(465) s(475) =< s(474)*s(456) s(476) =< s(466) s(477) =< s(476)*s(455) s(478) =< s(468) s(479) =< s(467) s(480) =< s(469) s(481) =< s(480)*aux(73) s(400) =< aux(65) s(401) =< aux(65) s(402) =< aux(65) s(403) =< aux(65) s(404) =< aux(65) s(405) =< aux(65) s(406) =< aux(65) s(396) =< aux(65) s(396) =< aux(66) s(402) =< aux(67) s(403) =< aux(67) s(405) =< aux(67) s(407) =< aux(68) s(404) =< aux(68) s(405) =< aux(68) s(401) =< aux(70) s(403) =< aux(70) s(408) =< aux(71) s(409) =< aux(72) s(410) =< aux(65)+1 s(411) =< aux(65)+2 s(412) =< aux(65) s(413) =< aux(65)-1 s(407) =< aux(66)*(1/3)+aux(68) s(404) =< aux(66)*(1/3)+aux(68) s(405) =< aux(66)*(1/3)+aux(68) s(406) =< aux(66)*(1/3)+aux(68) s(402) =< aux(66)*(1/2)+aux(67) s(403) =< aux(66)*(1/2)+aux(67) s(404) =< aux(66)*(1/2)+aux(67) s(405) =< aux(66)*(1/2)+aux(67) s(406) =< aux(66)*(1/2)+aux(67) s(401) =< aux(66)*(3/5)+s(396)*(1/5)+aux(70) s(402) =< aux(66)*(3/5)+s(396)*(1/5)+aux(70) s(403) =< aux(66)*(3/5)+s(396)*(1/5)+aux(70) s(404) =< aux(66)*(3/5)+s(396)*(1/5)+aux(70) s(405) =< aux(66)*(3/5)+s(396)*(1/5)+aux(70) s(406) =< aux(66)*(3/5)+s(396)*(1/5)+aux(70) s(408) =< aux(66)*(2/7)+aux(71) s(400) =< aux(66)*(2/7)+aux(71) s(409) =< aux(66)*(4/11)+s(396)*(1/11)+aux(72) s(408) =< aux(66)*(4/11)+s(396)*(1/11)+aux(72) s(400) =< aux(66)*(4/11)+s(396)*(1/11)+aux(72) s(414) =< s(406)*s(410) s(415) =< s(406)*s(410) s(416) =< s(406)*s(411) s(417) =< s(404)*s(411) s(418) =< s(405)*s(412) s(419) =< s(403)*s(413) s(420) =< s(402)*s(411) s(421) =< s(401)*s(410) s(422) =< s(408)*s(412) s(423) =< s(408)*s(413) s(424) =< s(409)*s(412) s(425) =< s(415) s(426) =< s(416) s(427) =< s(417) s(428) =< s(407) s(429) =< s(420) s(430) =< s(429)*s(411) s(431) =< s(421) s(432) =< s(431)*s(410) s(433) =< s(423) s(434) =< s(422) s(435) =< s(424) s(436) =< s(435)*aux(65) s(582) =< aux(64) s(634) =< s(485)*aux(64) with precondition: [Out=1,V1>=1,V>=0] * Chain [48]: 2*s(647)+6*s(648)+12*s(649)+2*s(650)+14*s(651)+2*s(652)+8*s(653)+8*s(655)+8*s(656)+2*s(661)+2*s(665)+2*s(666)+4*s(672)+4*s(673)+4*s(674)+4*s(675)+14*s(676)+2*s(677)+14*s(678)+2*s(679)+4*s(680)+4*s(681)+14*s(682)+2*s(683)+2*s(692)+6*s(693)+12*s(694)+2*s(695)+14*s(696)+2*s(697)+8*s(698)+8*s(700)+8*s(701)+2*s(706)+2*s(710)+2*s(711)+4*s(717)+4*s(718)+4*s(719)+4*s(720)+14*s(721)+2*s(722)+14*s(723)+2*s(724)+4*s(725)+4*s(726)+14*s(727)+2*s(728)+14*s(731)+2*s(733)+14*s(831)+2*s(833)+6 Such that:aux(85) =< 2 aux(86) =< V1 aux(87) =< 2*V1+1 aux(88) =< V1/2 aux(89) =< 2/3*V1 aux(90) =< 2/3*V1+1/3 aux(91) =< 2/5*V1 aux(92) =< 3/7*V1 aux(93) =< 3/11*V1 aux(94) =< V aux(95) =< 2*V+1 aux(96) =< V/2 aux(97) =< 2/3*V aux(98) =< 2/3*V+1/3 aux(99) =< 2/5*V aux(100) =< 3/7*V aux(101) =< 3/11*V s(643) =< aux(90) s(688) =< aux(98) s(831) =< aux(85) s(833) =< s(831)*aux(85) s(731) =< aux(86) s(733) =< s(731)*aux(86) s(692) =< aux(94) s(693) =< aux(94) s(694) =< aux(94) s(695) =< aux(94) s(696) =< aux(94) s(697) =< aux(94) s(698) =< aux(94) s(688) =< aux(94) s(688) =< aux(95) s(694) =< aux(96) s(695) =< aux(96) s(697) =< aux(96) s(699) =< aux(97) s(696) =< aux(97) s(697) =< aux(97) s(693) =< aux(99) s(695) =< aux(99) s(700) =< aux(100) s(701) =< aux(101) s(702) =< aux(94)+1 s(703) =< aux(94)+2 s(704) =< aux(94) s(705) =< aux(94)-1 s(699) =< aux(95)*(1/3)+aux(97) s(696) =< aux(95)*(1/3)+aux(97) s(697) =< aux(95)*(1/3)+aux(97) s(698) =< aux(95)*(1/3)+aux(97) s(694) =< aux(95)*(1/2)+aux(96) s(695) =< aux(95)*(1/2)+aux(96) s(696) =< aux(95)*(1/2)+aux(96) s(697) =< aux(95)*(1/2)+aux(96) s(698) =< aux(95)*(1/2)+aux(96) s(693) =< aux(95)*(3/5)+s(688)*(1/5)+aux(99) s(694) =< aux(95)*(3/5)+s(688)*(1/5)+aux(99) s(695) =< aux(95)*(3/5)+s(688)*(1/5)+aux(99) s(696) =< aux(95)*(3/5)+s(688)*(1/5)+aux(99) s(697) =< aux(95)*(3/5)+s(688)*(1/5)+aux(99) s(698) =< aux(95)*(3/5)+s(688)*(1/5)+aux(99) s(700) =< aux(95)*(2/7)+aux(100) s(692) =< aux(95)*(2/7)+aux(100) s(701) =< aux(95)*(4/11)+s(688)*(1/11)+aux(101) s(700) =< aux(95)*(4/11)+s(688)*(1/11)+aux(101) s(692) =< aux(95)*(4/11)+s(688)*(1/11)+aux(101) s(706) =< s(698)*s(702) s(707) =< s(698)*s(702) s(708) =< s(698)*s(703) s(709) =< s(696)*s(703) s(710) =< s(697)*s(704) s(711) =< s(695)*s(705) s(712) =< s(694)*s(703) s(713) =< s(693)*s(702) s(714) =< s(700)*s(704) s(715) =< s(700)*s(705) s(716) =< s(701)*s(704) s(717) =< s(707) s(718) =< s(708) s(719) =< s(709) s(720) =< s(699) s(721) =< s(712) s(722) =< s(721)*s(703) s(723) =< s(713) s(724) =< s(723)*s(702) s(725) =< s(715) s(726) =< s(714) s(727) =< s(716) s(728) =< s(727)*aux(94) s(647) =< aux(86) s(648) =< aux(86) s(649) =< aux(86) s(650) =< aux(86) s(651) =< aux(86) s(652) =< aux(86) s(653) =< aux(86) s(643) =< aux(86) s(643) =< aux(87) s(649) =< aux(88) s(650) =< aux(88) s(652) =< aux(88) s(654) =< aux(89) s(651) =< aux(89) s(652) =< aux(89) s(648) =< aux(91) s(650) =< aux(91) s(655) =< aux(92) s(656) =< aux(93) s(657) =< aux(86)+1 s(658) =< aux(86)+2 s(659) =< aux(86) s(660) =< aux(86)-1 s(654) =< aux(87)*(1/3)+aux(89) s(651) =< aux(87)*(1/3)+aux(89) s(652) =< aux(87)*(1/3)+aux(89) s(653) =< aux(87)*(1/3)+aux(89) s(649) =< aux(87)*(1/2)+aux(88) s(650) =< aux(87)*(1/2)+aux(88) s(651) =< aux(87)*(1/2)+aux(88) s(652) =< aux(87)*(1/2)+aux(88) s(653) =< aux(87)*(1/2)+aux(88) s(648) =< aux(87)*(3/5)+s(643)*(1/5)+aux(91) s(649) =< aux(87)*(3/5)+s(643)*(1/5)+aux(91) s(650) =< aux(87)*(3/5)+s(643)*(1/5)+aux(91) s(651) =< aux(87)*(3/5)+s(643)*(1/5)+aux(91) s(652) =< aux(87)*(3/5)+s(643)*(1/5)+aux(91) s(653) =< aux(87)*(3/5)+s(643)*(1/5)+aux(91) s(655) =< aux(87)*(2/7)+aux(92) s(647) =< aux(87)*(2/7)+aux(92) s(656) =< aux(87)*(4/11)+s(643)*(1/11)+aux(93) s(655) =< aux(87)*(4/11)+s(643)*(1/11)+aux(93) s(647) =< aux(87)*(4/11)+s(643)*(1/11)+aux(93) s(661) =< s(653)*s(657) s(662) =< s(653)*s(657) s(663) =< s(653)*s(658) s(664) =< s(651)*s(658) s(665) =< s(652)*s(659) s(666) =< s(650)*s(660) s(667) =< s(649)*s(658) s(668) =< s(648)*s(657) s(669) =< s(655)*s(659) s(670) =< s(655)*s(660) s(671) =< s(656)*s(659) s(672) =< s(662) s(673) =< s(663) s(674) =< s(664) s(675) =< s(654) s(676) =< s(667) s(677) =< s(676)*s(658) s(678) =< s(668) s(679) =< s(678)*s(657) s(680) =< s(670) s(681) =< s(669) s(682) =< s(671) s(683) =< s(682)*aux(86) with precondition: [V>=0,Out>=2,V1>=Out] * Chain [47]: 1*s(847)+3*s(848)+6*s(849)+1*s(850)+7*s(851)+1*s(852)+4*s(853)+4*s(855)+4*s(856)+1*s(861)+1*s(865)+1*s(866)+2*s(872)+2*s(873)+2*s(874)+2*s(875)+7*s(876)+1*s(877)+7*s(878)+1*s(879)+2*s(880)+2*s(881)+7*s(882)+1*s(883)+2*s(886)+4*s(887)+3 Such that:aux(102) =< V1 s(840) =< 2*V1+1 s(841) =< V1/2 s(842) =< 2/3*V1 s(843) =< 2/3*V1+1/3 s(844) =< 2/5*V1 s(845) =< 3/7*V1 s(846) =< 3/11*V1 aux(103) =< 2 s(886) =< aux(102) s(887) =< aux(103) s(847) =< aux(102) s(848) =< aux(102) s(849) =< aux(102) s(850) =< aux(102) s(851) =< aux(102) s(852) =< aux(102) s(853) =< aux(102) s(843) =< aux(102) s(843) =< s(840) s(849) =< s(841) s(850) =< s(841) s(852) =< s(841) s(854) =< s(842) s(851) =< s(842) s(852) =< s(842) s(848) =< s(844) s(850) =< s(844) s(855) =< s(845) s(856) =< s(846) s(857) =< aux(102)+1 s(858) =< aux(102)+2 s(859) =< aux(102) s(860) =< aux(102)-1 s(854) =< s(840)*(1/3)+s(842) s(851) =< s(840)*(1/3)+s(842) s(852) =< s(840)*(1/3)+s(842) s(853) =< s(840)*(1/3)+s(842) s(849) =< s(840)*(1/2)+s(841) s(850) =< s(840)*(1/2)+s(841) s(851) =< s(840)*(1/2)+s(841) s(852) =< s(840)*(1/2)+s(841) s(853) =< s(840)*(1/2)+s(841) s(848) =< s(840)*(3/5)+s(843)*(1/5)+s(844) s(849) =< s(840)*(3/5)+s(843)*(1/5)+s(844) s(850) =< s(840)*(3/5)+s(843)*(1/5)+s(844) s(851) =< s(840)*(3/5)+s(843)*(1/5)+s(844) s(852) =< s(840)*(3/5)+s(843)*(1/5)+s(844) s(853) =< s(840)*(3/5)+s(843)*(1/5)+s(844) s(855) =< s(840)*(2/7)+s(845) s(847) =< s(840)*(2/7)+s(845) s(856) =< s(840)*(4/11)+s(843)*(1/11)+s(846) s(855) =< s(840)*(4/11)+s(843)*(1/11)+s(846) s(847) =< s(840)*(4/11)+s(843)*(1/11)+s(846) s(861) =< s(853)*s(857) s(862) =< s(853)*s(857) s(863) =< s(853)*s(858) s(864) =< s(851)*s(858) s(865) =< s(852)*s(859) s(866) =< s(850)*s(860) s(867) =< s(849)*s(858) s(868) =< s(848)*s(857) s(869) =< s(855)*s(859) s(870) =< s(855)*s(860) s(871) =< s(856)*s(859) s(872) =< s(862) s(873) =< s(863) s(874) =< s(864) s(875) =< s(854) s(876) =< s(867) s(877) =< s(876)*s(858) s(878) =< s(868) s(879) =< s(878)*s(857) s(880) =< s(870) s(881) =< s(869) s(882) =< s(871) s(883) =< s(882)*aux(102) with precondition: [V=2,Out=0,V1>=0] * Chain [46]: 2*s(900)+6*s(901)+12*s(902)+2*s(903)+14*s(904)+2*s(905)+8*s(906)+8*s(908)+8*s(909)+2*s(914)+2*s(918)+2*s(919)+4*s(925)+4*s(926)+4*s(927)+4*s(928)+14*s(929)+2*s(930)+14*s(931)+2*s(932)+4*s(933)+4*s(934)+14*s(935)+2*s(936)+1*s(945)+3*s(946)+6*s(947)+1*s(948)+7*s(949)+1*s(950)+4*s(951)+4*s(953)+4*s(954)+1*s(959)+1*s(963)+1*s(964)+2*s(970)+2*s(971)+2*s(972)+2*s(973)+7*s(974)+1*s(975)+7*s(976)+1*s(977)+2*s(978)+2*s(979)+7*s(980)+1*s(981)+14*s(983)+2*s(987)+3 Such that:s(937) =< V s(938) =< 2*V+1 s(939) =< V/2 s(940) =< 2/3*V s(941) =< 2/3*V+1/3 s(942) =< 2/5*V s(943) =< 3/7*V s(944) =< 3/11*V aux(106) =< V1 aux(107) =< 2*V1+1 aux(108) =< V1/2 aux(109) =< 2/3*V1 aux(110) =< 2/3*V1+1/3 aux(111) =< 2/5*V1 aux(112) =< 3/7*V1 aux(113) =< 3/11*V1 s(896) =< aux(110) s(983) =< aux(106) s(987) =< s(983)*aux(106) s(945) =< s(937) s(946) =< s(937) s(947) =< s(937) s(948) =< s(937) s(949) =< s(937) s(950) =< s(937) s(951) =< s(937) s(941) =< s(937) s(941) =< s(938) s(947) =< s(939) s(948) =< s(939) s(950) =< s(939) s(952) =< s(940) s(949) =< s(940) s(950) =< s(940) s(946) =< s(942) s(948) =< s(942) s(953) =< s(943) s(954) =< s(944) s(955) =< s(937)+1 s(956) =< s(937)+2 s(957) =< s(937) s(958) =< s(937)-1 s(952) =< s(938)*(1/3)+s(940) s(949) =< s(938)*(1/3)+s(940) s(950) =< s(938)*(1/3)+s(940) s(951) =< s(938)*(1/3)+s(940) s(947) =< s(938)*(1/2)+s(939) s(948) =< s(938)*(1/2)+s(939) s(949) =< s(938)*(1/2)+s(939) s(950) =< s(938)*(1/2)+s(939) s(951) =< s(938)*(1/2)+s(939) s(946) =< s(938)*(3/5)+s(941)*(1/5)+s(942) s(947) =< s(938)*(3/5)+s(941)*(1/5)+s(942) s(948) =< s(938)*(3/5)+s(941)*(1/5)+s(942) s(949) =< s(938)*(3/5)+s(941)*(1/5)+s(942) s(950) =< s(938)*(3/5)+s(941)*(1/5)+s(942) s(951) =< s(938)*(3/5)+s(941)*(1/5)+s(942) s(953) =< s(938)*(2/7)+s(943) s(945) =< s(938)*(2/7)+s(943) s(954) =< s(938)*(4/11)+s(941)*(1/11)+s(944) s(953) =< s(938)*(4/11)+s(941)*(1/11)+s(944) s(945) =< s(938)*(4/11)+s(941)*(1/11)+s(944) s(959) =< s(951)*s(955) s(960) =< s(951)*s(955) s(961) =< s(951)*s(956) s(962) =< s(949)*s(956) s(963) =< s(950)*s(957) s(964) =< s(948)*s(958) s(965) =< s(947)*s(956) s(966) =< s(946)*s(955) s(967) =< s(953)*s(957) s(968) =< s(953)*s(958) s(969) =< s(954)*s(957) s(970) =< s(960) s(971) =< s(961) s(972) =< s(962) s(973) =< s(952) s(974) =< s(965) s(975) =< s(974)*s(956) s(976) =< s(966) s(977) =< s(976)*s(955) s(978) =< s(968) s(979) =< s(967) s(980) =< s(969) s(981) =< s(980)*s(937) s(900) =< aux(106) s(901) =< aux(106) s(902) =< aux(106) s(903) =< aux(106) s(904) =< aux(106) s(905) =< aux(106) s(906) =< aux(106) s(896) =< aux(106) s(896) =< aux(107) s(902) =< aux(108) s(903) =< aux(108) s(905) =< aux(108) s(907) =< aux(109) s(904) =< aux(109) s(905) =< aux(109) s(901) =< aux(111) s(903) =< aux(111) s(908) =< aux(112) s(909) =< aux(113) s(910) =< aux(106)+1 s(911) =< aux(106)+2 s(912) =< aux(106) s(913) =< aux(106)-1 s(907) =< aux(107)*(1/3)+aux(109) s(904) =< aux(107)*(1/3)+aux(109) s(905) =< aux(107)*(1/3)+aux(109) s(906) =< aux(107)*(1/3)+aux(109) s(902) =< aux(107)*(1/2)+aux(108) s(903) =< aux(107)*(1/2)+aux(108) s(904) =< aux(107)*(1/2)+aux(108) s(905) =< aux(107)*(1/2)+aux(108) s(906) =< aux(107)*(1/2)+aux(108) s(901) =< aux(107)*(3/5)+s(896)*(1/5)+aux(111) s(902) =< aux(107)*(3/5)+s(896)*(1/5)+aux(111) s(903) =< aux(107)*(3/5)+s(896)*(1/5)+aux(111) s(904) =< aux(107)*(3/5)+s(896)*(1/5)+aux(111) s(905) =< aux(107)*(3/5)+s(896)*(1/5)+aux(111) s(906) =< aux(107)*(3/5)+s(896)*(1/5)+aux(111) s(908) =< aux(107)*(2/7)+aux(112) s(900) =< aux(107)*(2/7)+aux(112) s(909) =< aux(107)*(4/11)+s(896)*(1/11)+aux(113) s(908) =< aux(107)*(4/11)+s(896)*(1/11)+aux(113) s(900) =< aux(107)*(4/11)+s(896)*(1/11)+aux(113) s(914) =< s(906)*s(910) s(915) =< s(906)*s(910) s(916) =< s(906)*s(911) s(917) =< s(904)*s(911) s(918) =< s(905)*s(912) s(919) =< s(903)*s(913) s(920) =< s(902)*s(911) s(921) =< s(901)*s(910) s(922) =< s(908)*s(912) s(923) =< s(908)*s(913) s(924) =< s(909)*s(912) s(925) =< s(915) s(926) =< s(916) s(927) =< s(917) s(928) =< s(907) s(929) =< s(920) s(930) =< s(929)*s(911) s(931) =< s(921) s(932) =< s(931)*s(910) s(933) =< s(923) s(934) =< s(922) s(935) =< s(924) s(936) =< s(935)*aux(106) with precondition: [V>=1,Out>=1,V1>=Out+1] #### Cost of chains of fun1(V1,V,V5,Out): * Chain [59]: 8*s(1191)+24*s(1192)+48*s(1193)+8*s(1194)+56*s(1195)+8*s(1196)+32*s(1197)+32*s(1199)+32*s(1200)+8*s(1205)+8*s(1209)+8*s(1210)+16*s(1216)+16*s(1217)+16*s(1218)+16*s(1219)+56*s(1220)+8*s(1221)+56*s(1222)+8*s(1223)+16*s(1224)+16*s(1225)+56*s(1226)+8*s(1227)+8*s(1236)+24*s(1237)+48*s(1238)+8*s(1239)+56*s(1240)+8*s(1241)+32*s(1242)+32*s(1244)+32*s(1245)+8*s(1250)+8*s(1254)+8*s(1255)+16*s(1261)+16*s(1262)+16*s(1263)+16*s(1264)+56*s(1265)+8*s(1266)+56*s(1267)+8*s(1268)+16*s(1269)+16*s(1270)+56*s(1271)+8*s(1272)+9*s(1281)+27*s(1282)+54*s(1283)+9*s(1284)+63*s(1285)+9*s(1286)+36*s(1287)+36*s(1289)+36*s(1290)+9*s(1295)+9*s(1299)+9*s(1300)+18*s(1306)+18*s(1307)+18*s(1308)+18*s(1309)+63*s(1310)+9*s(1311)+63*s(1312)+9*s(1313)+18*s(1314)+18*s(1315)+63*s(1316)+9*s(1317)+1 Such that:aux(123) =< V1 aux(124) =< 2*V1+1 aux(125) =< V1/2 aux(126) =< 2/3*V1 aux(127) =< 2/3*V1+1/3 aux(128) =< 2/5*V1 aux(129) =< 3/7*V1 aux(130) =< 3/11*V1 aux(131) =< V aux(132) =< 2*V+1 aux(133) =< V/2 aux(134) =< 2/3*V aux(135) =< 2/3*V+1/3 aux(136) =< 2/5*V aux(137) =< 3/7*V aux(138) =< 3/11*V aux(139) =< V5 aux(140) =< 2*V5+1 aux(141) =< V5/2 aux(142) =< 2/3*V5 aux(143) =< 2/3*V5+1/3 aux(144) =< 2/5*V5 aux(145) =< 3/7*V5 aux(146) =< 3/11*V5 s(1187) =< aux(127) s(1232) =< aux(135) s(1277) =< aux(143) s(1281) =< aux(139) s(1282) =< aux(139) s(1283) =< aux(139) s(1284) =< aux(139) s(1285) =< aux(139) s(1286) =< aux(139) s(1287) =< aux(139) s(1277) =< aux(139) s(1277) =< aux(140) s(1283) =< aux(141) s(1284) =< aux(141) s(1286) =< aux(141) s(1288) =< aux(142) s(1285) =< aux(142) s(1286) =< aux(142) s(1282) =< aux(144) s(1284) =< aux(144) s(1289) =< aux(145) s(1290) =< aux(146) s(1291) =< aux(139)+1 s(1292) =< aux(139)+2 s(1293) =< aux(139) s(1294) =< aux(139)-1 s(1288) =< aux(140)*(1/3)+aux(142) s(1285) =< aux(140)*(1/3)+aux(142) s(1286) =< aux(140)*(1/3)+aux(142) s(1287) =< aux(140)*(1/3)+aux(142) s(1283) =< aux(140)*(1/2)+aux(141) s(1284) =< aux(140)*(1/2)+aux(141) s(1285) =< aux(140)*(1/2)+aux(141) s(1286) =< aux(140)*(1/2)+aux(141) s(1287) =< aux(140)*(1/2)+aux(141) s(1282) =< aux(140)*(3/5)+s(1277)*(1/5)+aux(144) s(1283) =< aux(140)*(3/5)+s(1277)*(1/5)+aux(144) s(1284) =< aux(140)*(3/5)+s(1277)*(1/5)+aux(144) s(1285) =< aux(140)*(3/5)+s(1277)*(1/5)+aux(144) s(1286) =< aux(140)*(3/5)+s(1277)*(1/5)+aux(144) s(1287) =< aux(140)*(3/5)+s(1277)*(1/5)+aux(144) s(1289) =< aux(140)*(2/7)+aux(145) s(1281) =< aux(140)*(2/7)+aux(145) s(1290) =< aux(140)*(4/11)+s(1277)*(1/11)+aux(146) s(1289) =< aux(140)*(4/11)+s(1277)*(1/11)+aux(146) s(1281) =< aux(140)*(4/11)+s(1277)*(1/11)+aux(146) s(1295) =< s(1287)*s(1291) s(1296) =< s(1287)*s(1291) s(1297) =< s(1287)*s(1292) s(1298) =< s(1285)*s(1292) s(1299) =< s(1286)*s(1293) s(1300) =< s(1284)*s(1294) s(1301) =< s(1283)*s(1292) s(1302) =< s(1282)*s(1291) s(1303) =< s(1289)*s(1293) s(1304) =< s(1289)*s(1294) s(1305) =< s(1290)*s(1293) s(1306) =< s(1296) s(1307) =< s(1297) s(1308) =< s(1298) s(1309) =< s(1288) s(1310) =< s(1301) s(1311) =< s(1310)*s(1292) s(1312) =< s(1302) s(1313) =< s(1312)*s(1291) s(1314) =< s(1304) s(1315) =< s(1303) s(1316) =< s(1305) s(1317) =< s(1316)*aux(139) s(1236) =< aux(131) s(1237) =< aux(131) s(1238) =< aux(131) s(1239) =< aux(131) s(1240) =< aux(131) s(1241) =< aux(131) s(1242) =< aux(131) s(1232) =< aux(131) s(1232) =< aux(132) s(1238) =< aux(133) s(1239) =< aux(133) s(1241) =< aux(133) s(1243) =< aux(134) s(1240) =< aux(134) s(1241) =< aux(134) s(1237) =< aux(136) s(1239) =< aux(136) s(1244) =< aux(137) s(1245) =< aux(138) s(1246) =< aux(131)+1 s(1247) =< aux(131)+2 s(1248) =< aux(131) s(1249) =< aux(131)-1 s(1243) =< aux(132)*(1/3)+aux(134) s(1240) =< aux(132)*(1/3)+aux(134) s(1241) =< aux(132)*(1/3)+aux(134) s(1242) =< aux(132)*(1/3)+aux(134) s(1238) =< aux(132)*(1/2)+aux(133) s(1239) =< aux(132)*(1/2)+aux(133) s(1240) =< aux(132)*(1/2)+aux(133) s(1241) =< aux(132)*(1/2)+aux(133) s(1242) =< aux(132)*(1/2)+aux(133) s(1237) =< aux(132)*(3/5)+s(1232)*(1/5)+aux(136) s(1238) =< aux(132)*(3/5)+s(1232)*(1/5)+aux(136) s(1239) =< aux(132)*(3/5)+s(1232)*(1/5)+aux(136) s(1240) =< aux(132)*(3/5)+s(1232)*(1/5)+aux(136) s(1241) =< aux(132)*(3/5)+s(1232)*(1/5)+aux(136) s(1242) =< aux(132)*(3/5)+s(1232)*(1/5)+aux(136) s(1244) =< aux(132)*(2/7)+aux(137) s(1236) =< aux(132)*(2/7)+aux(137) s(1245) =< aux(132)*(4/11)+s(1232)*(1/11)+aux(138) s(1244) =< aux(132)*(4/11)+s(1232)*(1/11)+aux(138) s(1236) =< aux(132)*(4/11)+s(1232)*(1/11)+aux(138) s(1250) =< s(1242)*s(1246) s(1251) =< s(1242)*s(1246) s(1252) =< s(1242)*s(1247) s(1253) =< s(1240)*s(1247) s(1254) =< s(1241)*s(1248) s(1255) =< s(1239)*s(1249) s(1256) =< s(1238)*s(1247) s(1257) =< s(1237)*s(1246) s(1258) =< s(1244)*s(1248) s(1259) =< s(1244)*s(1249) s(1260) =< s(1245)*s(1248) s(1261) =< s(1251) s(1262) =< s(1252) s(1263) =< s(1253) s(1264) =< s(1243) s(1265) =< s(1256) s(1266) =< s(1265)*s(1247) s(1267) =< s(1257) s(1268) =< s(1267)*s(1246) s(1269) =< s(1259) s(1270) =< s(1258) s(1271) =< s(1260) s(1272) =< s(1271)*aux(131) s(1191) =< aux(123) s(1192) =< aux(123) s(1193) =< aux(123) s(1194) =< aux(123) s(1195) =< aux(123) s(1196) =< aux(123) s(1197) =< aux(123) s(1187) =< aux(123) s(1187) =< aux(124) s(1193) =< aux(125) s(1194) =< aux(125) s(1196) =< aux(125) s(1198) =< aux(126) s(1195) =< aux(126) s(1196) =< aux(126) s(1192) =< aux(128) s(1194) =< aux(128) s(1199) =< aux(129) s(1200) =< aux(130) s(1201) =< aux(123)+1 s(1202) =< aux(123)+2 s(1203) =< aux(123) s(1204) =< aux(123)-1 s(1198) =< aux(124)*(1/3)+aux(126) s(1195) =< aux(124)*(1/3)+aux(126) s(1196) =< aux(124)*(1/3)+aux(126) s(1197) =< aux(124)*(1/3)+aux(126) s(1193) =< aux(124)*(1/2)+aux(125) s(1194) =< aux(124)*(1/2)+aux(125) s(1195) =< aux(124)*(1/2)+aux(125) s(1196) =< aux(124)*(1/2)+aux(125) s(1197) =< aux(124)*(1/2)+aux(125) s(1192) =< aux(124)*(3/5)+s(1187)*(1/5)+aux(128) s(1193) =< aux(124)*(3/5)+s(1187)*(1/5)+aux(128) s(1194) =< aux(124)*(3/5)+s(1187)*(1/5)+aux(128) s(1195) =< aux(124)*(3/5)+s(1187)*(1/5)+aux(128) s(1196) =< aux(124)*(3/5)+s(1187)*(1/5)+aux(128) s(1197) =< aux(124)*(3/5)+s(1187)*(1/5)+aux(128) s(1199) =< aux(124)*(2/7)+aux(129) s(1191) =< aux(124)*(2/7)+aux(129) s(1200) =< aux(124)*(4/11)+s(1187)*(1/11)+aux(130) s(1199) =< aux(124)*(4/11)+s(1187)*(1/11)+aux(130) s(1191) =< aux(124)*(4/11)+s(1187)*(1/11)+aux(130) s(1205) =< s(1197)*s(1201) s(1206) =< s(1197)*s(1201) s(1207) =< s(1197)*s(1202) s(1208) =< s(1195)*s(1202) s(1209) =< s(1196)*s(1203) s(1210) =< s(1194)*s(1204) s(1211) =< s(1193)*s(1202) s(1212) =< s(1192)*s(1201) s(1213) =< s(1199)*s(1203) s(1214) =< s(1199)*s(1204) s(1215) =< s(1200)*s(1203) s(1216) =< s(1206) s(1217) =< s(1207) s(1218) =< s(1208) s(1219) =< s(1198) s(1220) =< s(1211) s(1221) =< s(1220)*s(1202) s(1222) =< s(1212) s(1223) =< s(1222)*s(1201) s(1224) =< s(1214) s(1225) =< s(1213) s(1226) =< s(1215) s(1227) =< s(1226)*aux(123) with precondition: [Out=0,V1>=0,V>=0,V5>=0] * Chain [58]: 4*s(2316)+12*s(2317)+24*s(2318)+4*s(2319)+28*s(2320)+4*s(2321)+16*s(2322)+16*s(2324)+16*s(2325)+4*s(2330)+4*s(2334)+4*s(2335)+8*s(2341)+8*s(2342)+8*s(2343)+8*s(2344)+28*s(2345)+4*s(2346)+28*s(2347)+4*s(2348)+8*s(2349)+8*s(2350)+28*s(2351)+4*s(2352)+4*s(2361)+12*s(2362)+24*s(2363)+4*s(2364)+28*s(2365)+4*s(2366)+16*s(2367)+16*s(2369)+16*s(2370)+4*s(2375)+4*s(2379)+4*s(2380)+8*s(2386)+8*s(2387)+8*s(2388)+8*s(2389)+28*s(2390)+4*s(2391)+28*s(2392)+4*s(2393)+8*s(2394)+8*s(2395)+28*s(2396)+4*s(2397)+5*s(2406)+15*s(2407)+30*s(2408)+5*s(2409)+35*s(2410)+5*s(2411)+20*s(2412)+20*s(2414)+20*s(2415)+5*s(2420)+5*s(2424)+5*s(2425)+10*s(2431)+10*s(2432)+10*s(2433)+10*s(2434)+35*s(2435)+5*s(2436)+35*s(2437)+5*s(2438)+10*s(2439)+10*s(2440)+35*s(2441)+5*s(2442)+8*s(2445)+10*s(2446)+10*s(2540)+6*s(2874)+2*s(2879)+4 Such that:s(2877) =< 3 aux(151) =< 1 aux(152) =< 2 aux(153) =< V1 aux(154) =< 2*V1+1 aux(155) =< V1/2 aux(156) =< 2/3*V1 aux(157) =< 2/3*V1+1/3 aux(158) =< 2/5*V1 aux(159) =< 3/7*V1 aux(160) =< 3/11*V1 aux(161) =< V aux(162) =< 2*V+1 aux(163) =< V/2 aux(164) =< 2/3*V aux(165) =< 2/3*V+1/3 aux(166) =< 2/5*V aux(167) =< 3/7*V aux(168) =< 3/11*V aux(169) =< V5 aux(170) =< V5+1 aux(171) =< 2*V5+1 aux(172) =< V5/2 aux(173) =< 2/3*V5 aux(174) =< 2/3*V5+1/3 aux(175) =< 2/5*V5 aux(176) =< 3/7*V5 aux(177) =< 3/11*V5 s(2312) =< aux(157) s(2357) =< aux(165) s(2402) =< aux(174) s(2445) =< aux(161) s(2540) =< aux(151) s(2361) =< aux(161) s(2362) =< aux(161) s(2363) =< aux(161) s(2364) =< aux(161) s(2365) =< aux(161) s(2366) =< aux(161) s(2367) =< aux(161) s(2357) =< aux(161) s(2357) =< aux(162) s(2363) =< aux(163) s(2364) =< aux(163) s(2366) =< aux(163) s(2368) =< aux(164) s(2365) =< aux(164) s(2366) =< aux(164) s(2362) =< aux(166) s(2364) =< aux(166) s(2369) =< aux(167) s(2370) =< aux(168) s(2371) =< aux(161)+1 s(2372) =< aux(161)+2 s(2373) =< aux(161) s(2374) =< aux(161)-1 s(2368) =< aux(162)*(1/3)+aux(164) s(2365) =< aux(162)*(1/3)+aux(164) s(2366) =< aux(162)*(1/3)+aux(164) s(2367) =< aux(162)*(1/3)+aux(164) s(2363) =< aux(162)*(1/2)+aux(163) s(2364) =< aux(162)*(1/2)+aux(163) s(2365) =< aux(162)*(1/2)+aux(163) s(2366) =< aux(162)*(1/2)+aux(163) s(2367) =< aux(162)*(1/2)+aux(163) s(2362) =< aux(162)*(3/5)+s(2357)*(1/5)+aux(166) s(2363) =< aux(162)*(3/5)+s(2357)*(1/5)+aux(166) s(2364) =< aux(162)*(3/5)+s(2357)*(1/5)+aux(166) s(2365) =< aux(162)*(3/5)+s(2357)*(1/5)+aux(166) s(2366) =< aux(162)*(3/5)+s(2357)*(1/5)+aux(166) s(2367) =< aux(162)*(3/5)+s(2357)*(1/5)+aux(166) s(2369) =< aux(162)*(2/7)+aux(167) s(2361) =< aux(162)*(2/7)+aux(167) s(2370) =< aux(162)*(4/11)+s(2357)*(1/11)+aux(168) s(2369) =< aux(162)*(4/11)+s(2357)*(1/11)+aux(168) s(2361) =< aux(162)*(4/11)+s(2357)*(1/11)+aux(168) s(2375) =< s(2367)*s(2371) s(2376) =< s(2367)*s(2371) s(2377) =< s(2367)*s(2372) s(2378) =< s(2365)*s(2372) s(2379) =< s(2366)*s(2373) s(2380) =< s(2364)*s(2374) s(2381) =< s(2363)*s(2372) s(2382) =< s(2362)*s(2371) s(2383) =< s(2369)*s(2373) s(2384) =< s(2369)*s(2374) s(2385) =< s(2370)*s(2373) s(2386) =< s(2376) s(2387) =< s(2377) s(2388) =< s(2378) s(2389) =< s(2368) s(2390) =< s(2381) s(2391) =< s(2390)*s(2372) s(2392) =< s(2382) s(2393) =< s(2392)*s(2371) s(2394) =< s(2384) s(2395) =< s(2383) s(2396) =< s(2385) s(2397) =< s(2396)*aux(161) s(2316) =< aux(153) s(2317) =< aux(153) s(2318) =< aux(153) s(2319) =< aux(153) s(2320) =< aux(153) s(2321) =< aux(153) s(2322) =< aux(153) s(2312) =< aux(153) s(2312) =< aux(154) s(2318) =< aux(155) s(2319) =< aux(155) s(2321) =< aux(155) s(2323) =< aux(156) s(2320) =< aux(156) s(2321) =< aux(156) s(2317) =< aux(158) s(2319) =< aux(158) s(2324) =< aux(159) s(2325) =< aux(160) s(2326) =< aux(153)+1 s(2327) =< aux(153)+2 s(2328) =< aux(153) s(2329) =< aux(153)-1 s(2323) =< aux(154)*(1/3)+aux(156) s(2320) =< aux(154)*(1/3)+aux(156) s(2321) =< aux(154)*(1/3)+aux(156) s(2322) =< aux(154)*(1/3)+aux(156) s(2318) =< aux(154)*(1/2)+aux(155) s(2319) =< aux(154)*(1/2)+aux(155) s(2320) =< aux(154)*(1/2)+aux(155) s(2321) =< aux(154)*(1/2)+aux(155) s(2322) =< aux(154)*(1/2)+aux(155) s(2317) =< aux(154)*(3/5)+s(2312)*(1/5)+aux(158) s(2318) =< aux(154)*(3/5)+s(2312)*(1/5)+aux(158) s(2319) =< aux(154)*(3/5)+s(2312)*(1/5)+aux(158) s(2320) =< aux(154)*(3/5)+s(2312)*(1/5)+aux(158) s(2321) =< aux(154)*(3/5)+s(2312)*(1/5)+aux(158) s(2322) =< aux(154)*(3/5)+s(2312)*(1/5)+aux(158) s(2324) =< aux(154)*(2/7)+aux(159) s(2316) =< aux(154)*(2/7)+aux(159) s(2325) =< aux(154)*(4/11)+s(2312)*(1/11)+aux(160) s(2324) =< aux(154)*(4/11)+s(2312)*(1/11)+aux(160) s(2316) =< aux(154)*(4/11)+s(2312)*(1/11)+aux(160) s(2330) =< s(2322)*s(2326) s(2331) =< s(2322)*s(2326) s(2332) =< s(2322)*s(2327) s(2333) =< s(2320)*s(2327) s(2334) =< s(2321)*s(2328) s(2335) =< s(2319)*s(2329) s(2336) =< s(2318)*s(2327) s(2337) =< s(2317)*s(2326) s(2338) =< s(2324)*s(2328) s(2339) =< s(2324)*s(2329) s(2340) =< s(2325)*s(2328) s(2341) =< s(2331) s(2342) =< s(2332) s(2343) =< s(2333) s(2344) =< s(2323) s(2345) =< s(2336) s(2346) =< s(2345)*s(2327) s(2347) =< s(2337) s(2348) =< s(2347)*s(2326) s(2349) =< s(2339) s(2350) =< s(2338) s(2351) =< s(2340) s(2352) =< s(2351)*aux(153) s(2874) =< aux(152) s(2446) =< aux(170) s(2406) =< aux(169) s(2407) =< aux(169) s(2408) =< aux(169) s(2409) =< aux(169) s(2410) =< aux(169) s(2411) =< aux(169) s(2412) =< aux(169) s(2402) =< aux(169) s(2402) =< aux(171) s(2408) =< aux(172) s(2409) =< aux(172) s(2411) =< aux(172) s(2413) =< aux(173) s(2410) =< aux(173) s(2411) =< aux(173) s(2407) =< aux(175) s(2409) =< aux(175) s(2414) =< aux(176) s(2415) =< aux(177) s(2416) =< aux(169)+1 s(2417) =< aux(169)+2 s(2418) =< aux(169) s(2419) =< aux(169)-1 s(2413) =< aux(171)*(1/3)+aux(173) s(2410) =< aux(171)*(1/3)+aux(173) s(2411) =< aux(171)*(1/3)+aux(173) s(2412) =< aux(171)*(1/3)+aux(173) s(2408) =< aux(171)*(1/2)+aux(172) s(2409) =< aux(171)*(1/2)+aux(172) s(2410) =< aux(171)*(1/2)+aux(172) s(2411) =< aux(171)*(1/2)+aux(172) s(2412) =< aux(171)*(1/2)+aux(172) s(2407) =< aux(171)*(3/5)+s(2402)*(1/5)+aux(175) s(2408) =< aux(171)*(3/5)+s(2402)*(1/5)+aux(175) s(2409) =< aux(171)*(3/5)+s(2402)*(1/5)+aux(175) s(2410) =< aux(171)*(3/5)+s(2402)*(1/5)+aux(175) s(2411) =< aux(171)*(3/5)+s(2402)*(1/5)+aux(175) s(2412) =< aux(171)*(3/5)+s(2402)*(1/5)+aux(175) s(2414) =< aux(171)*(2/7)+aux(176) s(2406) =< aux(171)*(2/7)+aux(176) s(2415) =< aux(171)*(4/11)+s(2402)*(1/11)+aux(177) s(2414) =< aux(171)*(4/11)+s(2402)*(1/11)+aux(177) s(2406) =< aux(171)*(4/11)+s(2402)*(1/11)+aux(177) s(2420) =< s(2412)*s(2416) s(2421) =< s(2412)*s(2416) s(2422) =< s(2412)*s(2417) s(2423) =< s(2410)*s(2417) s(2424) =< s(2411)*s(2418) s(2425) =< s(2409)*s(2419) s(2426) =< s(2408)*s(2417) s(2427) =< s(2407)*s(2416) s(2428) =< s(2414)*s(2418) s(2429) =< s(2414)*s(2419) s(2430) =< s(2415)*s(2418) s(2431) =< s(2421) s(2432) =< s(2422) s(2433) =< s(2423) s(2434) =< s(2413) s(2435) =< s(2426) s(2436) =< s(2435)*s(2417) s(2437) =< s(2427) s(2438) =< s(2437)*s(2416) s(2439) =< s(2429) s(2440) =< s(2428) s(2441) =< s(2430) s(2442) =< s(2441)*aux(169) s(2879) =< s(2877) with precondition: [Out=1,V1>=2,V>=0,V5>=0] * Chain [57]: 2*s(2945)+6*s(2946)+12*s(2947)+2*s(2948)+14*s(2949)+2*s(2950)+8*s(2951)+8*s(2953)+8*s(2954)+2*s(2959)+2*s(2963)+2*s(2964)+4*s(2970)+4*s(2971)+4*s(2972)+4*s(2973)+14*s(2974)+2*s(2975)+14*s(2976)+2*s(2977)+4*s(2978)+4*s(2979)+14*s(2980)+2*s(2981)+4*s(2990)+12*s(2991)+24*s(2992)+4*s(2993)+28*s(2994)+4*s(2995)+16*s(2996)+16*s(2998)+16*s(2999)+4*s(3004)+4*s(3008)+4*s(3009)+8*s(3015)+8*s(3016)+8*s(3017)+8*s(3018)+28*s(3019)+4*s(3020)+28*s(3021)+4*s(3022)+8*s(3023)+8*s(3024)+28*s(3025)+4*s(3026)+3*s(3035)+9*s(3036)+18*s(3037)+3*s(3038)+21*s(3039)+3*s(3040)+12*s(3041)+12*s(3043)+12*s(3044)+3*s(3049)+3*s(3053)+3*s(3054)+6*s(3060)+6*s(3061)+6*s(3062)+6*s(3063)+21*s(3064)+3*s(3065)+21*s(3066)+3*s(3067)+6*s(3068)+6*s(3069)+21*s(3070)+3*s(3071)+28*s(3073)+4*s(3077)+6*s(3367)+8*s(3369)+2*s(3371)+4 Such that:aux(184) =< 1 aux(185) =< 2 aux(186) =< V1 aux(187) =< 2*V1+1 aux(188) =< V1/2 aux(189) =< 2/3*V1 aux(190) =< 2/3*V1+1/3 aux(191) =< 2/5*V1 aux(192) =< 3/7*V1 aux(193) =< 3/11*V1 aux(194) =< V aux(195) =< 2*V+1 aux(196) =< V/2 aux(197) =< 2/3*V aux(198) =< 2/3*V+1/3 aux(199) =< 2/5*V aux(200) =< 3/7*V aux(201) =< 3/11*V aux(202) =< V5 aux(203) =< 2*V5+1 aux(204) =< V5/2 aux(205) =< 2/3*V5 aux(206) =< 2/3*V5+1/3 aux(207) =< 2/5*V5 aux(208) =< 3/7*V5 aux(209) =< 3/11*V5 s(3367) =< aux(184) s(2941) =< aux(190) s(2986) =< aux(198) s(3031) =< aux(206) s(3369) =< aux(185) s(3371) =< s(3367)*aux(185) s(3035) =< aux(202) s(3036) =< aux(202) s(3037) =< aux(202) s(3038) =< aux(202) s(3039) =< aux(202) s(3040) =< aux(202) s(3041) =< aux(202) s(3031) =< aux(202) s(3031) =< aux(203) s(3037) =< aux(204) s(3038) =< aux(204) s(3040) =< aux(204) s(3042) =< aux(205) s(3039) =< aux(205) s(3040) =< aux(205) s(3036) =< aux(207) s(3038) =< aux(207) s(3043) =< aux(208) s(3044) =< aux(209) s(3045) =< aux(202)+1 s(3046) =< aux(202)+2 s(3047) =< aux(202) s(3048) =< aux(202)-1 s(3042) =< aux(203)*(1/3)+aux(205) s(3039) =< aux(203)*(1/3)+aux(205) s(3040) =< aux(203)*(1/3)+aux(205) s(3041) =< aux(203)*(1/3)+aux(205) s(3037) =< aux(203)*(1/2)+aux(204) s(3038) =< aux(203)*(1/2)+aux(204) s(3039) =< aux(203)*(1/2)+aux(204) s(3040) =< aux(203)*(1/2)+aux(204) s(3041) =< aux(203)*(1/2)+aux(204) s(3036) =< aux(203)*(3/5)+s(3031)*(1/5)+aux(207) s(3037) =< aux(203)*(3/5)+s(3031)*(1/5)+aux(207) s(3038) =< aux(203)*(3/5)+s(3031)*(1/5)+aux(207) s(3039) =< aux(203)*(3/5)+s(3031)*(1/5)+aux(207) s(3040) =< aux(203)*(3/5)+s(3031)*(1/5)+aux(207) s(3041) =< aux(203)*(3/5)+s(3031)*(1/5)+aux(207) s(3043) =< aux(203)*(2/7)+aux(208) s(3035) =< aux(203)*(2/7)+aux(208) s(3044) =< aux(203)*(4/11)+s(3031)*(1/11)+aux(209) s(3043) =< aux(203)*(4/11)+s(3031)*(1/11)+aux(209) s(3035) =< aux(203)*(4/11)+s(3031)*(1/11)+aux(209) s(3049) =< s(3041)*s(3045) s(3050) =< s(3041)*s(3045) s(3051) =< s(3041)*s(3046) s(3052) =< s(3039)*s(3046) s(3053) =< s(3040)*s(3047) s(3054) =< s(3038)*s(3048) s(3055) =< s(3037)*s(3046) s(3056) =< s(3036)*s(3045) s(3057) =< s(3043)*s(3047) s(3058) =< s(3043)*s(3048) s(3059) =< s(3044)*s(3047) s(3060) =< s(3050) s(3061) =< s(3051) s(3062) =< s(3052) s(3063) =< s(3042) s(3064) =< s(3055) s(3065) =< s(3064)*s(3046) s(3066) =< s(3056) s(3067) =< s(3066)*s(3045) s(3068) =< s(3058) s(3069) =< s(3057) s(3070) =< s(3059) s(3071) =< s(3070)*aux(202) s(3073) =< aux(194) s(3077) =< s(3073)*aux(194) s(2990) =< aux(194) s(2991) =< aux(194) s(2992) =< aux(194) s(2993) =< aux(194) s(2994) =< aux(194) s(2995) =< aux(194) s(2996) =< aux(194) s(2986) =< aux(194) s(2986) =< aux(195) s(2992) =< aux(196) s(2993) =< aux(196) s(2995) =< aux(196) s(2997) =< aux(197) s(2994) =< aux(197) s(2995) =< aux(197) s(2991) =< aux(199) s(2993) =< aux(199) s(2998) =< aux(200) s(2999) =< aux(201) s(3000) =< aux(194)+1 s(3001) =< aux(194)+2 s(3002) =< aux(194) s(3003) =< aux(194)-1 s(2997) =< aux(195)*(1/3)+aux(197) s(2994) =< aux(195)*(1/3)+aux(197) s(2995) =< aux(195)*(1/3)+aux(197) s(2996) =< aux(195)*(1/3)+aux(197) s(2992) =< aux(195)*(1/2)+aux(196) s(2993) =< aux(195)*(1/2)+aux(196) s(2994) =< aux(195)*(1/2)+aux(196) s(2995) =< aux(195)*(1/2)+aux(196) s(2996) =< aux(195)*(1/2)+aux(196) s(2991) =< aux(195)*(3/5)+s(2986)*(1/5)+aux(199) s(2992) =< aux(195)*(3/5)+s(2986)*(1/5)+aux(199) s(2993) =< aux(195)*(3/5)+s(2986)*(1/5)+aux(199) s(2994) =< aux(195)*(3/5)+s(2986)*(1/5)+aux(199) s(2995) =< aux(195)*(3/5)+s(2986)*(1/5)+aux(199) s(2996) =< aux(195)*(3/5)+s(2986)*(1/5)+aux(199) s(2998) =< aux(195)*(2/7)+aux(200) s(2990) =< aux(195)*(2/7)+aux(200) s(2999) =< aux(195)*(4/11)+s(2986)*(1/11)+aux(201) s(2998) =< aux(195)*(4/11)+s(2986)*(1/11)+aux(201) s(2990) =< aux(195)*(4/11)+s(2986)*(1/11)+aux(201) s(3004) =< s(2996)*s(3000) s(3005) =< s(2996)*s(3000) s(3006) =< s(2996)*s(3001) s(3007) =< s(2994)*s(3001) s(3008) =< s(2995)*s(3002) s(3009) =< s(2993)*s(3003) s(3010) =< s(2992)*s(3001) s(3011) =< s(2991)*s(3000) s(3012) =< s(2998)*s(3002) s(3013) =< s(2998)*s(3003) s(3014) =< s(2999)*s(3002) s(3015) =< s(3005) s(3016) =< s(3006) s(3017) =< s(3007) s(3018) =< s(2997) s(3019) =< s(3010) s(3020) =< s(3019)*s(3001) s(3021) =< s(3011) s(3022) =< s(3021)*s(3000) s(3023) =< s(3013) s(3024) =< s(3012) s(3025) =< s(3014) s(3026) =< s(3025)*aux(194) s(2945) =< aux(186) s(2946) =< aux(186) s(2947) =< aux(186) s(2948) =< aux(186) s(2949) =< aux(186) s(2950) =< aux(186) s(2951) =< aux(186) s(2941) =< aux(186) s(2941) =< aux(187) s(2947) =< aux(188) s(2948) =< aux(188) s(2950) =< aux(188) s(2952) =< aux(189) s(2949) =< aux(189) s(2950) =< aux(189) s(2946) =< aux(191) s(2948) =< aux(191) s(2953) =< aux(192) s(2954) =< aux(193) s(2955) =< aux(186)+1 s(2956) =< aux(186)+2 s(2957) =< aux(186) s(2958) =< aux(186)-1 s(2952) =< aux(187)*(1/3)+aux(189) s(2949) =< aux(187)*(1/3)+aux(189) s(2950) =< aux(187)*(1/3)+aux(189) s(2951) =< aux(187)*(1/3)+aux(189) s(2947) =< aux(187)*(1/2)+aux(188) s(2948) =< aux(187)*(1/2)+aux(188) s(2949) =< aux(187)*(1/2)+aux(188) s(2950) =< aux(187)*(1/2)+aux(188) s(2951) =< aux(187)*(1/2)+aux(188) s(2946) =< aux(187)*(3/5)+s(2941)*(1/5)+aux(191) s(2947) =< aux(187)*(3/5)+s(2941)*(1/5)+aux(191) s(2948) =< aux(187)*(3/5)+s(2941)*(1/5)+aux(191) s(2949) =< aux(187)*(3/5)+s(2941)*(1/5)+aux(191) s(2950) =< aux(187)*(3/5)+s(2941)*(1/5)+aux(191) s(2951) =< aux(187)*(3/5)+s(2941)*(1/5)+aux(191) s(2953) =< aux(187)*(2/7)+aux(192) s(2945) =< aux(187)*(2/7)+aux(192) s(2954) =< aux(187)*(4/11)+s(2941)*(1/11)+aux(193) s(2953) =< aux(187)*(4/11)+s(2941)*(1/11)+aux(193) s(2945) =< aux(187)*(4/11)+s(2941)*(1/11)+aux(193) s(2959) =< s(2951)*s(2955) s(2960) =< s(2951)*s(2955) s(2961) =< s(2951)*s(2956) s(2962) =< s(2949)*s(2956) s(2963) =< s(2950)*s(2957) s(2964) =< s(2948)*s(2958) s(2965) =< s(2947)*s(2956) s(2966) =< s(2946)*s(2955) s(2967) =< s(2953)*s(2957) s(2968) =< s(2953)*s(2958) s(2969) =< s(2954)*s(2957) s(2970) =< s(2960) s(2971) =< s(2961) s(2972) =< s(2962) s(2973) =< s(2952) s(2974) =< s(2965) s(2975) =< s(2974)*s(2956) s(2976) =< s(2966) s(2977) =< s(2976)*s(2955) s(2978) =< s(2968) s(2979) =< s(2967) s(2980) =< s(2969) s(2981) =< s(2980)*aux(186) with precondition: [V1>=2,V5>=0,Out>=2,V>=Out] * Chain [56]: 4*s(3386)+12*s(3387)+24*s(3388)+4*s(3389)+28*s(3390)+4*s(3391)+16*s(3392)+16*s(3394)+16*s(3395)+4*s(3400)+4*s(3404)+4*s(3405)+8*s(3411)+8*s(3412)+8*s(3413)+8*s(3414)+28*s(3415)+4*s(3416)+28*s(3417)+4*s(3418)+8*s(3419)+8*s(3420)+28*s(3421)+4*s(3422)+4*s(3431)+12*s(3432)+24*s(3433)+4*s(3434)+28*s(3435)+4*s(3436)+16*s(3437)+16*s(3439)+16*s(3440)+4*s(3445)+4*s(3449)+4*s(3450)+8*s(3456)+8*s(3457)+8*s(3458)+8*s(3459)+28*s(3460)+4*s(3461)+28*s(3462)+4*s(3463)+8*s(3464)+8*s(3465)+28*s(3466)+4*s(3467)+1 Such that:aux(210) =< V1 aux(211) =< 2*V1+1 aux(212) =< V1/2 aux(213) =< 2/3*V1 aux(214) =< 2/3*V1+1/3 aux(215) =< 2/5*V1 aux(216) =< 3/7*V1 aux(217) =< 3/11*V1 aux(218) =< V aux(219) =< 2*V+1 aux(220) =< V/2 aux(221) =< 2/3*V aux(222) =< 2/3*V+1/3 aux(223) =< 2/5*V aux(224) =< 3/7*V aux(225) =< 3/11*V s(3382) =< aux(214) s(3427) =< aux(222) s(3431) =< aux(218) s(3432) =< aux(218) s(3433) =< aux(218) s(3434) =< aux(218) s(3435) =< aux(218) s(3436) =< aux(218) s(3437) =< aux(218) s(3427) =< aux(218) s(3427) =< aux(219) s(3433) =< aux(220) s(3434) =< aux(220) s(3436) =< aux(220) s(3438) =< aux(221) s(3435) =< aux(221) s(3436) =< aux(221) s(3432) =< aux(223) s(3434) =< aux(223) s(3439) =< aux(224) s(3440) =< aux(225) s(3441) =< aux(218)+1 s(3442) =< aux(218)+2 s(3443) =< aux(218) s(3444) =< aux(218)-1 s(3438) =< aux(219)*(1/3)+aux(221) s(3435) =< aux(219)*(1/3)+aux(221) s(3436) =< aux(219)*(1/3)+aux(221) s(3437) =< aux(219)*(1/3)+aux(221) s(3433) =< aux(219)*(1/2)+aux(220) s(3434) =< aux(219)*(1/2)+aux(220) s(3435) =< aux(219)*(1/2)+aux(220) s(3436) =< aux(219)*(1/2)+aux(220) s(3437) =< aux(219)*(1/2)+aux(220) s(3432) =< aux(219)*(3/5)+s(3427)*(1/5)+aux(223) s(3433) =< aux(219)*(3/5)+s(3427)*(1/5)+aux(223) s(3434) =< aux(219)*(3/5)+s(3427)*(1/5)+aux(223) s(3435) =< aux(219)*(3/5)+s(3427)*(1/5)+aux(223) s(3436) =< aux(219)*(3/5)+s(3427)*(1/5)+aux(223) s(3437) =< aux(219)*(3/5)+s(3427)*(1/5)+aux(223) s(3439) =< aux(219)*(2/7)+aux(224) s(3431) =< aux(219)*(2/7)+aux(224) s(3440) =< aux(219)*(4/11)+s(3427)*(1/11)+aux(225) s(3439) =< aux(219)*(4/11)+s(3427)*(1/11)+aux(225) s(3431) =< aux(219)*(4/11)+s(3427)*(1/11)+aux(225) s(3445) =< s(3437)*s(3441) s(3446) =< s(3437)*s(3441) s(3447) =< s(3437)*s(3442) s(3448) =< s(3435)*s(3442) s(3449) =< s(3436)*s(3443) s(3450) =< s(3434)*s(3444) s(3451) =< s(3433)*s(3442) s(3452) =< s(3432)*s(3441) s(3453) =< s(3439)*s(3443) s(3454) =< s(3439)*s(3444) s(3455) =< s(3440)*s(3443) s(3456) =< s(3446) s(3457) =< s(3447) s(3458) =< s(3448) s(3459) =< s(3438) s(3460) =< s(3451) s(3461) =< s(3460)*s(3442) s(3462) =< s(3452) s(3463) =< s(3462)*s(3441) s(3464) =< s(3454) s(3465) =< s(3453) s(3466) =< s(3455) s(3467) =< s(3466)*aux(218) s(3386) =< aux(210) s(3387) =< aux(210) s(3388) =< aux(210) s(3389) =< aux(210) s(3390) =< aux(210) s(3391) =< aux(210) s(3392) =< aux(210) s(3382) =< aux(210) s(3382) =< aux(211) s(3388) =< aux(212) s(3389) =< aux(212) s(3391) =< aux(212) s(3393) =< aux(213) s(3390) =< aux(213) s(3391) =< aux(213) s(3387) =< aux(215) s(3389) =< aux(215) s(3394) =< aux(216) s(3395) =< aux(217) s(3396) =< aux(210)+1 s(3397) =< aux(210)+2 s(3398) =< aux(210) s(3399) =< aux(210)-1 s(3393) =< aux(211)*(1/3)+aux(213) s(3390) =< aux(211)*(1/3)+aux(213) s(3391) =< aux(211)*(1/3)+aux(213) s(3392) =< aux(211)*(1/3)+aux(213) s(3388) =< aux(211)*(1/2)+aux(212) s(3389) =< aux(211)*(1/2)+aux(212) s(3390) =< aux(211)*(1/2)+aux(212) s(3391) =< aux(211)*(1/2)+aux(212) s(3392) =< aux(211)*(1/2)+aux(212) s(3387) =< aux(211)*(3/5)+s(3382)*(1/5)+aux(215) s(3388) =< aux(211)*(3/5)+s(3382)*(1/5)+aux(215) s(3389) =< aux(211)*(3/5)+s(3382)*(1/5)+aux(215) s(3390) =< aux(211)*(3/5)+s(3382)*(1/5)+aux(215) s(3391) =< aux(211)*(3/5)+s(3382)*(1/5)+aux(215) s(3392) =< aux(211)*(3/5)+s(3382)*(1/5)+aux(215) s(3394) =< aux(211)*(2/7)+aux(216) s(3386) =< aux(211)*(2/7)+aux(216) s(3395) =< aux(211)*(4/11)+s(3382)*(1/11)+aux(217) s(3394) =< aux(211)*(4/11)+s(3382)*(1/11)+aux(217) s(3386) =< aux(211)*(4/11)+s(3382)*(1/11)+aux(217) s(3400) =< s(3392)*s(3396) s(3401) =< s(3392)*s(3396) s(3402) =< s(3392)*s(3397) s(3403) =< s(3390)*s(3397) s(3404) =< s(3391)*s(3398) s(3405) =< s(3389)*s(3399) s(3406) =< s(3388)*s(3397) s(3407) =< s(3387)*s(3396) s(3408) =< s(3394)*s(3398) s(3409) =< s(3394)*s(3399) s(3410) =< s(3395)*s(3398) s(3411) =< s(3401) s(3412) =< s(3402) s(3413) =< s(3403) s(3414) =< s(3393) s(3415) =< s(3406) s(3416) =< s(3415)*s(3397) s(3417) =< s(3407) s(3418) =< s(3417)*s(3396) s(3419) =< s(3409) s(3420) =< s(3408) s(3421) =< s(3410) s(3422) =< s(3421)*aux(210) with precondition: [V5=2,Out=0,V1>=0,V>=0] * Chain [55]: 2*s(3746)+6*s(3747)+12*s(3748)+2*s(3749)+14*s(3750)+2*s(3751)+8*s(3752)+8*s(3754)+8*s(3755)+2*s(3760)+2*s(3764)+2*s(3765)+4*s(3771)+4*s(3772)+4*s(3773)+4*s(3774)+14*s(3775)+2*s(3776)+14*s(3777)+2*s(3778)+4*s(3779)+4*s(3780)+14*s(3781)+2*s(3782)+2*s(3791)+6*s(3792)+12*s(3793)+2*s(3794)+14*s(3795)+2*s(3796)+8*s(3797)+8*s(3799)+8*s(3800)+2*s(3805)+2*s(3809)+2*s(3810)+4*s(3816)+4*s(3817)+4*s(3818)+4*s(3819)+14*s(3820)+2*s(3821)+14*s(3822)+2*s(3823)+4*s(3824)+4*s(3825)+14*s(3826)+2*s(3827)+4*s(3830)+8*s(3831)+4 Such that:aux(228) =< 3 aux(229) =< V1 aux(230) =< 2*V1+1 aux(231) =< V1/2 aux(232) =< 2/3*V1 aux(233) =< 2/3*V1+1/3 aux(234) =< 2/5*V1 aux(235) =< 3/7*V1 aux(236) =< 3/11*V1 aux(237) =< V aux(238) =< 2*V+1 aux(239) =< V/2 aux(240) =< 2/3*V aux(241) =< 2/3*V+1/3 aux(242) =< 2/5*V aux(243) =< 3/7*V aux(244) =< 3/11*V s(3742) =< aux(233) s(3787) =< aux(241) s(3830) =< aux(237) s(3831) =< aux(228) s(3791) =< aux(237) s(3792) =< aux(237) s(3793) =< aux(237) s(3794) =< aux(237) s(3795) =< aux(237) s(3796) =< aux(237) s(3797) =< aux(237) s(3787) =< aux(237) s(3787) =< aux(238) s(3793) =< aux(239) s(3794) =< aux(239) s(3796) =< aux(239) s(3798) =< aux(240) s(3795) =< aux(240) s(3796) =< aux(240) s(3792) =< aux(242) s(3794) =< aux(242) s(3799) =< aux(243) s(3800) =< aux(244) s(3801) =< aux(237)+1 s(3802) =< aux(237)+2 s(3803) =< aux(237) s(3804) =< aux(237)-1 s(3798) =< aux(238)*(1/3)+aux(240) s(3795) =< aux(238)*(1/3)+aux(240) s(3796) =< aux(238)*(1/3)+aux(240) s(3797) =< aux(238)*(1/3)+aux(240) s(3793) =< aux(238)*(1/2)+aux(239) s(3794) =< aux(238)*(1/2)+aux(239) s(3795) =< aux(238)*(1/2)+aux(239) s(3796) =< aux(238)*(1/2)+aux(239) s(3797) =< aux(238)*(1/2)+aux(239) s(3792) =< aux(238)*(3/5)+s(3787)*(1/5)+aux(242) s(3793) =< aux(238)*(3/5)+s(3787)*(1/5)+aux(242) s(3794) =< aux(238)*(3/5)+s(3787)*(1/5)+aux(242) s(3795) =< aux(238)*(3/5)+s(3787)*(1/5)+aux(242) s(3796) =< aux(238)*(3/5)+s(3787)*(1/5)+aux(242) s(3797) =< aux(238)*(3/5)+s(3787)*(1/5)+aux(242) s(3799) =< aux(238)*(2/7)+aux(243) s(3791) =< aux(238)*(2/7)+aux(243) s(3800) =< aux(238)*(4/11)+s(3787)*(1/11)+aux(244) s(3799) =< aux(238)*(4/11)+s(3787)*(1/11)+aux(244) s(3791) =< aux(238)*(4/11)+s(3787)*(1/11)+aux(244) s(3805) =< s(3797)*s(3801) s(3806) =< s(3797)*s(3801) s(3807) =< s(3797)*s(3802) s(3808) =< s(3795)*s(3802) s(3809) =< s(3796)*s(3803) s(3810) =< s(3794)*s(3804) s(3811) =< s(3793)*s(3802) s(3812) =< s(3792)*s(3801) s(3813) =< s(3799)*s(3803) s(3814) =< s(3799)*s(3804) s(3815) =< s(3800)*s(3803) s(3816) =< s(3806) s(3817) =< s(3807) s(3818) =< s(3808) s(3819) =< s(3798) s(3820) =< s(3811) s(3821) =< s(3820)*s(3802) s(3822) =< s(3812) s(3823) =< s(3822)*s(3801) s(3824) =< s(3814) s(3825) =< s(3813) s(3826) =< s(3815) s(3827) =< s(3826)*aux(237) s(3746) =< aux(229) s(3747) =< aux(229) s(3748) =< aux(229) s(3749) =< aux(229) s(3750) =< aux(229) s(3751) =< aux(229) s(3752) =< aux(229) s(3742) =< aux(229) s(3742) =< aux(230) s(3748) =< aux(231) s(3749) =< aux(231) s(3751) =< aux(231) s(3753) =< aux(232) s(3750) =< aux(232) s(3751) =< aux(232) s(3747) =< aux(234) s(3749) =< aux(234) s(3754) =< aux(235) s(3755) =< aux(236) s(3756) =< aux(229)+1 s(3757) =< aux(229)+2 s(3758) =< aux(229) s(3759) =< aux(229)-1 s(3753) =< aux(230)*(1/3)+aux(232) s(3750) =< aux(230)*(1/3)+aux(232) s(3751) =< aux(230)*(1/3)+aux(232) s(3752) =< aux(230)*(1/3)+aux(232) s(3748) =< aux(230)*(1/2)+aux(231) s(3749) =< aux(230)*(1/2)+aux(231) s(3750) =< aux(230)*(1/2)+aux(231) s(3751) =< aux(230)*(1/2)+aux(231) s(3752) =< aux(230)*(1/2)+aux(231) s(3747) =< aux(230)*(3/5)+s(3742)*(1/5)+aux(234) s(3748) =< aux(230)*(3/5)+s(3742)*(1/5)+aux(234) s(3749) =< aux(230)*(3/5)+s(3742)*(1/5)+aux(234) s(3750) =< aux(230)*(3/5)+s(3742)*(1/5)+aux(234) s(3751) =< aux(230)*(3/5)+s(3742)*(1/5)+aux(234) s(3752) =< aux(230)*(3/5)+s(3742)*(1/5)+aux(234) s(3754) =< aux(230)*(2/7)+aux(235) s(3746) =< aux(230)*(2/7)+aux(235) s(3755) =< aux(230)*(4/11)+s(3742)*(1/11)+aux(236) s(3754) =< aux(230)*(4/11)+s(3742)*(1/11)+aux(236) s(3746) =< aux(230)*(4/11)+s(3742)*(1/11)+aux(236) s(3760) =< s(3752)*s(3756) s(3761) =< s(3752)*s(3756) s(3762) =< s(3752)*s(3757) s(3763) =< s(3750)*s(3757) s(3764) =< s(3751)*s(3758) s(3765) =< s(3749)*s(3759) s(3766) =< s(3748)*s(3757) s(3767) =< s(3747)*s(3756) s(3768) =< s(3754)*s(3758) s(3769) =< s(3754)*s(3759) s(3770) =< s(3755)*s(3758) s(3771) =< s(3761) s(3772) =< s(3762) s(3773) =< s(3763) s(3774) =< s(3753) s(3775) =< s(3766) s(3776) =< s(3775)*s(3757) s(3777) =< s(3767) s(3778) =< s(3777)*s(3756) s(3779) =< s(3769) s(3780) =< s(3768) s(3781) =< s(3770) s(3782) =< s(3781)*aux(229) with precondition: [V5=2,Out=1,V1>=2,V>=0] * Chain [54]: 1*s(3942)+3*s(3943)+6*s(3944)+1*s(3945)+7*s(3946)+1*s(3947)+4*s(3948)+4*s(3950)+4*s(3951)+1*s(3956)+1*s(3960)+1*s(3961)+2*s(3967)+2*s(3968)+2*s(3969)+2*s(3970)+7*s(3971)+1*s(3972)+7*s(3973)+1*s(3974)+2*s(3975)+2*s(3976)+7*s(3977)+1*s(3978)+2*s(3987)+6*s(3988)+12*s(3989)+2*s(3990)+14*s(3991)+2*s(3992)+8*s(3993)+8*s(3995)+8*s(3996)+2*s(4001)+2*s(4005)+2*s(4006)+4*s(4012)+4*s(4013)+4*s(4014)+4*s(4015)+14*s(4016)+2*s(4017)+14*s(4018)+2*s(4019)+4*s(4020)+4*s(4021)+14*s(4022)+2*s(4023)+14*s(4025)+2*s(4029)+4 Such that:s(3934) =< V1 s(3935) =< 2*V1+1 s(3936) =< V1/2 s(3937) =< 2/3*V1 s(3938) =< 2/3*V1+1/3 s(3939) =< 2/5*V1 s(3940) =< 3/7*V1 s(3941) =< 3/11*V1 aux(247) =< V aux(248) =< 2*V+1 aux(249) =< V/2 aux(250) =< 2/3*V aux(251) =< 2/3*V+1/3 aux(252) =< 2/5*V aux(253) =< 3/7*V aux(254) =< 3/11*V s(3983) =< aux(251) s(4025) =< aux(247) s(4029) =< s(4025)*aux(247) s(3987) =< aux(247) s(3988) =< aux(247) s(3989) =< aux(247) s(3990) =< aux(247) s(3991) =< aux(247) s(3992) =< aux(247) s(3993) =< aux(247) s(3983) =< aux(247) s(3983) =< aux(248) s(3989) =< aux(249) s(3990) =< aux(249) s(3992) =< aux(249) s(3994) =< aux(250) s(3991) =< aux(250) s(3992) =< aux(250) s(3988) =< aux(252) s(3990) =< aux(252) s(3995) =< aux(253) s(3996) =< aux(254) s(3997) =< aux(247)+1 s(3998) =< aux(247)+2 s(3999) =< aux(247) s(4000) =< aux(247)-1 s(3994) =< aux(248)*(1/3)+aux(250) s(3991) =< aux(248)*(1/3)+aux(250) s(3992) =< aux(248)*(1/3)+aux(250) s(3993) =< aux(248)*(1/3)+aux(250) s(3989) =< aux(248)*(1/2)+aux(249) s(3990) =< aux(248)*(1/2)+aux(249) s(3991) =< aux(248)*(1/2)+aux(249) s(3992) =< aux(248)*(1/2)+aux(249) s(3993) =< aux(248)*(1/2)+aux(249) s(3988) =< aux(248)*(3/5)+s(3983)*(1/5)+aux(252) s(3989) =< aux(248)*(3/5)+s(3983)*(1/5)+aux(252) s(3990) =< aux(248)*(3/5)+s(3983)*(1/5)+aux(252) s(3991) =< aux(248)*(3/5)+s(3983)*(1/5)+aux(252) s(3992) =< aux(248)*(3/5)+s(3983)*(1/5)+aux(252) s(3993) =< aux(248)*(3/5)+s(3983)*(1/5)+aux(252) s(3995) =< aux(248)*(2/7)+aux(253) s(3987) =< aux(248)*(2/7)+aux(253) s(3996) =< aux(248)*(4/11)+s(3983)*(1/11)+aux(254) s(3995) =< aux(248)*(4/11)+s(3983)*(1/11)+aux(254) s(3987) =< aux(248)*(4/11)+s(3983)*(1/11)+aux(254) s(4001) =< s(3993)*s(3997) s(4002) =< s(3993)*s(3997) s(4003) =< s(3993)*s(3998) s(4004) =< s(3991)*s(3998) s(4005) =< s(3992)*s(3999) s(4006) =< s(3990)*s(4000) s(4007) =< s(3989)*s(3998) s(4008) =< s(3988)*s(3997) s(4009) =< s(3995)*s(3999) s(4010) =< s(3995)*s(4000) s(4011) =< s(3996)*s(3999) s(4012) =< s(4002) s(4013) =< s(4003) s(4014) =< s(4004) s(4015) =< s(3994) s(4016) =< s(4007) s(4017) =< s(4016)*s(3998) s(4018) =< s(4008) s(4019) =< s(4018)*s(3997) s(4020) =< s(4010) s(4021) =< s(4009) s(4022) =< s(4011) s(4023) =< s(4022)*aux(247) s(3942) =< s(3934) s(3943) =< s(3934) s(3944) =< s(3934) s(3945) =< s(3934) s(3946) =< s(3934) s(3947) =< s(3934) s(3948) =< s(3934) s(3938) =< s(3934) s(3938) =< s(3935) s(3944) =< s(3936) s(3945) =< s(3936) s(3947) =< s(3936) s(3949) =< s(3937) s(3946) =< s(3937) s(3947) =< s(3937) s(3943) =< s(3939) s(3945) =< s(3939) s(3950) =< s(3940) s(3951) =< s(3941) s(3952) =< s(3934)+1 s(3953) =< s(3934)+2 s(3954) =< s(3934) s(3955) =< s(3934)-1 s(3949) =< s(3935)*(1/3)+s(3937) s(3946) =< s(3935)*(1/3)+s(3937) s(3947) =< s(3935)*(1/3)+s(3937) s(3948) =< s(3935)*(1/3)+s(3937) s(3944) =< s(3935)*(1/2)+s(3936) s(3945) =< s(3935)*(1/2)+s(3936) s(3946) =< s(3935)*(1/2)+s(3936) s(3947) =< s(3935)*(1/2)+s(3936) s(3948) =< s(3935)*(1/2)+s(3936) s(3943) =< s(3935)*(3/5)+s(3938)*(1/5)+s(3939) s(3944) =< s(3935)*(3/5)+s(3938)*(1/5)+s(3939) s(3945) =< s(3935)*(3/5)+s(3938)*(1/5)+s(3939) s(3946) =< s(3935)*(3/5)+s(3938)*(1/5)+s(3939) s(3947) =< s(3935)*(3/5)+s(3938)*(1/5)+s(3939) s(3948) =< s(3935)*(3/5)+s(3938)*(1/5)+s(3939) s(3950) =< s(3935)*(2/7)+s(3940) s(3942) =< s(3935)*(2/7)+s(3940) s(3951) =< s(3935)*(4/11)+s(3938)*(1/11)+s(3941) s(3950) =< s(3935)*(4/11)+s(3938)*(1/11)+s(3941) s(3942) =< s(3935)*(4/11)+s(3938)*(1/11)+s(3941) s(3956) =< s(3948)*s(3952) s(3957) =< s(3948)*s(3952) s(3958) =< s(3948)*s(3953) s(3959) =< s(3946)*s(3953) s(3960) =< s(3947)*s(3954) s(3961) =< s(3945)*s(3955) s(3962) =< s(3944)*s(3953) s(3963) =< s(3943)*s(3952) s(3964) =< s(3950)*s(3954) s(3965) =< s(3950)*s(3955) s(3966) =< s(3951)*s(3954) s(3967) =< s(3957) s(3968) =< s(3958) s(3969) =< s(3959) s(3970) =< s(3949) s(3971) =< s(3962) s(3972) =< s(3971)*s(3953) s(3973) =< s(3963) s(3974) =< s(3973)*s(3952) s(3975) =< s(3965) s(3976) =< s(3964) s(3977) =< s(3966) s(3978) =< s(3977)*s(3934) with precondition: [V5=2,V1>=2,Out>=2,V>=Out+2] * Chain [53]: 6*s(4089)+18*s(4090)+36*s(4091)+6*s(4092)+42*s(4093)+6*s(4094)+24*s(4095)+24*s(4097)+24*s(4098)+6*s(4103)+6*s(4107)+6*s(4108)+12*s(4114)+12*s(4115)+12*s(4116)+12*s(4117)+42*s(4118)+6*s(4119)+42*s(4120)+6*s(4121)+12*s(4122)+12*s(4123)+42*s(4124)+6*s(4125)+3*s(4134)+9*s(4135)+18*s(4136)+3*s(4137)+21*s(4138)+3*s(4139)+12*s(4140)+12*s(4142)+12*s(4143)+3*s(4148)+3*s(4152)+3*s(4153)+6*s(4159)+6*s(4160)+6*s(4161)+6*s(4162)+21*s(4163)+3*s(4164)+21*s(4165)+3*s(4166)+6*s(4167)+6*s(4168)+21*s(4169)+3*s(4170)+1 Such that:aux(255) =< V1 aux(256) =< 2*V1+1 aux(257) =< V1/2 aux(258) =< 2/3*V1 aux(259) =< 2/3*V1+1/3 aux(260) =< 2/5*V1 aux(261) =< 3/7*V1 aux(262) =< 3/11*V1 aux(263) =< V5 aux(264) =< 2*V5+1 aux(265) =< V5/2 aux(266) =< 2/3*V5 aux(267) =< 2/3*V5+1/3 aux(268) =< 2/5*V5 aux(269) =< 3/7*V5 aux(270) =< 3/11*V5 s(4085) =< aux(259) s(4130) =< aux(267) s(4134) =< aux(263) s(4135) =< aux(263) s(4136) =< aux(263) s(4137) =< aux(263) s(4138) =< aux(263) s(4139) =< aux(263) s(4140) =< aux(263) s(4130) =< aux(263) s(4130) =< aux(264) s(4136) =< aux(265) s(4137) =< aux(265) s(4139) =< aux(265) s(4141) =< aux(266) s(4138) =< aux(266) s(4139) =< aux(266) s(4135) =< aux(268) s(4137) =< aux(268) s(4142) =< aux(269) s(4143) =< aux(270) s(4144) =< aux(263)+1 s(4145) =< aux(263)+2 s(4146) =< aux(263) s(4147) =< aux(263)-1 s(4141) =< aux(264)*(1/3)+aux(266) s(4138) =< aux(264)*(1/3)+aux(266) s(4139) =< aux(264)*(1/3)+aux(266) s(4140) =< aux(264)*(1/3)+aux(266) s(4136) =< aux(264)*(1/2)+aux(265) s(4137) =< aux(264)*(1/2)+aux(265) s(4138) =< aux(264)*(1/2)+aux(265) s(4139) =< aux(264)*(1/2)+aux(265) s(4140) =< aux(264)*(1/2)+aux(265) s(4135) =< aux(264)*(3/5)+s(4130)*(1/5)+aux(268) s(4136) =< aux(264)*(3/5)+s(4130)*(1/5)+aux(268) s(4137) =< aux(264)*(3/5)+s(4130)*(1/5)+aux(268) s(4138) =< aux(264)*(3/5)+s(4130)*(1/5)+aux(268) s(4139) =< aux(264)*(3/5)+s(4130)*(1/5)+aux(268) s(4140) =< aux(264)*(3/5)+s(4130)*(1/5)+aux(268) s(4142) =< aux(264)*(2/7)+aux(269) s(4134) =< aux(264)*(2/7)+aux(269) s(4143) =< aux(264)*(4/11)+s(4130)*(1/11)+aux(270) s(4142) =< aux(264)*(4/11)+s(4130)*(1/11)+aux(270) s(4134) =< aux(264)*(4/11)+s(4130)*(1/11)+aux(270) s(4148) =< s(4140)*s(4144) s(4149) =< s(4140)*s(4144) s(4150) =< s(4140)*s(4145) s(4151) =< s(4138)*s(4145) s(4152) =< s(4139)*s(4146) s(4153) =< s(4137)*s(4147) s(4154) =< s(4136)*s(4145) s(4155) =< s(4135)*s(4144) s(4156) =< s(4142)*s(4146) s(4157) =< s(4142)*s(4147) s(4158) =< s(4143)*s(4146) s(4159) =< s(4149) s(4160) =< s(4150) s(4161) =< s(4151) s(4162) =< s(4141) s(4163) =< s(4154) s(4164) =< s(4163)*s(4145) s(4165) =< s(4155) s(4166) =< s(4165)*s(4144) s(4167) =< s(4157) s(4168) =< s(4156) s(4169) =< s(4158) s(4170) =< s(4169)*aux(263) s(4089) =< aux(255) s(4090) =< aux(255) s(4091) =< aux(255) s(4092) =< aux(255) s(4093) =< aux(255) s(4094) =< aux(255) s(4095) =< aux(255) s(4085) =< aux(255) s(4085) =< aux(256) s(4091) =< aux(257) s(4092) =< aux(257) s(4094) =< aux(257) s(4096) =< aux(258) s(4093) =< aux(258) s(4094) =< aux(258) s(4090) =< aux(260) s(4092) =< aux(260) s(4097) =< aux(261) s(4098) =< aux(262) s(4099) =< aux(255)+1 s(4100) =< aux(255)+2 s(4101) =< aux(255) s(4102) =< aux(255)-1 s(4096) =< aux(256)*(1/3)+aux(258) s(4093) =< aux(256)*(1/3)+aux(258) s(4094) =< aux(256)*(1/3)+aux(258) s(4095) =< aux(256)*(1/3)+aux(258) s(4091) =< aux(256)*(1/2)+aux(257) s(4092) =< aux(256)*(1/2)+aux(257) s(4093) =< aux(256)*(1/2)+aux(257) s(4094) =< aux(256)*(1/2)+aux(257) s(4095) =< aux(256)*(1/2)+aux(257) s(4090) =< aux(256)*(3/5)+s(4085)*(1/5)+aux(260) s(4091) =< aux(256)*(3/5)+s(4085)*(1/5)+aux(260) s(4092) =< aux(256)*(3/5)+s(4085)*(1/5)+aux(260) s(4093) =< aux(256)*(3/5)+s(4085)*(1/5)+aux(260) s(4094) =< aux(256)*(3/5)+s(4085)*(1/5)+aux(260) s(4095) =< aux(256)*(3/5)+s(4085)*(1/5)+aux(260) s(4097) =< aux(256)*(2/7)+aux(261) s(4089) =< aux(256)*(2/7)+aux(261) s(4098) =< aux(256)*(4/11)+s(4085)*(1/11)+aux(262) s(4097) =< aux(256)*(4/11)+s(4085)*(1/11)+aux(262) s(4089) =< aux(256)*(4/11)+s(4085)*(1/11)+aux(262) s(4103) =< s(4095)*s(4099) s(4104) =< s(4095)*s(4099) s(4105) =< s(4095)*s(4100) s(4106) =< s(4093)*s(4100) s(4107) =< s(4094)*s(4101) s(4108) =< s(4092)*s(4102) s(4109) =< s(4091)*s(4100) s(4110) =< s(4090)*s(4099) s(4111) =< s(4097)*s(4101) s(4112) =< s(4097)*s(4102) s(4113) =< s(4098)*s(4101) s(4114) =< s(4104) s(4115) =< s(4105) s(4116) =< s(4106) s(4117) =< s(4096) s(4118) =< s(4109) s(4119) =< s(4118)*s(4100) s(4120) =< s(4110) s(4121) =< s(4120)*s(4099) s(4122) =< s(4112) s(4123) =< s(4111) s(4124) =< s(4113) s(4125) =< s(4124)*aux(255) with precondition: [V=2,Out=0,V1>=0,V5>=0] * Chain [52]: 3*s(4494)+9*s(4495)+18*s(4496)+3*s(4497)+21*s(4498)+3*s(4499)+12*s(4500)+12*s(4502)+12*s(4503)+3*s(4508)+3*s(4512)+3*s(4513)+6*s(4519)+6*s(4520)+6*s(4521)+6*s(4522)+21*s(4523)+3*s(4524)+21*s(4525)+3*s(4526)+6*s(4527)+6*s(4528)+21*s(4529)+3*s(4530)+1*s(4539)+3*s(4540)+6*s(4541)+1*s(4542)+7*s(4543)+1*s(4544)+4*s(4545)+4*s(4547)+4*s(4548)+1*s(4553)+1*s(4557)+1*s(4558)+2*s(4564)+2*s(4565)+2*s(4566)+2*s(4567)+7*s(4568)+1*s(4569)+7*s(4570)+1*s(4571)+2*s(4572)+2*s(4573)+7*s(4574)+1*s(4575)+6*s(4578)+2*s(4579)+2*s(4628)+2*s(4677)+4 Such that:s(4675) =< 1 s(4626) =< 3 s(4531) =< V5 s(4577) =< V5+1 s(4532) =< 2*V5+1 s(4533) =< V5/2 s(4534) =< 2/3*V5 s(4535) =< 2/3*V5+1/3 s(4536) =< 2/5*V5 s(4537) =< 3/7*V5 s(4538) =< 3/11*V5 aux(271) =< 2 aux(272) =< V1 aux(273) =< 2*V1+1 aux(274) =< V1/2 aux(275) =< 2/3*V1 aux(276) =< 2/3*V1+1/3 aux(277) =< 2/5*V1 aux(278) =< 3/7*V1 aux(279) =< 3/11*V1 s(4490) =< aux(276) s(4578) =< aux(271) s(4677) =< s(4675) s(4494) =< aux(272) s(4495) =< aux(272) s(4496) =< aux(272) s(4497) =< aux(272) s(4498) =< aux(272) s(4499) =< aux(272) s(4500) =< aux(272) s(4490) =< aux(272) s(4490) =< aux(273) s(4496) =< aux(274) s(4497) =< aux(274) s(4499) =< aux(274) s(4501) =< aux(275) s(4498) =< aux(275) s(4499) =< aux(275) s(4495) =< aux(277) s(4497) =< aux(277) s(4502) =< aux(278) s(4503) =< aux(279) s(4504) =< aux(272)+1 s(4505) =< aux(272)+2 s(4506) =< aux(272) s(4507) =< aux(272)-1 s(4501) =< aux(273)*(1/3)+aux(275) s(4498) =< aux(273)*(1/3)+aux(275) s(4499) =< aux(273)*(1/3)+aux(275) s(4500) =< aux(273)*(1/3)+aux(275) s(4496) =< aux(273)*(1/2)+aux(274) s(4497) =< aux(273)*(1/2)+aux(274) s(4498) =< aux(273)*(1/2)+aux(274) s(4499) =< aux(273)*(1/2)+aux(274) s(4500) =< aux(273)*(1/2)+aux(274) s(4495) =< aux(273)*(3/5)+s(4490)*(1/5)+aux(277) s(4496) =< aux(273)*(3/5)+s(4490)*(1/5)+aux(277) s(4497) =< aux(273)*(3/5)+s(4490)*(1/5)+aux(277) s(4498) =< aux(273)*(3/5)+s(4490)*(1/5)+aux(277) s(4499) =< aux(273)*(3/5)+s(4490)*(1/5)+aux(277) s(4500) =< aux(273)*(3/5)+s(4490)*(1/5)+aux(277) s(4502) =< aux(273)*(2/7)+aux(278) s(4494) =< aux(273)*(2/7)+aux(278) s(4503) =< aux(273)*(4/11)+s(4490)*(1/11)+aux(279) s(4502) =< aux(273)*(4/11)+s(4490)*(1/11)+aux(279) s(4494) =< aux(273)*(4/11)+s(4490)*(1/11)+aux(279) s(4508) =< s(4500)*s(4504) s(4509) =< s(4500)*s(4504) s(4510) =< s(4500)*s(4505) s(4511) =< s(4498)*s(4505) s(4512) =< s(4499)*s(4506) s(4513) =< s(4497)*s(4507) s(4514) =< s(4496)*s(4505) s(4515) =< s(4495)*s(4504) s(4516) =< s(4502)*s(4506) s(4517) =< s(4502)*s(4507) s(4518) =< s(4503)*s(4506) s(4519) =< s(4509) s(4520) =< s(4510) s(4521) =< s(4511) s(4522) =< s(4501) s(4523) =< s(4514) s(4524) =< s(4523)*s(4505) s(4525) =< s(4515) s(4526) =< s(4525)*s(4504) s(4527) =< s(4517) s(4528) =< s(4516) s(4529) =< s(4518) s(4530) =< s(4529)*aux(272) s(4579) =< s(4577) s(4539) =< s(4531) s(4540) =< s(4531) s(4541) =< s(4531) s(4542) =< s(4531) s(4543) =< s(4531) s(4544) =< s(4531) s(4545) =< s(4531) s(4535) =< s(4531) s(4535) =< s(4532) s(4541) =< s(4533) s(4542) =< s(4533) s(4544) =< s(4533) s(4546) =< s(4534) s(4543) =< s(4534) s(4544) =< s(4534) s(4540) =< s(4536) s(4542) =< s(4536) s(4547) =< s(4537) s(4548) =< s(4538) s(4549) =< s(4531)+1 s(4550) =< s(4531)+2 s(4551) =< s(4531) s(4552) =< s(4531)-1 s(4546) =< s(4532)*(1/3)+s(4534) s(4543) =< s(4532)*(1/3)+s(4534) s(4544) =< s(4532)*(1/3)+s(4534) s(4545) =< s(4532)*(1/3)+s(4534) s(4541) =< s(4532)*(1/2)+s(4533) s(4542) =< s(4532)*(1/2)+s(4533) s(4543) =< s(4532)*(1/2)+s(4533) s(4544) =< s(4532)*(1/2)+s(4533) s(4545) =< s(4532)*(1/2)+s(4533) s(4540) =< s(4532)*(3/5)+s(4535)*(1/5)+s(4536) s(4541) =< s(4532)*(3/5)+s(4535)*(1/5)+s(4536) s(4542) =< s(4532)*(3/5)+s(4535)*(1/5)+s(4536) s(4543) =< s(4532)*(3/5)+s(4535)*(1/5)+s(4536) s(4544) =< s(4532)*(3/5)+s(4535)*(1/5)+s(4536) s(4545) =< s(4532)*(3/5)+s(4535)*(1/5)+s(4536) s(4547) =< s(4532)*(2/7)+s(4537) s(4539) =< s(4532)*(2/7)+s(4537) s(4548) =< s(4532)*(4/11)+s(4535)*(1/11)+s(4538) s(4547) =< s(4532)*(4/11)+s(4535)*(1/11)+s(4538) s(4539) =< s(4532)*(4/11)+s(4535)*(1/11)+s(4538) s(4553) =< s(4545)*s(4549) s(4554) =< s(4545)*s(4549) s(4555) =< s(4545)*s(4550) s(4556) =< s(4543)*s(4550) s(4557) =< s(4544)*s(4551) s(4558) =< s(4542)*s(4552) s(4559) =< s(4541)*s(4550) s(4560) =< s(4540)*s(4549) s(4561) =< s(4547)*s(4551) s(4562) =< s(4547)*s(4552) s(4563) =< s(4548)*s(4551) s(4564) =< s(4554) s(4565) =< s(4555) s(4566) =< s(4556) s(4567) =< s(4546) s(4568) =< s(4559) s(4569) =< s(4568)*s(4550) s(4570) =< s(4560) s(4571) =< s(4570)*s(4549) s(4572) =< s(4562) s(4573) =< s(4561) s(4574) =< s(4563) s(4575) =< s(4574)*s(4531) s(4628) =< s(4626) with precondition: [V=2,Out=1,V1>=2,V5>=0] * Chain [51]: 2*s(4686)+6*s(4687)+12*s(4688)+2*s(4689)+14*s(4690)+2*s(4691)+8*s(4692)+8*s(4694)+8*s(4695)+2*s(4700)+2*s(4704)+2*s(4705)+4*s(4711)+4*s(4712)+4*s(4713)+4*s(4714)+14*s(4715)+2*s(4716)+14*s(4717)+2*s(4718)+4*s(4719)+4*s(4720)+14*s(4721)+2*s(4722)+1*s(4731)+3*s(4732)+6*s(4733)+1*s(4734)+7*s(4735)+1*s(4736)+4*s(4737)+4*s(4739)+4*s(4740)+1*s(4745)+1*s(4749)+1*s(4750)+2*s(4756)+2*s(4757)+2*s(4758)+2*s(4759)+7*s(4760)+1*s(4761)+7*s(4762)+1*s(4763)+2*s(4764)+2*s(4765)+7*s(4766)+1*s(4767)+6*s(4769)+8*s(4771)+2*s(4773)+4 Such that:s(4723) =< V5 s(4724) =< 2*V5+1 s(4725) =< V5/2 s(4726) =< 2/3*V5 s(4727) =< 2/3*V5+1/3 s(4728) =< 2/5*V5 s(4729) =< 3/7*V5 s(4730) =< 3/11*V5 aux(282) =< 1 aux(283) =< 2 aux(284) =< V1 aux(285) =< 2*V1+1 aux(286) =< V1/2 aux(287) =< 2/3*V1 aux(288) =< 2/3*V1+1/3 aux(289) =< 2/5*V1 aux(290) =< 3/7*V1 aux(291) =< 3/11*V1 s(4769) =< aux(282) s(4682) =< aux(288) s(4771) =< aux(283) s(4773) =< s(4769)*aux(283) s(4731) =< s(4723) s(4732) =< s(4723) s(4733) =< s(4723) s(4734) =< s(4723) s(4735) =< s(4723) s(4736) =< s(4723) s(4737) =< s(4723) s(4727) =< s(4723) s(4727) =< s(4724) s(4733) =< s(4725) s(4734) =< s(4725) s(4736) =< s(4725) s(4738) =< s(4726) s(4735) =< s(4726) s(4736) =< s(4726) s(4732) =< s(4728) s(4734) =< s(4728) s(4739) =< s(4729) s(4740) =< s(4730) s(4741) =< s(4723)+1 s(4742) =< s(4723)+2 s(4743) =< s(4723) s(4744) =< s(4723)-1 s(4738) =< s(4724)*(1/3)+s(4726) s(4735) =< s(4724)*(1/3)+s(4726) s(4736) =< s(4724)*(1/3)+s(4726) s(4737) =< s(4724)*(1/3)+s(4726) s(4733) =< s(4724)*(1/2)+s(4725) s(4734) =< s(4724)*(1/2)+s(4725) s(4735) =< s(4724)*(1/2)+s(4725) s(4736) =< s(4724)*(1/2)+s(4725) s(4737) =< s(4724)*(1/2)+s(4725) s(4732) =< s(4724)*(3/5)+s(4727)*(1/5)+s(4728) s(4733) =< s(4724)*(3/5)+s(4727)*(1/5)+s(4728) s(4734) =< s(4724)*(3/5)+s(4727)*(1/5)+s(4728) s(4735) =< s(4724)*(3/5)+s(4727)*(1/5)+s(4728) s(4736) =< s(4724)*(3/5)+s(4727)*(1/5)+s(4728) s(4737) =< s(4724)*(3/5)+s(4727)*(1/5)+s(4728) s(4739) =< s(4724)*(2/7)+s(4729) s(4731) =< s(4724)*(2/7)+s(4729) s(4740) =< s(4724)*(4/11)+s(4727)*(1/11)+s(4730) s(4739) =< s(4724)*(4/11)+s(4727)*(1/11)+s(4730) s(4731) =< s(4724)*(4/11)+s(4727)*(1/11)+s(4730) s(4745) =< s(4737)*s(4741) s(4746) =< s(4737)*s(4741) s(4747) =< s(4737)*s(4742) s(4748) =< s(4735)*s(4742) s(4749) =< s(4736)*s(4743) s(4750) =< s(4734)*s(4744) s(4751) =< s(4733)*s(4742) s(4752) =< s(4732)*s(4741) s(4753) =< s(4739)*s(4743) s(4754) =< s(4739)*s(4744) s(4755) =< s(4740)*s(4743) s(4756) =< s(4746) s(4757) =< s(4747) s(4758) =< s(4748) s(4759) =< s(4738) s(4760) =< s(4751) s(4761) =< s(4760)*s(4742) s(4762) =< s(4752) s(4763) =< s(4762)*s(4741) s(4764) =< s(4754) s(4765) =< s(4753) s(4766) =< s(4755) s(4767) =< s(4766)*s(4723) s(4686) =< aux(284) s(4687) =< aux(284) s(4688) =< aux(284) s(4689) =< aux(284) s(4690) =< aux(284) s(4691) =< aux(284) s(4692) =< aux(284) s(4682) =< aux(284) s(4682) =< aux(285) s(4688) =< aux(286) s(4689) =< aux(286) s(4691) =< aux(286) s(4693) =< aux(287) s(4690) =< aux(287) s(4691) =< aux(287) s(4687) =< aux(289) s(4689) =< aux(289) s(4694) =< aux(290) s(4695) =< aux(291) s(4696) =< aux(284)+1 s(4697) =< aux(284)+2 s(4698) =< aux(284) s(4699) =< aux(284)-1 s(4693) =< aux(285)*(1/3)+aux(287) s(4690) =< aux(285)*(1/3)+aux(287) s(4691) =< aux(285)*(1/3)+aux(287) s(4692) =< aux(285)*(1/3)+aux(287) s(4688) =< aux(285)*(1/2)+aux(286) s(4689) =< aux(285)*(1/2)+aux(286) s(4690) =< aux(285)*(1/2)+aux(286) s(4691) =< aux(285)*(1/2)+aux(286) s(4692) =< aux(285)*(1/2)+aux(286) s(4687) =< aux(285)*(3/5)+s(4682)*(1/5)+aux(289) s(4688) =< aux(285)*(3/5)+s(4682)*(1/5)+aux(289) s(4689) =< aux(285)*(3/5)+s(4682)*(1/5)+aux(289) s(4690) =< aux(285)*(3/5)+s(4682)*(1/5)+aux(289) s(4691) =< aux(285)*(3/5)+s(4682)*(1/5)+aux(289) s(4692) =< aux(285)*(3/5)+s(4682)*(1/5)+aux(289) s(4694) =< aux(285)*(2/7)+aux(290) s(4686) =< aux(285)*(2/7)+aux(290) s(4695) =< aux(285)*(4/11)+s(4682)*(1/11)+aux(291) s(4694) =< aux(285)*(4/11)+s(4682)*(1/11)+aux(291) s(4686) =< aux(285)*(4/11)+s(4682)*(1/11)+aux(291) s(4700) =< s(4692)*s(4696) s(4701) =< s(4692)*s(4696) s(4702) =< s(4692)*s(4697) s(4703) =< s(4690)*s(4697) s(4704) =< s(4691)*s(4698) s(4705) =< s(4689)*s(4699) s(4706) =< s(4688)*s(4697) s(4707) =< s(4687)*s(4696) s(4708) =< s(4694)*s(4698) s(4709) =< s(4694)*s(4699) s(4710) =< s(4695)*s(4698) s(4711) =< s(4701) s(4712) =< s(4702) s(4713) =< s(4703) s(4714) =< s(4693) s(4715) =< s(4706) s(4716) =< s(4715)*s(4697) s(4717) =< s(4707) s(4718) =< s(4717)*s(4696) s(4719) =< s(4709) s(4720) =< s(4708) s(4721) =< s(4710) s(4722) =< s(4721)*aux(284) with precondition: [V=2,Out=2,V1>=2,V5>=0] #### Cost of chains of fun2(V1,V,Out): * Chain [65]: 2*s(5550)+6*s(5551)+12*s(5552)+2*s(5553)+14*s(5554)+2*s(5555)+8*s(5556)+8*s(5558)+8*s(5559)+2*s(5564)+2*s(5568)+2*s(5569)+4*s(5575)+4*s(5576)+4*s(5577)+4*s(5578)+14*s(5579)+2*s(5580)+14*s(5581)+2*s(5582)+4*s(5583)+4*s(5584)+14*s(5585)+2*s(5586)+3*s(5595)+9*s(5596)+18*s(5597)+3*s(5598)+21*s(5599)+3*s(5600)+12*s(5601)+12*s(5603)+12*s(5604)+3*s(5609)+3*s(5613)+3*s(5614)+6*s(5620)+6*s(5621)+6*s(5622)+6*s(5623)+21*s(5624)+3*s(5625)+21*s(5626)+3*s(5627)+6*s(5628)+6*s(5629)+21*s(5630)+3*s(5631)+3*s(5632)+1*s(5725)+0 Such that:s(5725) =< 2 aux(349) =< V1 aux(350) =< 2*V1+1 aux(351) =< V1/2 aux(352) =< 2/3*V1 aux(353) =< 2/3*V1+1/3 aux(354) =< 2/5*V1 aux(355) =< 3/7*V1 aux(356) =< 3/11*V1 aux(357) =< V aux(358) =< 2*V+1 aux(359) =< V/2 aux(360) =< 2/3*V aux(361) =< 2/3*V+1/3 aux(362) =< 2/5*V aux(363) =< 3/7*V aux(364) =< 3/11*V s(5546) =< aux(353) s(5591) =< aux(361) s(5632) =< aux(357) s(5595) =< aux(357) s(5596) =< aux(357) s(5597) =< aux(357) s(5598) =< aux(357) s(5599) =< aux(357) s(5600) =< aux(357) s(5601) =< aux(357) s(5591) =< aux(357) s(5591) =< aux(358) s(5597) =< aux(359) s(5598) =< aux(359) s(5600) =< aux(359) s(5602) =< aux(360) s(5599) =< aux(360) s(5600) =< aux(360) s(5596) =< aux(362) s(5598) =< aux(362) s(5603) =< aux(363) s(5604) =< aux(364) s(5605) =< aux(357)+1 s(5606) =< aux(357)+2 s(5607) =< aux(357) s(5608) =< aux(357)-1 s(5602) =< aux(358)*(1/3)+aux(360) s(5599) =< aux(358)*(1/3)+aux(360) s(5600) =< aux(358)*(1/3)+aux(360) s(5601) =< aux(358)*(1/3)+aux(360) s(5597) =< aux(358)*(1/2)+aux(359) s(5598) =< aux(358)*(1/2)+aux(359) s(5599) =< aux(358)*(1/2)+aux(359) s(5600) =< aux(358)*(1/2)+aux(359) s(5601) =< aux(358)*(1/2)+aux(359) s(5596) =< aux(358)*(3/5)+s(5591)*(1/5)+aux(362) s(5597) =< aux(358)*(3/5)+s(5591)*(1/5)+aux(362) s(5598) =< aux(358)*(3/5)+s(5591)*(1/5)+aux(362) s(5599) =< aux(358)*(3/5)+s(5591)*(1/5)+aux(362) s(5600) =< aux(358)*(3/5)+s(5591)*(1/5)+aux(362) s(5601) =< aux(358)*(3/5)+s(5591)*(1/5)+aux(362) s(5603) =< aux(358)*(2/7)+aux(363) s(5595) =< aux(358)*(2/7)+aux(363) s(5604) =< aux(358)*(4/11)+s(5591)*(1/11)+aux(364) s(5603) =< aux(358)*(4/11)+s(5591)*(1/11)+aux(364) s(5595) =< aux(358)*(4/11)+s(5591)*(1/11)+aux(364) s(5609) =< s(5601)*s(5605) s(5610) =< s(5601)*s(5605) s(5611) =< s(5601)*s(5606) s(5612) =< s(5599)*s(5606) s(5613) =< s(5600)*s(5607) s(5614) =< s(5598)*s(5608) s(5615) =< s(5597)*s(5606) s(5616) =< s(5596)*s(5605) s(5617) =< s(5603)*s(5607) s(5618) =< s(5603)*s(5608) s(5619) =< s(5604)*s(5607) s(5620) =< s(5610) s(5621) =< s(5611) s(5622) =< s(5612) s(5623) =< s(5602) s(5624) =< s(5615) s(5625) =< s(5624)*s(5606) s(5626) =< s(5616) s(5627) =< s(5626)*s(5605) s(5628) =< s(5618) s(5629) =< s(5617) s(5630) =< s(5619) s(5631) =< s(5630)*aux(357) s(5550) =< aux(349) s(5551) =< aux(349) s(5552) =< aux(349) s(5553) =< aux(349) s(5554) =< aux(349) s(5555) =< aux(349) s(5556) =< aux(349) s(5546) =< aux(349) s(5546) =< aux(350) s(5552) =< aux(351) s(5553) =< aux(351) s(5555) =< aux(351) s(5557) =< aux(352) s(5554) =< aux(352) s(5555) =< aux(352) s(5551) =< aux(354) s(5553) =< aux(354) s(5558) =< aux(355) s(5559) =< aux(356) s(5560) =< aux(349)+1 s(5561) =< aux(349)+2 s(5562) =< aux(349) s(5563) =< aux(349)-1 s(5557) =< aux(350)*(1/3)+aux(352) s(5554) =< aux(350)*(1/3)+aux(352) s(5555) =< aux(350)*(1/3)+aux(352) s(5556) =< aux(350)*(1/3)+aux(352) s(5552) =< aux(350)*(1/2)+aux(351) s(5553) =< aux(350)*(1/2)+aux(351) s(5554) =< aux(350)*(1/2)+aux(351) s(5555) =< aux(350)*(1/2)+aux(351) s(5556) =< aux(350)*(1/2)+aux(351) s(5551) =< aux(350)*(3/5)+s(5546)*(1/5)+aux(354) s(5552) =< aux(350)*(3/5)+s(5546)*(1/5)+aux(354) s(5553) =< aux(350)*(3/5)+s(5546)*(1/5)+aux(354) s(5554) =< aux(350)*(3/5)+s(5546)*(1/5)+aux(354) s(5555) =< aux(350)*(3/5)+s(5546)*(1/5)+aux(354) s(5556) =< aux(350)*(3/5)+s(5546)*(1/5)+aux(354) s(5558) =< aux(350)*(2/7)+aux(355) s(5550) =< aux(350)*(2/7)+aux(355) s(5559) =< aux(350)*(4/11)+s(5546)*(1/11)+aux(356) s(5558) =< aux(350)*(4/11)+s(5546)*(1/11)+aux(356) s(5550) =< aux(350)*(4/11)+s(5546)*(1/11)+aux(356) s(5564) =< s(5556)*s(5560) s(5565) =< s(5556)*s(5560) s(5566) =< s(5556)*s(5561) s(5567) =< s(5554)*s(5561) s(5568) =< s(5555)*s(5562) s(5569) =< s(5553)*s(5563) s(5570) =< s(5552)*s(5561) s(5571) =< s(5551)*s(5560) s(5572) =< s(5558)*s(5562) s(5573) =< s(5558)*s(5563) s(5574) =< s(5559)*s(5562) s(5575) =< s(5565) s(5576) =< s(5566) s(5577) =< s(5567) s(5578) =< s(5557) s(5579) =< s(5570) s(5580) =< s(5579)*s(5561) s(5581) =< s(5571) s(5582) =< s(5581)*s(5560) s(5583) =< s(5573) s(5584) =< s(5572) s(5585) =< s(5574) s(5586) =< s(5585)*aux(349) with precondition: [Out=0,V1>=0,V>=0] * Chain [64]: 3*s(5782)+9*s(5783)+18*s(5784)+3*s(5785)+21*s(5786)+3*s(5787)+12*s(5788)+12*s(5790)+12*s(5791)+3*s(5796)+3*s(5800)+3*s(5801)+6*s(5807)+6*s(5808)+6*s(5809)+6*s(5810)+21*s(5811)+3*s(5812)+21*s(5813)+3*s(5814)+6*s(5815)+6*s(5816)+21*s(5817)+3*s(5818)+4*s(5827)+12*s(5828)+24*s(5829)+4*s(5830)+28*s(5831)+4*s(5832)+16*s(5833)+16*s(5835)+16*s(5836)+4*s(5841)+4*s(5845)+4*s(5846)+8*s(5852)+8*s(5853)+8*s(5854)+8*s(5855)+28*s(5856)+4*s(5857)+28*s(5858)+4*s(5859)+8*s(5860)+8*s(5861)+28*s(5862)+4*s(5863)+1*s(5954)+2*s(6045)+1 Such that:aux(366) =< 2 aux(367) =< V1 aux(368) =< 2*V1+1 aux(369) =< V1/2 aux(370) =< 2/3*V1 aux(371) =< 2/3*V1+1/3 aux(372) =< 2/5*V1 aux(373) =< 3/7*V1 aux(374) =< 3/11*V1 aux(375) =< V aux(376) =< 2*V+1 aux(377) =< V/2 aux(378) =< 2/3*V aux(379) =< 2/3*V+1/3 aux(380) =< 2/5*V aux(381) =< 3/7*V aux(382) =< 3/11*V s(6045) =< aux(366) s(5778) =< aux(371) s(5823) =< aux(379) s(5827) =< aux(375) s(5828) =< aux(375) s(5829) =< aux(375) s(5830) =< aux(375) s(5831) =< aux(375) s(5832) =< aux(375) s(5833) =< aux(375) s(5823) =< aux(375) s(5823) =< aux(376) s(5829) =< aux(377) s(5830) =< aux(377) s(5832) =< aux(377) s(5834) =< aux(378) s(5831) =< aux(378) s(5832) =< aux(378) s(5828) =< aux(380) s(5830) =< aux(380) s(5835) =< aux(381) s(5836) =< aux(382) s(5837) =< aux(375)+1 s(5838) =< aux(375)+2 s(5839) =< aux(375) s(5840) =< aux(375)-1 s(5834) =< aux(376)*(1/3)+aux(378) s(5831) =< aux(376)*(1/3)+aux(378) s(5832) =< aux(376)*(1/3)+aux(378) s(5833) =< aux(376)*(1/3)+aux(378) s(5829) =< aux(376)*(1/2)+aux(377) s(5830) =< aux(376)*(1/2)+aux(377) s(5831) =< aux(376)*(1/2)+aux(377) s(5832) =< aux(376)*(1/2)+aux(377) s(5833) =< aux(376)*(1/2)+aux(377) s(5828) =< aux(376)*(3/5)+s(5823)*(1/5)+aux(380) s(5829) =< aux(376)*(3/5)+s(5823)*(1/5)+aux(380) s(5830) =< aux(376)*(3/5)+s(5823)*(1/5)+aux(380) s(5831) =< aux(376)*(3/5)+s(5823)*(1/5)+aux(380) s(5832) =< aux(376)*(3/5)+s(5823)*(1/5)+aux(380) s(5833) =< aux(376)*(3/5)+s(5823)*(1/5)+aux(380) s(5835) =< aux(376)*(2/7)+aux(381) s(5827) =< aux(376)*(2/7)+aux(381) s(5836) =< aux(376)*(4/11)+s(5823)*(1/11)+aux(382) s(5835) =< aux(376)*(4/11)+s(5823)*(1/11)+aux(382) s(5827) =< aux(376)*(4/11)+s(5823)*(1/11)+aux(382) s(5841) =< s(5833)*s(5837) s(5842) =< s(5833)*s(5837) s(5843) =< s(5833)*s(5838) s(5844) =< s(5831)*s(5838) s(5845) =< s(5832)*s(5839) s(5846) =< s(5830)*s(5840) s(5847) =< s(5829)*s(5838) s(5848) =< s(5828)*s(5837) s(5849) =< s(5835)*s(5839) s(5850) =< s(5835)*s(5840) s(5851) =< s(5836)*s(5839) s(5852) =< s(5842) s(5853) =< s(5843) s(5854) =< s(5844) s(5855) =< s(5834) s(5856) =< s(5847) s(5857) =< s(5856)*s(5838) s(5858) =< s(5848) s(5859) =< s(5858)*s(5837) s(5860) =< s(5850) s(5861) =< s(5849) s(5862) =< s(5851) s(5863) =< s(5862)*aux(375) s(5782) =< aux(367) s(5783) =< aux(367) s(5784) =< aux(367) s(5785) =< aux(367) s(5786) =< aux(367) s(5787) =< aux(367) s(5788) =< aux(367) s(5778) =< aux(367) s(5778) =< aux(368) s(5784) =< aux(369) s(5785) =< aux(369) s(5787) =< aux(369) s(5789) =< aux(370) s(5786) =< aux(370) s(5787) =< aux(370) s(5783) =< aux(372) s(5785) =< aux(372) s(5790) =< aux(373) s(5791) =< aux(374) s(5792) =< aux(367)+1 s(5793) =< aux(367)+2 s(5794) =< aux(367) s(5795) =< aux(367)-1 s(5789) =< aux(368)*(1/3)+aux(370) s(5786) =< aux(368)*(1/3)+aux(370) s(5787) =< aux(368)*(1/3)+aux(370) s(5788) =< aux(368)*(1/3)+aux(370) s(5784) =< aux(368)*(1/2)+aux(369) s(5785) =< aux(368)*(1/2)+aux(369) s(5786) =< aux(368)*(1/2)+aux(369) s(5787) =< aux(368)*(1/2)+aux(369) s(5788) =< aux(368)*(1/2)+aux(369) s(5783) =< aux(368)*(3/5)+s(5778)*(1/5)+aux(372) s(5784) =< aux(368)*(3/5)+s(5778)*(1/5)+aux(372) s(5785) =< aux(368)*(3/5)+s(5778)*(1/5)+aux(372) s(5786) =< aux(368)*(3/5)+s(5778)*(1/5)+aux(372) s(5787) =< aux(368)*(3/5)+s(5778)*(1/5)+aux(372) s(5788) =< aux(368)*(3/5)+s(5778)*(1/5)+aux(372) s(5790) =< aux(368)*(2/7)+aux(373) s(5782) =< aux(368)*(2/7)+aux(373) s(5791) =< aux(368)*(4/11)+s(5778)*(1/11)+aux(374) s(5790) =< aux(368)*(4/11)+s(5778)*(1/11)+aux(374) s(5782) =< aux(368)*(4/11)+s(5778)*(1/11)+aux(374) s(5796) =< s(5788)*s(5792) s(5797) =< s(5788)*s(5792) s(5798) =< s(5788)*s(5793) s(5799) =< s(5786)*s(5793) s(5800) =< s(5787)*s(5794) s(5801) =< s(5785)*s(5795) s(5802) =< s(5784)*s(5793) s(5803) =< s(5783)*s(5792) s(5804) =< s(5790)*s(5794) s(5805) =< s(5790)*s(5795) s(5806) =< s(5791)*s(5794) s(5807) =< s(5797) s(5808) =< s(5798) s(5809) =< s(5799) s(5810) =< s(5789) s(5811) =< s(5802) s(5812) =< s(5811)*s(5793) s(5813) =< s(5803) s(5814) =< s(5813)*s(5792) s(5815) =< s(5805) s(5816) =< s(5804) s(5817) =< s(5806) s(5818) =< s(5817)*aux(367) s(5954) =< aux(375) with precondition: [Out=1,V1>=0,V>=0] * Chain [63]: 3*s(6100)+9*s(6101)+18*s(6102)+3*s(6103)+21*s(6104)+3*s(6105)+12*s(6106)+12*s(6108)+12*s(6109)+3*s(6114)+3*s(6118)+3*s(6119)+6*s(6125)+6*s(6126)+6*s(6127)+6*s(6128)+21*s(6129)+3*s(6130)+21*s(6131)+3*s(6132)+6*s(6133)+6*s(6134)+21*s(6135)+3*s(6136)+4*s(6145)+12*s(6146)+24*s(6147)+4*s(6148)+28*s(6149)+4*s(6150)+16*s(6151)+16*s(6153)+16*s(6154)+4*s(6159)+4*s(6163)+4*s(6164)+8*s(6170)+8*s(6171)+8*s(6172)+8*s(6173)+28*s(6174)+4*s(6175)+28*s(6176)+4*s(6177)+8*s(6178)+8*s(6179)+28*s(6180)+4*s(6181)+1*s(6272)+1*s(6408)+1 Such that:s(6408) =< 1 aux(384) =< V1 aux(385) =< 2*V1+1 aux(386) =< V1/2 aux(387) =< 2/3*V1 aux(388) =< 2/3*V1+1/3 aux(389) =< 2/5*V1 aux(390) =< 3/7*V1 aux(391) =< 3/11*V1 aux(392) =< V aux(393) =< 2*V+1 aux(394) =< V/2 aux(395) =< 2/3*V aux(396) =< 2/3*V+1/3 aux(397) =< 2/5*V aux(398) =< 3/7*V aux(399) =< 3/11*V s(6096) =< aux(388) s(6141) =< aux(396) s(6145) =< aux(392) s(6146) =< aux(392) s(6147) =< aux(392) s(6148) =< aux(392) s(6149) =< aux(392) s(6150) =< aux(392) s(6151) =< aux(392) s(6141) =< aux(392) s(6141) =< aux(393) s(6147) =< aux(394) s(6148) =< aux(394) s(6150) =< aux(394) s(6152) =< aux(395) s(6149) =< aux(395) s(6150) =< aux(395) s(6146) =< aux(397) s(6148) =< aux(397) s(6153) =< aux(398) s(6154) =< aux(399) s(6155) =< aux(392)+1 s(6156) =< aux(392)+2 s(6157) =< aux(392) s(6158) =< aux(392)-1 s(6152) =< aux(393)*(1/3)+aux(395) s(6149) =< aux(393)*(1/3)+aux(395) s(6150) =< aux(393)*(1/3)+aux(395) s(6151) =< aux(393)*(1/3)+aux(395) s(6147) =< aux(393)*(1/2)+aux(394) s(6148) =< aux(393)*(1/2)+aux(394) s(6149) =< aux(393)*(1/2)+aux(394) s(6150) =< aux(393)*(1/2)+aux(394) s(6151) =< aux(393)*(1/2)+aux(394) s(6146) =< aux(393)*(3/5)+s(6141)*(1/5)+aux(397) s(6147) =< aux(393)*(3/5)+s(6141)*(1/5)+aux(397) s(6148) =< aux(393)*(3/5)+s(6141)*(1/5)+aux(397) s(6149) =< aux(393)*(3/5)+s(6141)*(1/5)+aux(397) s(6150) =< aux(393)*(3/5)+s(6141)*(1/5)+aux(397) s(6151) =< aux(393)*(3/5)+s(6141)*(1/5)+aux(397) s(6153) =< aux(393)*(2/7)+aux(398) s(6145) =< aux(393)*(2/7)+aux(398) s(6154) =< aux(393)*(4/11)+s(6141)*(1/11)+aux(399) s(6153) =< aux(393)*(4/11)+s(6141)*(1/11)+aux(399) s(6145) =< aux(393)*(4/11)+s(6141)*(1/11)+aux(399) s(6159) =< s(6151)*s(6155) s(6160) =< s(6151)*s(6155) s(6161) =< s(6151)*s(6156) s(6162) =< s(6149)*s(6156) s(6163) =< s(6150)*s(6157) s(6164) =< s(6148)*s(6158) s(6165) =< s(6147)*s(6156) s(6166) =< s(6146)*s(6155) s(6167) =< s(6153)*s(6157) s(6168) =< s(6153)*s(6158) s(6169) =< s(6154)*s(6157) s(6170) =< s(6160) s(6171) =< s(6161) s(6172) =< s(6162) s(6173) =< s(6152) s(6174) =< s(6165) s(6175) =< s(6174)*s(6156) s(6176) =< s(6166) s(6177) =< s(6176)*s(6155) s(6178) =< s(6168) s(6179) =< s(6167) s(6180) =< s(6169) s(6181) =< s(6180)*aux(392) s(6100) =< aux(384) s(6101) =< aux(384) s(6102) =< aux(384) s(6103) =< aux(384) s(6104) =< aux(384) s(6105) =< aux(384) s(6106) =< aux(384) s(6096) =< aux(384) s(6096) =< aux(385) s(6102) =< aux(386) s(6103) =< aux(386) s(6105) =< aux(386) s(6107) =< aux(387) s(6104) =< aux(387) s(6105) =< aux(387) s(6101) =< aux(389) s(6103) =< aux(389) s(6108) =< aux(390) s(6109) =< aux(391) s(6110) =< aux(384)+1 s(6111) =< aux(384)+2 s(6112) =< aux(384) s(6113) =< aux(384)-1 s(6107) =< aux(385)*(1/3)+aux(387) s(6104) =< aux(385)*(1/3)+aux(387) s(6105) =< aux(385)*(1/3)+aux(387) s(6106) =< aux(385)*(1/3)+aux(387) s(6102) =< aux(385)*(1/2)+aux(386) s(6103) =< aux(385)*(1/2)+aux(386) s(6104) =< aux(385)*(1/2)+aux(386) s(6105) =< aux(385)*(1/2)+aux(386) s(6106) =< aux(385)*(1/2)+aux(386) s(6101) =< aux(385)*(3/5)+s(6096)*(1/5)+aux(389) s(6102) =< aux(385)*(3/5)+s(6096)*(1/5)+aux(389) s(6103) =< aux(385)*(3/5)+s(6096)*(1/5)+aux(389) s(6104) =< aux(385)*(3/5)+s(6096)*(1/5)+aux(389) s(6105) =< aux(385)*(3/5)+s(6096)*(1/5)+aux(389) s(6106) =< aux(385)*(3/5)+s(6096)*(1/5)+aux(389) s(6108) =< aux(385)*(2/7)+aux(390) s(6100) =< aux(385)*(2/7)+aux(390) s(6109) =< aux(385)*(4/11)+s(6096)*(1/11)+aux(391) s(6108) =< aux(385)*(4/11)+s(6096)*(1/11)+aux(391) s(6100) =< aux(385)*(4/11)+s(6096)*(1/11)+aux(391) s(6114) =< s(6106)*s(6110) s(6115) =< s(6106)*s(6110) s(6116) =< s(6106)*s(6111) s(6117) =< s(6104)*s(6111) s(6118) =< s(6105)*s(6112) s(6119) =< s(6103)*s(6113) s(6120) =< s(6102)*s(6111) s(6121) =< s(6101)*s(6110) s(6122) =< s(6108)*s(6112) s(6123) =< s(6108)*s(6113) s(6124) =< s(6109)*s(6112) s(6125) =< s(6115) s(6126) =< s(6116) s(6127) =< s(6117) s(6128) =< s(6107) s(6129) =< s(6120) s(6130) =< s(6129)*s(6111) s(6131) =< s(6121) s(6132) =< s(6131)*s(6110) s(6133) =< s(6123) s(6134) =< s(6122) s(6135) =< s(6124) s(6136) =< s(6135)*aux(384) s(6272) =< aux(392) with precondition: [Out=2,V1>=1,V>=0] * Chain [62]: 1*s(6417)+3*s(6418)+6*s(6419)+1*s(6420)+7*s(6421)+1*s(6422)+4*s(6423)+4*s(6425)+4*s(6426)+1*s(6431)+1*s(6435)+1*s(6436)+2*s(6442)+2*s(6443)+2*s(6444)+2*s(6445)+7*s(6446)+1*s(6447)+7*s(6448)+1*s(6449)+2*s(6450)+2*s(6451)+7*s(6452)+1*s(6453)+2*s(6454)+0 Such that:s(6409) =< V1 s(6410) =< 2*V1+1 s(6411) =< V1/2 s(6412) =< 2/3*V1 s(6413) =< 2/3*V1+1/3 s(6414) =< 2/5*V1 s(6415) =< 3/7*V1 s(6416) =< 3/11*V1 aux(400) =< 2 s(6454) =< aux(400) s(6417) =< s(6409) s(6418) =< s(6409) s(6419) =< s(6409) s(6420) =< s(6409) s(6421) =< s(6409) s(6422) =< s(6409) s(6423) =< s(6409) s(6413) =< s(6409) s(6413) =< s(6410) s(6419) =< s(6411) s(6420) =< s(6411) s(6422) =< s(6411) s(6424) =< s(6412) s(6421) =< s(6412) s(6422) =< s(6412) s(6418) =< s(6414) s(6420) =< s(6414) s(6425) =< s(6415) s(6426) =< s(6416) s(6427) =< s(6409)+1 s(6428) =< s(6409)+2 s(6429) =< s(6409) s(6430) =< s(6409)-1 s(6424) =< s(6410)*(1/3)+s(6412) s(6421) =< s(6410)*(1/3)+s(6412) s(6422) =< s(6410)*(1/3)+s(6412) s(6423) =< s(6410)*(1/3)+s(6412) s(6419) =< s(6410)*(1/2)+s(6411) s(6420) =< s(6410)*(1/2)+s(6411) s(6421) =< s(6410)*(1/2)+s(6411) s(6422) =< s(6410)*(1/2)+s(6411) s(6423) =< s(6410)*(1/2)+s(6411) s(6418) =< s(6410)*(3/5)+s(6413)*(1/5)+s(6414) s(6419) =< s(6410)*(3/5)+s(6413)*(1/5)+s(6414) s(6420) =< s(6410)*(3/5)+s(6413)*(1/5)+s(6414) s(6421) =< s(6410)*(3/5)+s(6413)*(1/5)+s(6414) s(6422) =< s(6410)*(3/5)+s(6413)*(1/5)+s(6414) s(6423) =< s(6410)*(3/5)+s(6413)*(1/5)+s(6414) s(6425) =< s(6410)*(2/7)+s(6415) s(6417) =< s(6410)*(2/7)+s(6415) s(6426) =< s(6410)*(4/11)+s(6413)*(1/11)+s(6416) s(6425) =< s(6410)*(4/11)+s(6413)*(1/11)+s(6416) s(6417) =< s(6410)*(4/11)+s(6413)*(1/11)+s(6416) s(6431) =< s(6423)*s(6427) s(6432) =< s(6423)*s(6427) s(6433) =< s(6423)*s(6428) s(6434) =< s(6421)*s(6428) s(6435) =< s(6422)*s(6429) s(6436) =< s(6420)*s(6430) s(6437) =< s(6419)*s(6428) s(6438) =< s(6418)*s(6427) s(6439) =< s(6425)*s(6429) s(6440) =< s(6425)*s(6430) s(6441) =< s(6426)*s(6429) s(6442) =< s(6432) s(6443) =< s(6433) s(6444) =< s(6434) s(6445) =< s(6424) s(6446) =< s(6437) s(6447) =< s(6446)*s(6428) s(6448) =< s(6438) s(6449) =< s(6448)*s(6427) s(6450) =< s(6440) s(6451) =< s(6439) s(6452) =< s(6441) s(6453) =< s(6452)*s(6409) with precondition: [V=2,Out=0,V1>=0] * Chain [61]: 2*s(6464)+6*s(6465)+12*s(6466)+2*s(6467)+14*s(6468)+2*s(6469)+8*s(6470)+8*s(6472)+8*s(6473)+2*s(6478)+2*s(6482)+2*s(6483)+4*s(6489)+4*s(6490)+4*s(6491)+4*s(6492)+14*s(6493)+2*s(6494)+14*s(6495)+2*s(6496)+4*s(6497)+4*s(6498)+14*s(6499)+2*s(6500)+1*s(6546)+1 Such that:aux(402) =< V1 aux(403) =< 2*V1+1 aux(404) =< V1/2 aux(405) =< 2/3*V1 aux(406) =< 2/3*V1+1/3 aux(407) =< 2/5*V1 aux(408) =< 3/7*V1 aux(409) =< 3/11*V1 s(6460) =< aux(406) s(6464) =< aux(402) s(6465) =< aux(402) s(6466) =< aux(402) s(6467) =< aux(402) s(6468) =< aux(402) s(6469) =< aux(402) s(6470) =< aux(402) s(6460) =< aux(402) s(6460) =< aux(403) s(6466) =< aux(404) s(6467) =< aux(404) s(6469) =< aux(404) s(6471) =< aux(405) s(6468) =< aux(405) s(6469) =< aux(405) s(6465) =< aux(407) s(6467) =< aux(407) s(6472) =< aux(408) s(6473) =< aux(409) s(6474) =< aux(402)+1 s(6475) =< aux(402)+2 s(6476) =< aux(402) s(6477) =< aux(402)-1 s(6471) =< aux(403)*(1/3)+aux(405) s(6468) =< aux(403)*(1/3)+aux(405) s(6469) =< aux(403)*(1/3)+aux(405) s(6470) =< aux(403)*(1/3)+aux(405) s(6466) =< aux(403)*(1/2)+aux(404) s(6467) =< aux(403)*(1/2)+aux(404) s(6468) =< aux(403)*(1/2)+aux(404) s(6469) =< aux(403)*(1/2)+aux(404) s(6470) =< aux(403)*(1/2)+aux(404) s(6465) =< aux(403)*(3/5)+s(6460)*(1/5)+aux(407) s(6466) =< aux(403)*(3/5)+s(6460)*(1/5)+aux(407) s(6467) =< aux(403)*(3/5)+s(6460)*(1/5)+aux(407) s(6468) =< aux(403)*(3/5)+s(6460)*(1/5)+aux(407) s(6469) =< aux(403)*(3/5)+s(6460)*(1/5)+aux(407) s(6470) =< aux(403)*(3/5)+s(6460)*(1/5)+aux(407) s(6472) =< aux(403)*(2/7)+aux(408) s(6464) =< aux(403)*(2/7)+aux(408) s(6473) =< aux(403)*(4/11)+s(6460)*(1/11)+aux(409) s(6472) =< aux(403)*(4/11)+s(6460)*(1/11)+aux(409) s(6464) =< aux(403)*(4/11)+s(6460)*(1/11)+aux(409) s(6478) =< s(6470)*s(6474) s(6479) =< s(6470)*s(6474) s(6480) =< s(6470)*s(6475) s(6481) =< s(6468)*s(6475) s(6482) =< s(6469)*s(6476) s(6483) =< s(6467)*s(6477) s(6484) =< s(6466)*s(6475) s(6485) =< s(6465)*s(6474) s(6486) =< s(6472)*s(6476) s(6487) =< s(6472)*s(6477) s(6488) =< s(6473)*s(6476) s(6489) =< s(6479) s(6490) =< s(6480) s(6491) =< s(6481) s(6492) =< s(6471) s(6493) =< s(6484) s(6494) =< s(6493)*s(6475) s(6495) =< s(6485) s(6496) =< s(6495)*s(6474) s(6497) =< s(6487) s(6498) =< s(6486) s(6499) =< s(6488) s(6500) =< s(6499)*aux(402) s(6546) =< aux(402) with precondition: [V=2,Out=1,V1>=0] * Chain [60]: 1*s(6555)+3*s(6556)+6*s(6557)+1*s(6558)+7*s(6559)+1*s(6560)+4*s(6561)+4*s(6563)+4*s(6564)+1*s(6569)+1*s(6573)+1*s(6574)+2*s(6580)+2*s(6581)+2*s(6582)+2*s(6583)+7*s(6584)+1*s(6585)+7*s(6586)+1*s(6587)+2*s(6588)+2*s(6589)+7*s(6590)+1*s(6591)+1*s(6592)+1 Such that:s(6592) =< 2 s(6547) =< V1 s(6548) =< 2*V1+1 s(6549) =< V1/2 s(6550) =< 2/3*V1 s(6551) =< 2/3*V1+1/3 s(6552) =< 2/5*V1 s(6553) =< 3/7*V1 s(6554) =< 3/11*V1 s(6555) =< s(6547) s(6556) =< s(6547) s(6557) =< s(6547) s(6558) =< s(6547) s(6559) =< s(6547) s(6560) =< s(6547) s(6561) =< s(6547) s(6551) =< s(6547) s(6551) =< s(6548) s(6557) =< s(6549) s(6558) =< s(6549) s(6560) =< s(6549) s(6562) =< s(6550) s(6559) =< s(6550) s(6560) =< s(6550) s(6556) =< s(6552) s(6558) =< s(6552) s(6563) =< s(6553) s(6564) =< s(6554) s(6565) =< s(6547)+1 s(6566) =< s(6547)+2 s(6567) =< s(6547) s(6568) =< s(6547)-1 s(6562) =< s(6548)*(1/3)+s(6550) s(6559) =< s(6548)*(1/3)+s(6550) s(6560) =< s(6548)*(1/3)+s(6550) s(6561) =< s(6548)*(1/3)+s(6550) s(6557) =< s(6548)*(1/2)+s(6549) s(6558) =< s(6548)*(1/2)+s(6549) s(6559) =< s(6548)*(1/2)+s(6549) s(6560) =< s(6548)*(1/2)+s(6549) s(6561) =< s(6548)*(1/2)+s(6549) s(6556) =< s(6548)*(3/5)+s(6551)*(1/5)+s(6552) s(6557) =< s(6548)*(3/5)+s(6551)*(1/5)+s(6552) s(6558) =< s(6548)*(3/5)+s(6551)*(1/5)+s(6552) s(6559) =< s(6548)*(3/5)+s(6551)*(1/5)+s(6552) s(6560) =< s(6548)*(3/5)+s(6551)*(1/5)+s(6552) s(6561) =< s(6548)*(3/5)+s(6551)*(1/5)+s(6552) s(6563) =< s(6548)*(2/7)+s(6553) s(6555) =< s(6548)*(2/7)+s(6553) s(6564) =< s(6548)*(4/11)+s(6551)*(1/11)+s(6554) s(6563) =< s(6548)*(4/11)+s(6551)*(1/11)+s(6554) s(6555) =< s(6548)*(4/11)+s(6551)*(1/11)+s(6554) s(6569) =< s(6561)*s(6565) s(6570) =< s(6561)*s(6565) s(6571) =< s(6561)*s(6566) s(6572) =< s(6559)*s(6566) s(6573) =< s(6560)*s(6567) s(6574) =< s(6558)*s(6568) s(6575) =< s(6557)*s(6566) s(6576) =< s(6556)*s(6565) s(6577) =< s(6563)*s(6567) s(6578) =< s(6563)*s(6568) s(6579) =< s(6564)*s(6567) s(6580) =< s(6570) s(6581) =< s(6571) s(6582) =< s(6572) s(6583) =< s(6562) s(6584) =< s(6575) s(6585) =< s(6584)*s(6566) s(6586) =< s(6576) s(6587) =< s(6586)*s(6565) s(6588) =< s(6578) s(6589) =< s(6577) s(6590) =< s(6579) s(6591) =< s(6590)*s(6547) with precondition: [V=2,Out=2,V1>=3] #### Cost of chains of fun3(Out): * Chain [67]: 0 with precondition: [Out=0] * Chain [66]: 0 with precondition: [Out=1] #### Cost of chains of fun5(Out): * Chain [69]: 0 with precondition: [Out=0] * Chain [68]: 0 with precondition: [Out=2] #### Cost of chains of fun6(V1,Out): * Chain [72]: 1*s(7024)+3*s(7025)+6*s(7026)+1*s(7027)+7*s(7028)+1*s(7029)+4*s(7030)+4*s(7032)+4*s(7033)+1*s(7038)+1*s(7042)+1*s(7043)+2*s(7049)+2*s(7050)+2*s(7051)+2*s(7052)+7*s(7053)+1*s(7054)+7*s(7055)+1*s(7056)+2*s(7057)+2*s(7058)+7*s(7059)+1*s(7060)+0 Such that:s(7016) =< V1 s(7017) =< 2*V1+1 s(7018) =< V1/2 s(7019) =< 2/3*V1 s(7020) =< 2/3*V1+1/3 s(7021) =< 2/5*V1 s(7022) =< 3/7*V1 s(7023) =< 3/11*V1 s(7024) =< s(7016) s(7025) =< s(7016) s(7026) =< s(7016) s(7027) =< s(7016) s(7028) =< s(7016) s(7029) =< s(7016) s(7030) =< s(7016) s(7020) =< s(7016) s(7020) =< s(7017) s(7026) =< s(7018) s(7027) =< s(7018) s(7029) =< s(7018) s(7031) =< s(7019) s(7028) =< s(7019) s(7029) =< s(7019) s(7025) =< s(7021) s(7027) =< s(7021) s(7032) =< s(7022) s(7033) =< s(7023) s(7034) =< s(7016)+1 s(7035) =< s(7016)+2 s(7036) =< s(7016) s(7037) =< s(7016)-1 s(7031) =< s(7017)*(1/3)+s(7019) s(7028) =< s(7017)*(1/3)+s(7019) s(7029) =< s(7017)*(1/3)+s(7019) s(7030) =< s(7017)*(1/3)+s(7019) s(7026) =< s(7017)*(1/2)+s(7018) s(7027) =< s(7017)*(1/2)+s(7018) s(7028) =< s(7017)*(1/2)+s(7018) s(7029) =< s(7017)*(1/2)+s(7018) s(7030) =< s(7017)*(1/2)+s(7018) s(7025) =< s(7017)*(3/5)+s(7020)*(1/5)+s(7021) s(7026) =< s(7017)*(3/5)+s(7020)*(1/5)+s(7021) s(7027) =< s(7017)*(3/5)+s(7020)*(1/5)+s(7021) s(7028) =< s(7017)*(3/5)+s(7020)*(1/5)+s(7021) s(7029) =< s(7017)*(3/5)+s(7020)*(1/5)+s(7021) s(7030) =< s(7017)*(3/5)+s(7020)*(1/5)+s(7021) s(7032) =< s(7017)*(2/7)+s(7022) s(7024) =< s(7017)*(2/7)+s(7022) s(7033) =< s(7017)*(4/11)+s(7020)*(1/11)+s(7023) s(7032) =< s(7017)*(4/11)+s(7020)*(1/11)+s(7023) s(7024) =< s(7017)*(4/11)+s(7020)*(1/11)+s(7023) s(7038) =< s(7030)*s(7034) s(7039) =< s(7030)*s(7034) s(7040) =< s(7030)*s(7035) s(7041) =< s(7028)*s(7035) s(7042) =< s(7029)*s(7036) s(7043) =< s(7027)*s(7037) s(7044) =< s(7026)*s(7035) s(7045) =< s(7025)*s(7034) s(7046) =< s(7032)*s(7036) s(7047) =< s(7032)*s(7037) s(7048) =< s(7033)*s(7036) s(7049) =< s(7039) s(7050) =< s(7040) s(7051) =< s(7041) s(7052) =< s(7031) s(7053) =< s(7044) s(7054) =< s(7053)*s(7035) s(7055) =< s(7045) s(7056) =< s(7055)*s(7034) s(7057) =< s(7047) s(7058) =< s(7046) s(7059) =< s(7048) s(7060) =< s(7059)*s(7016) with precondition: [V1>=1,Out>=1,V1+1>=Out] * Chain [71]: 0 with precondition: [Out=0,V1>=0] * Chain [70]: 0 with precondition: [Out=1,V1>=0] #### Cost of chains of start(V1,V,V5): * Chain [73]: 75*s(7063)+14*s(7064)+3*s(7066)+1*s(7070)+55*s(7073)+38*s(7078)+5*s(7083)+3*s(7085)+1*s(7089)+55*s(7101)+165*s(7102)+330*s(7103)+55*s(7104)+385*s(7105)+55*s(7106)+220*s(7107)+220*s(7109)+220*s(7110)+55*s(7115)+55*s(7119)+55*s(7120)+110*s(7126)+110*s(7127)+110*s(7128)+110*s(7129)+385*s(7130)+55*s(7131)+385*s(7132)+55*s(7133)+110*s(7134)+110*s(7135)+385*s(7136)+55*s(7137)+68*s(7157)+44*s(7159)+132*s(7160)+264*s(7161)+44*s(7162)+308*s(7163)+44*s(7164)+176*s(7165)+176*s(7167)+176*s(7168)+44*s(7173)+44*s(7177)+44*s(7178)+88*s(7184)+88*s(7185)+88*s(7186)+88*s(7187)+308*s(7188)+44*s(7189)+308*s(7190)+44*s(7191)+88*s(7192)+88*s(7193)+308*s(7194)+44*s(7195)+5*s(7331)+2*s(7352)+22*s(7548)+66*s(7549)+132*s(7550)+22*s(7551)+154*s(7552)+22*s(7553)+88*s(7554)+88*s(7556)+88*s(7557)+22*s(7562)+22*s(7566)+22*s(7567)+44*s(7573)+44*s(7574)+44*s(7575)+44*s(7576)+154*s(7577)+22*s(7578)+154*s(7579)+22*s(7580)+44*s(7581)+44*s(7582)+154*s(7583)+22*s(7584)+12*s(7767)+6*s(7877)+6 Such that:s(7085) =< V1-V s(7066) =< V-V5 aux(438) =< 1 aux(439) =< 2 aux(440) =< 3 aux(441) =< V1 aux(442) =< 2*V1+1 aux(443) =< V1/2 aux(444) =< 2/3*V1 aux(445) =< 2/3*V1+1/3 aux(446) =< 2/5*V1 aux(447) =< 3/7*V1 aux(448) =< 3/11*V1 aux(449) =< V aux(450) =< 2*V+1 aux(451) =< V/2 aux(452) =< 2/3*V aux(453) =< 2/3*V+1/3 aux(454) =< 2/5*V aux(455) =< 3/7*V aux(456) =< 3/11*V aux(457) =< V5 aux(458) =< V5+1 aux(459) =< 2*V5+1 aux(460) =< V5/2 aux(461) =< 2/3*V5 aux(462) =< 2/3*V5+1/3 aux(463) =< 2/5*V5 aux(464) =< 3/7*V5 aux(465) =< 3/11*V5 s(7078) =< aux(438) s(7157) =< aux(439) s(7073) =< aux(441) s(7097) =< aux(445) s(7063) =< aux(449) s(7156) =< aux(453) s(7159) =< aux(449) s(7160) =< aux(449) s(7161) =< aux(449) s(7162) =< aux(449) s(7163) =< aux(449) s(7164) =< aux(449) s(7165) =< aux(449) s(7156) =< aux(449) s(7156) =< aux(450) s(7161) =< aux(451) s(7162) =< aux(451) s(7164) =< aux(451) s(7166) =< aux(452) s(7163) =< aux(452) s(7164) =< aux(452) s(7160) =< aux(454) s(7162) =< aux(454) s(7167) =< aux(455) s(7168) =< aux(456) s(7169) =< aux(449)+1 s(7170) =< aux(449)+2 s(7171) =< aux(449) s(7172) =< aux(449)-1 s(7166) =< aux(450)*(1/3)+aux(452) s(7163) =< aux(450)*(1/3)+aux(452) s(7164) =< aux(450)*(1/3)+aux(452) s(7165) =< aux(450)*(1/3)+aux(452) s(7161) =< aux(450)*(1/2)+aux(451) s(7162) =< aux(450)*(1/2)+aux(451) s(7163) =< aux(450)*(1/2)+aux(451) s(7164) =< aux(450)*(1/2)+aux(451) s(7165) =< aux(450)*(1/2)+aux(451) s(7160) =< aux(450)*(3/5)+s(7156)*(1/5)+aux(454) s(7161) =< aux(450)*(3/5)+s(7156)*(1/5)+aux(454) s(7162) =< aux(450)*(3/5)+s(7156)*(1/5)+aux(454) s(7163) =< aux(450)*(3/5)+s(7156)*(1/5)+aux(454) s(7164) =< aux(450)*(3/5)+s(7156)*(1/5)+aux(454) s(7165) =< aux(450)*(3/5)+s(7156)*(1/5)+aux(454) s(7167) =< aux(450)*(2/7)+aux(455) s(7159) =< aux(450)*(2/7)+aux(455) s(7168) =< aux(450)*(4/11)+s(7156)*(1/11)+aux(456) s(7167) =< aux(450)*(4/11)+s(7156)*(1/11)+aux(456) s(7159) =< aux(450)*(4/11)+s(7156)*(1/11)+aux(456) s(7173) =< s(7165)*s(7169) s(7174) =< s(7165)*s(7169) s(7175) =< s(7165)*s(7170) s(7176) =< s(7163)*s(7170) s(7177) =< s(7164)*s(7171) s(7178) =< s(7162)*s(7172) s(7179) =< s(7161)*s(7170) s(7180) =< s(7160)*s(7169) s(7181) =< s(7167)*s(7171) s(7182) =< s(7167)*s(7172) s(7183) =< s(7168)*s(7171) s(7184) =< s(7174) s(7185) =< s(7175) s(7186) =< s(7176) s(7187) =< s(7166) s(7188) =< s(7179) s(7189) =< s(7188)*s(7170) s(7190) =< s(7180) s(7191) =< s(7190)*s(7169) s(7192) =< s(7182) s(7193) =< s(7181) s(7194) =< s(7183) s(7195) =< s(7194)*aux(449) s(7101) =< aux(441) s(7102) =< aux(441) s(7103) =< aux(441) s(7104) =< aux(441) s(7105) =< aux(441) s(7106) =< aux(441) s(7107) =< aux(441) s(7097) =< aux(441) s(7097) =< aux(442) s(7103) =< aux(443) s(7104) =< aux(443) s(7106) =< aux(443) s(7108) =< aux(444) s(7105) =< aux(444) s(7106) =< aux(444) s(7102) =< aux(446) s(7104) =< aux(446) s(7109) =< aux(447) s(7110) =< aux(448) s(7111) =< aux(441)+1 s(7112) =< aux(441)+2 s(7113) =< aux(441) s(7114) =< aux(441)-1 s(7108) =< aux(442)*(1/3)+aux(444) s(7105) =< aux(442)*(1/3)+aux(444) s(7106) =< aux(442)*(1/3)+aux(444) s(7107) =< aux(442)*(1/3)+aux(444) s(7103) =< aux(442)*(1/2)+aux(443) s(7104) =< aux(442)*(1/2)+aux(443) s(7105) =< aux(442)*(1/2)+aux(443) s(7106) =< aux(442)*(1/2)+aux(443) s(7107) =< aux(442)*(1/2)+aux(443) s(7102) =< aux(442)*(3/5)+s(7097)*(1/5)+aux(446) s(7103) =< aux(442)*(3/5)+s(7097)*(1/5)+aux(446) s(7104) =< aux(442)*(3/5)+s(7097)*(1/5)+aux(446) s(7105) =< aux(442)*(3/5)+s(7097)*(1/5)+aux(446) s(7106) =< aux(442)*(3/5)+s(7097)*(1/5)+aux(446) s(7107) =< aux(442)*(3/5)+s(7097)*(1/5)+aux(446) s(7109) =< aux(442)*(2/7)+aux(447) s(7101) =< aux(442)*(2/7)+aux(447) s(7110) =< aux(442)*(4/11)+s(7097)*(1/11)+aux(448) s(7109) =< aux(442)*(4/11)+s(7097)*(1/11)+aux(448) s(7101) =< aux(442)*(4/11)+s(7097)*(1/11)+aux(448) s(7115) =< s(7107)*s(7111) s(7116) =< s(7107)*s(7111) s(7117) =< s(7107)*s(7112) s(7118) =< s(7105)*s(7112) s(7119) =< s(7106)*s(7113) s(7120) =< s(7104)*s(7114) s(7121) =< s(7103)*s(7112) s(7122) =< s(7102)*s(7111) s(7123) =< s(7109)*s(7113) s(7124) =< s(7109)*s(7114) s(7125) =< s(7110)*s(7113) s(7126) =< s(7116) s(7127) =< s(7117) s(7128) =< s(7118) s(7129) =< s(7108) s(7130) =< s(7121) s(7131) =< s(7130)*s(7112) s(7132) =< s(7122) s(7133) =< s(7132)*s(7111) s(7134) =< s(7124) s(7135) =< s(7123) s(7136) =< s(7125) s(7137) =< s(7136)*aux(441) s(7331) =< s(7078)*aux(439) s(7547) =< aux(462) s(7064) =< aux(458) s(7548) =< aux(457) s(7549) =< aux(457) s(7550) =< aux(457) s(7551) =< aux(457) s(7552) =< aux(457) s(7553) =< aux(457) s(7554) =< aux(457) s(7547) =< aux(457) s(7547) =< aux(459) s(7550) =< aux(460) s(7551) =< aux(460) s(7553) =< aux(460) s(7555) =< aux(461) s(7552) =< aux(461) s(7553) =< aux(461) s(7549) =< aux(463) s(7551) =< aux(463) s(7556) =< aux(464) s(7557) =< aux(465) s(7558) =< aux(457)+1 s(7559) =< aux(457)+2 s(7560) =< aux(457) s(7561) =< aux(457)-1 s(7555) =< aux(459)*(1/3)+aux(461) s(7552) =< aux(459)*(1/3)+aux(461) s(7553) =< aux(459)*(1/3)+aux(461) s(7554) =< aux(459)*(1/3)+aux(461) s(7550) =< aux(459)*(1/2)+aux(460) s(7551) =< aux(459)*(1/2)+aux(460) s(7552) =< aux(459)*(1/2)+aux(460) s(7553) =< aux(459)*(1/2)+aux(460) s(7554) =< aux(459)*(1/2)+aux(460) s(7549) =< aux(459)*(3/5)+s(7547)*(1/5)+aux(463) s(7550) =< aux(459)*(3/5)+s(7547)*(1/5)+aux(463) s(7551) =< aux(459)*(3/5)+s(7547)*(1/5)+aux(463) s(7552) =< aux(459)*(3/5)+s(7547)*(1/5)+aux(463) s(7553) =< aux(459)*(3/5)+s(7547)*(1/5)+aux(463) s(7554) =< aux(459)*(3/5)+s(7547)*(1/5)+aux(463) s(7556) =< aux(459)*(2/7)+aux(464) s(7548) =< aux(459)*(2/7)+aux(464) s(7557) =< aux(459)*(4/11)+s(7547)*(1/11)+aux(465) s(7556) =< aux(459)*(4/11)+s(7547)*(1/11)+aux(465) s(7548) =< aux(459)*(4/11)+s(7547)*(1/11)+aux(465) s(7562) =< s(7554)*s(7558) s(7563) =< s(7554)*s(7558) s(7564) =< s(7554)*s(7559) s(7565) =< s(7552)*s(7559) s(7566) =< s(7553)*s(7560) s(7567) =< s(7551)*s(7561) s(7568) =< s(7550)*s(7559) s(7569) =< s(7549)*s(7558) s(7570) =< s(7556)*s(7560) s(7571) =< s(7556)*s(7561) s(7572) =< s(7557)*s(7560) s(7573) =< s(7563) s(7574) =< s(7564) s(7575) =< s(7565) s(7576) =< s(7555) s(7577) =< s(7568) s(7578) =< s(7577)*s(7559) s(7579) =< s(7569) s(7580) =< s(7579)*s(7558) s(7581) =< s(7571) s(7582) =< s(7570) s(7583) =< s(7572) s(7584) =< s(7583)*aux(457) s(7767) =< aux(440) s(7877) =< s(7063)*aux(449) s(7352) =< s(7157)*aux(439) s(7083) =< s(7073)*aux(441) s(7089) =< s(7085)*aux(441) s(7070) =< s(7066)*aux(449) with precondition: [] Closed-form bounds of start(V1,V,V5): ------------------------------------- * Chain [73] with precondition: [] - Upper bound: nat(V1)*3355+234+nat(V1)*1545*nat(V1)+nat(V1)*110*nat(V1)*nat(V1)+nat(V1)*55*nat(V1)*nat(3/11*V1)+nat(V1)*55*nat(nat(V1)+ -1)+nat(V1)*110*nat(3/7*V1)+nat(V1)*385*nat(3/11*V1)+nat(V1-V)*nat(V1)+nat(V)*2715+nat(V)*1238*nat(V)+nat(V)*88*nat(V)*nat(V)+nat(V)*44*nat(V)*nat(3/11*V)+nat(V)*44*nat(nat(V)+ -1)+nat(V)*88*nat(3/7*V)+nat(V)*308*nat(3/11*V)+nat(V-V5)*nat(V)+nat(V5)*1320+nat(V5)*616*nat(V5)+nat(V5)*44*nat(V5)*nat(V5)+nat(V5)*22*nat(V5)*nat(3/11*V5)+nat(V5)*22*nat(nat(V5)+ -1)+nat(V5)*44*nat(3/7*V5)+nat(V5)*154*nat(3/11*V5)+nat(nat(V1)+ -1)*110*nat(3/7*V1)+nat(nat(V)+ -1)*88*nat(3/7*V)+nat(nat(V5)+ -1)*44*nat(3/7*V5)+nat(2/3*V1)*110+nat(2/3*V)*88+nat(2/3*V5)*44+nat(3/7*V1)*220+nat(3/7*V)*176+nat(3/7*V5)*88+nat(3/11*V1)*220+nat(3/11*V)*176+nat(3/11*V5)*88+nat(V5+1)*14+nat(V1-V)*3+nat(V-V5)*3 - Complexity: n^3 ### Maximum cost of start(V1,V,V5): nat(V1)*3355+234+nat(V1)*1545*nat(V1)+nat(V1)*110*nat(V1)*nat(V1)+nat(V1)*55*nat(V1)*nat(3/11*V1)+nat(V1)*55*nat(nat(V1)+ -1)+nat(V1)*110*nat(3/7*V1)+nat(V1)*385*nat(3/11*V1)+nat(V1-V)*nat(V1)+nat(V)*2715+nat(V)*1238*nat(V)+nat(V)*88*nat(V)*nat(V)+nat(V)*44*nat(V)*nat(3/11*V)+nat(V)*44*nat(nat(V)+ -1)+nat(V)*88*nat(3/7*V)+nat(V)*308*nat(3/11*V)+nat(V-V5)*nat(V)+nat(V5)*1320+nat(V5)*616*nat(V5)+nat(V5)*44*nat(V5)*nat(V5)+nat(V5)*22*nat(V5)*nat(3/11*V5)+nat(V5)*22*nat(nat(V5)+ -1)+nat(V5)*44*nat(3/7*V5)+nat(V5)*154*nat(3/11*V5)+nat(nat(V1)+ -1)*110*nat(3/7*V1)+nat(nat(V)+ -1)*88*nat(3/7*V)+nat(nat(V5)+ -1)*44*nat(3/7*V5)+nat(2/3*V1)*110+nat(2/3*V)*88+nat(2/3*V5)*44+nat(3/7*V1)*220+nat(3/7*V)*176+nat(3/7*V5)*88+nat(3/11*V1)*220+nat(3/11*V)*176+nat(3/11*V5)*88+nat(V5+1)*14+nat(V1-V)*3+nat(V-V5)*3 Asymptotic class: n^3 * Total analysis performed in 37286 ms. ---------------------------------------- (14) BOUNDS(1, n^3) ---------------------------------------- (15) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (16) 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: minus(x, y) -> cond(gt(x, y), x, y) cond(false, x, y) -> 0' cond(true, x, y) -> s(minus(x, s(y))) gt(0', v) -> false gt(s(u), 0') -> true gt(s(u), s(v)) -> gt(u, v) The (relative) TRS S consists of the following rules: encArg(false) -> false encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gt(x_1, x_2)) -> gt(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gt(x_1, x_2) -> gt(encArg(x_1), encArg(x_2)) encode_false -> false encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (17) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (18) Obligation: Innermost TRS: Rules: minus(x, y) -> cond(gt(x, y), x, y) cond(false, x, y) -> 0' cond(true, x, y) -> s(minus(x, s(y))) gt(0', v) -> false gt(s(u), 0') -> true gt(s(u), s(v)) -> gt(u, v) encArg(false) -> false encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gt(x_1, x_2)) -> gt(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gt(x_1, x_2) -> gt(encArg(x_1), encArg(x_2)) encode_false -> false encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) Types: minus :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cond :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt gt :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt false :: false:0':true:s:cons_minus:cons_cond:cons_gt 0' :: false:0':true:s:cons_minus:cons_cond:cons_gt true :: false:0':true:s:cons_minus:cons_cond:cons_gt s :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encArg :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cons_minus :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cons_cond :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cons_gt :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_minus :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_cond :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_gt :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_false :: false:0':true:s:cons_minus:cons_cond:cons_gt encode_0 :: false:0':true:s:cons_minus:cons_cond:cons_gt encode_true :: false:0':true:s:cons_minus:cons_cond:cons_gt encode_s :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt hole_false:0':true:s:cons_minus:cons_cond:cons_gt1_4 :: false:0':true:s:cons_minus:cons_cond:cons_gt gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4 :: Nat -> false:0':true:s:cons_minus:cons_cond:cons_gt ---------------------------------------- (19) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: minus, cond, gt, encArg They will be analysed ascendingly in the following order: minus = cond gt < minus minus < encArg cond < encArg gt < encArg ---------------------------------------- (20) Obligation: Innermost TRS: Rules: minus(x, y) -> cond(gt(x, y), x, y) cond(false, x, y) -> 0' cond(true, x, y) -> s(minus(x, s(y))) gt(0', v) -> false gt(s(u), 0') -> true gt(s(u), s(v)) -> gt(u, v) encArg(false) -> false encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gt(x_1, x_2)) -> gt(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gt(x_1, x_2) -> gt(encArg(x_1), encArg(x_2)) encode_false -> false encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) Types: minus :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cond :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt gt :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt false :: false:0':true:s:cons_minus:cons_cond:cons_gt 0' :: false:0':true:s:cons_minus:cons_cond:cons_gt true :: false:0':true:s:cons_minus:cons_cond:cons_gt s :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encArg :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cons_minus :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cons_cond :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cons_gt :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_minus :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_cond :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_gt :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_false :: false:0':true:s:cons_minus:cons_cond:cons_gt encode_0 :: false:0':true:s:cons_minus:cons_cond:cons_gt encode_true :: false:0':true:s:cons_minus:cons_cond:cons_gt encode_s :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt hole_false:0':true:s:cons_minus:cons_cond:cons_gt1_4 :: false:0':true:s:cons_minus:cons_cond:cons_gt gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4 :: Nat -> false:0':true:s:cons_minus:cons_cond:cons_gt Generator Equations: gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(0) <=> false gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(+(x, 1)) <=> s(gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(x)) The following defined symbols remain to be analysed: gt, minus, cond, encArg They will be analysed ascendingly in the following order: minus = cond gt < minus minus < encArg cond < encArg gt < encArg ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: gt(gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(+(1, n4_4)), gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) Induction Base: gt(gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(+(1, 0)), gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(+(1, 0))) Induction Step: gt(gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(+(1, +(n4_4, 1))), gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(+(1, +(n4_4, 1)))) ->_R^Omega(1) gt(gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(+(1, n4_4)), gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(+(1, n4_4))) ->_IH *3_4 We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (22) Complex Obligation (BEST) ---------------------------------------- (23) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: minus(x, y) -> cond(gt(x, y), x, y) cond(false, x, y) -> 0' cond(true, x, y) -> s(minus(x, s(y))) gt(0', v) -> false gt(s(u), 0') -> true gt(s(u), s(v)) -> gt(u, v) encArg(false) -> false encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gt(x_1, x_2)) -> gt(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gt(x_1, x_2) -> gt(encArg(x_1), encArg(x_2)) encode_false -> false encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) Types: minus :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cond :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt gt :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt false :: false:0':true:s:cons_minus:cons_cond:cons_gt 0' :: false:0':true:s:cons_minus:cons_cond:cons_gt true :: false:0':true:s:cons_minus:cons_cond:cons_gt s :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encArg :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cons_minus :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cons_cond :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cons_gt :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_minus :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_cond :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_gt :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_false :: false:0':true:s:cons_minus:cons_cond:cons_gt encode_0 :: false:0':true:s:cons_minus:cons_cond:cons_gt encode_true :: false:0':true:s:cons_minus:cons_cond:cons_gt encode_s :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt hole_false:0':true:s:cons_minus:cons_cond:cons_gt1_4 :: false:0':true:s:cons_minus:cons_cond:cons_gt gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4 :: Nat -> false:0':true:s:cons_minus:cons_cond:cons_gt Generator Equations: gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(0) <=> false gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(+(x, 1)) <=> s(gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(x)) The following defined symbols remain to be analysed: gt, minus, cond, encArg They will be analysed ascendingly in the following order: minus = cond gt < minus minus < encArg cond < encArg gt < encArg ---------------------------------------- (24) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (25) BOUNDS(n^1, INF) ---------------------------------------- (26) Obligation: Innermost TRS: Rules: minus(x, y) -> cond(gt(x, y), x, y) cond(false, x, y) -> 0' cond(true, x, y) -> s(minus(x, s(y))) gt(0', v) -> false gt(s(u), 0') -> true gt(s(u), s(v)) -> gt(u, v) encArg(false) -> false encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gt(x_1, x_2)) -> gt(encArg(x_1), encArg(x_2)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gt(x_1, x_2) -> gt(encArg(x_1), encArg(x_2)) encode_false -> false encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) Types: minus :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cond :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt gt :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt false :: false:0':true:s:cons_minus:cons_cond:cons_gt 0' :: false:0':true:s:cons_minus:cons_cond:cons_gt true :: false:0':true:s:cons_minus:cons_cond:cons_gt s :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encArg :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cons_minus :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cons_cond :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt cons_gt :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_minus :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_cond :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_gt :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt encode_false :: false:0':true:s:cons_minus:cons_cond:cons_gt encode_0 :: false:0':true:s:cons_minus:cons_cond:cons_gt encode_true :: false:0':true:s:cons_minus:cons_cond:cons_gt encode_s :: false:0':true:s:cons_minus:cons_cond:cons_gt -> false:0':true:s:cons_minus:cons_cond:cons_gt hole_false:0':true:s:cons_minus:cons_cond:cons_gt1_4 :: false:0':true:s:cons_minus:cons_cond:cons_gt gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4 :: Nat -> false:0':true:s:cons_minus:cons_cond:cons_gt Lemmas: gt(gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(+(1, n4_4)), gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) Generator Equations: gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(0) <=> false gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(+(x, 1)) <=> s(gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(x)) The following defined symbols remain to be analysed: cond, minus, encArg They will be analysed ascendingly in the following order: minus = cond minus < encArg cond < encArg ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(n2283_4)) -> gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(n2283_4), rt in Omega(0) Induction Base: encArg(gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(0)) ->_R^Omega(0) false Induction Step: encArg(gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(+(n2283_4, 1))) ->_R^Omega(0) s(encArg(gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(n2283_4))) ->_IH s(gen_false:0':true:s:cons_minus:cons_cond:cons_gt2_4(c2284_4)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (28) BOUNDS(1, INF)