/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3).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), 207 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, 37.0 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), 0 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 286 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), 748 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: lt(0, s(x)) -> true lt(x, 0) -> false lt(s(x), s(y)) -> lt(x, y) minus(x, y) -> help(lt(y, x), x, y) help(true, x, y) -> s(minus(x, s(y))) help(false, x, y) -> 0 S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_lt(x_1, x_2)) -> lt(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_help(x_1, x_2, x_3)) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) encode_lt(x_1, x_2) -> lt(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_help(x_1, x_2, x_3) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) ---------------------------------------- (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: lt(0, s(x)) -> true lt(x, 0) -> false lt(s(x), s(y)) -> lt(x, y) minus(x, y) -> help(lt(y, x), x, y) help(true, x, y) -> s(minus(x, s(y))) help(false, x, y) -> 0 The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_lt(x_1, x_2)) -> lt(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_help(x_1, x_2, x_3)) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) encode_lt(x_1, x_2) -> lt(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_help(x_1, x_2, x_3) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) 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: lt(0, s(x)) -> true lt(x, 0) -> false lt(s(x), s(y)) -> lt(x, y) minus(x, y) -> help(lt(y, x), x, y) help(true, x, y) -> s(minus(x, s(y))) help(false, x, y) -> 0 The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_lt(x_1, x_2)) -> lt(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_help(x_1, x_2, x_3)) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) encode_lt(x_1, x_2) -> lt(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_help(x_1, x_2, x_3) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) 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: lt(0, s(x)) -> true [1] lt(x, 0) -> false [1] lt(s(x), s(y)) -> lt(x, y) [1] minus(x, y) -> help(lt(y, x), x, y) [1] help(true, x, y) -> s(minus(x, s(y))) [1] help(false, x, y) -> 0 [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(cons_lt(x_1, x_2)) -> lt(encArg(x_1), encArg(x_2)) [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_help(x_1, x_2, x_3)) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_lt(x_1, x_2) -> lt(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_true -> true [0] encode_false -> false [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_help(x_1, x_2, x_3) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) [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: lt(0, s(x)) -> true [1] lt(x, 0) -> false [1] lt(s(x), s(y)) -> lt(x, y) [1] minus(x, y) -> help(lt(y, x), x, y) [1] help(true, x, y) -> s(minus(x, s(y))) [1] help(false, x, y) -> 0 [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(cons_lt(x_1, x_2)) -> lt(encArg(x_1), encArg(x_2)) [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_help(x_1, x_2, x_3)) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_lt(x_1, x_2) -> lt(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_true -> true [0] encode_false -> false [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_help(x_1, x_2, x_3) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) [0] The TRS has the following type information: lt :: 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help 0 :: 0:s:true:false:cons_lt:cons_minus:cons_help s :: 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help true :: 0:s:true:false:cons_lt:cons_minus:cons_help false :: 0:s:true:false:cons_lt:cons_minus:cons_help minus :: 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help help :: 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help encArg :: 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help cons_lt :: 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help cons_minus :: 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help cons_help :: 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help encode_lt :: 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help encode_0 :: 0:s:true:false:cons_lt:cons_minus:cons_help encode_s :: 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help encode_true :: 0:s:true:false:cons_lt:cons_minus:cons_help encode_false :: 0:s:true:false:cons_lt:cons_minus:cons_help encode_minus :: 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help encode_help :: 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help -> 0:s:true:false:cons_lt:cons_minus:cons_help 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_lt(v0, v1) -> null_encode_lt [0] encode_0 -> null_encode_0 [0] encode_s(v0) -> null_encode_s [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_minus(v0, v1) -> null_encode_minus [0] encode_help(v0, v1, v2) -> null_encode_help [0] lt(v0, v1) -> null_lt [0] help(v0, v1, v2) -> null_help [0] And the following fresh constants: null_encArg, null_encode_lt, null_encode_0, null_encode_s, null_encode_true, null_encode_false, null_encode_minus, null_encode_help, null_lt, null_help ---------------------------------------- (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: lt(0, s(x)) -> true [1] lt(x, 0) -> false [1] lt(s(x), s(y)) -> lt(x, y) [1] minus(x, y) -> help(lt(y, x), x, y) [1] help(true, x, y) -> s(minus(x, s(y))) [1] help(false, x, y) -> 0 [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(cons_lt(x_1, x_2)) -> lt(encArg(x_1), encArg(x_2)) [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_help(x_1, x_2, x_3)) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_lt(x_1, x_2) -> lt(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_true -> true [0] encode_false -> false [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_help(x_1, x_2, x_3) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(v0) -> null_encArg [0] encode_lt(v0, v1) -> null_encode_lt [0] encode_0 -> null_encode_0 [0] encode_s(v0) -> null_encode_s [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_minus(v0, v1) -> null_encode_minus [0] encode_help(v0, v1, v2) -> null_encode_help [0] lt(v0, v1) -> null_lt [0] help(v0, v1, v2) -> null_help [0] The TRS has the following type information: lt :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help 0 :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help s :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help true :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help false :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help minus :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help help :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help encArg :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help cons_lt :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help cons_minus :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help cons_help :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help encode_lt :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help encode_0 :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help encode_s :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help encode_true :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help encode_false :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help encode_minus :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help encode_help :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help -> 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help null_encArg :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help null_encode_lt :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help null_encode_0 :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help null_encode_s :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help null_encode_true :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help null_encode_false :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help null_encode_minus :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help null_encode_help :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help null_lt :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help null_help :: 0:s:true:false:cons_lt:cons_minus:cons_help:null_encArg:null_encode_lt:null_encode_0:null_encode_s:null_encode_true:null_encode_false:null_encode_minus:null_encode_help:null_lt:null_help 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: 0 => 0 true => 2 false => 1 null_encArg => 0 null_encode_lt => 0 null_encode_0 => 0 null_encode_s => 0 null_encode_true => 0 null_encode_false => 0 null_encode_minus => 0 null_encode_help => 0 null_lt => 0 null_help => 0 ---------------------------------------- (12) Obligation: Complexity RNTS consisting of the following rules: encArg(z) -{ 0 }-> minus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> lt(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> help(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_false -{ 0 }-> 1 :|: encode_false -{ 0 }-> 0 :|: encode_help(z, z', z'') -{ 0 }-> help(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_help(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_lt(z, z') -{ 0 }-> lt(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_lt(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 :|: help(z, z', z'') -{ 1 }-> 0 :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0 help(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 help(z, z', z'') -{ 1 }-> 1 + minus(x, 1 + y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0 lt(z, z') -{ 1 }-> lt(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x lt(z, z') -{ 1 }-> 2 :|: z' = 1 + x, x >= 0, z = 0 lt(z, z') -{ 1 }-> 1 :|: x >= 0, z = x, z' = 0 lt(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 minus(z, z') -{ 1 }-> help(lt(y, x), 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, V10),0,[lt(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V10),0,[minus(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V10),0,[help(V1, V, V10, Out)],[V1 >= 0,V >= 0,V10 >= 0]). eq(start(V1, V, V10),0,[encArg(V1, Out)],[V1 >= 0]). eq(start(V1, V, V10),0,[fun(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V10),0,[fun1(Out)],[]). eq(start(V1, V, V10),0,[fun2(V1, Out)],[V1 >= 0]). eq(start(V1, V, V10),0,[fun3(Out)],[]). eq(start(V1, V, V10),0,[fun4(Out)],[]). eq(start(V1, V, V10),0,[fun5(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V10),0,[fun6(V1, V, V10, Out)],[V1 >= 0,V >= 0,V10 >= 0]). eq(lt(V1, V, Out),1,[],[Out = 2,V = 1 + V2,V2 >= 0,V1 = 0]). eq(lt(V1, V, Out),1,[],[Out = 1,V3 >= 0,V1 = V3,V = 0]). eq(lt(V1, V, Out),1,[lt(V4, V5, Ret)],[Out = Ret,V = 1 + V5,V4 >= 0,V5 >= 0,V1 = 1 + V4]). eq(minus(V1, V, Out),1,[lt(V7, V6, Ret0),help(Ret0, V6, V7, Ret1)],[Out = Ret1,V6 >= 0,V7 >= 0,V1 = V6,V = V7]). eq(help(V1, V, V10, Out),1,[minus(V8, 1 + V9, Ret11)],[Out = 1 + Ret11,V1 = 2,V = V8,V10 = V9,V8 >= 0,V9 >= 0]). eq(help(V1, V, V10, Out),1,[],[Out = 0,V = V12,V10 = V11,V1 = 1,V12 >= 0,V11 >= 0]). eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]). eq(encArg(V1, Out),0,[encArg(V13, Ret12)],[Out = 1 + Ret12,V1 = 1 + V13,V13 >= 0]). eq(encArg(V1, Out),0,[],[Out = 2,V1 = 2]). eq(encArg(V1, Out),0,[],[Out = 1,V1 = 1]). eq(encArg(V1, Out),0,[encArg(V14, Ret01),encArg(V15, Ret13),lt(Ret01, Ret13, Ret2)],[Out = Ret2,V14 >= 0,V1 = 1 + V14 + V15,V15 >= 0]). eq(encArg(V1, Out),0,[encArg(V16, Ret02),encArg(V17, Ret14),minus(Ret02, Ret14, Ret3)],[Out = Ret3,V16 >= 0,V1 = 1 + V16 + V17,V17 >= 0]). eq(encArg(V1, Out),0,[encArg(V20, Ret03),encArg(V19, Ret15),encArg(V18, Ret21),help(Ret03, Ret15, Ret21, Ret4)],[Out = Ret4,V20 >= 0,V1 = 1 + V18 + V19 + V20,V18 >= 0,V19 >= 0]). eq(fun(V1, V, Out),0,[encArg(V22, Ret04),encArg(V21, Ret16),lt(Ret04, Ret16, Ret5)],[Out = Ret5,V22 >= 0,V21 >= 0,V1 = V22,V = V21]). eq(fun1(Out),0,[],[Out = 0]). eq(fun2(V1, Out),0,[encArg(V23, Ret17)],[Out = 1 + Ret17,V23 >= 0,V1 = V23]). eq(fun3(Out),0,[],[Out = 2]). eq(fun4(Out),0,[],[Out = 1]). eq(fun5(V1, V, Out),0,[encArg(V24, Ret05),encArg(V25, Ret18),minus(Ret05, Ret18, Ret6)],[Out = Ret6,V24 >= 0,V25 >= 0,V1 = V24,V = V25]). eq(fun6(V1, V, V10, Out),0,[encArg(V28, Ret06),encArg(V27, Ret19),encArg(V26, Ret22),help(Ret06, Ret19, Ret22, Ret7)],[Out = Ret7,V28 >= 0,V26 >= 0,V27 >= 0,V1 = V28,V = V27,V10 = V26]). 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(fun2(V1, Out),0,[],[Out = 0,V32 >= 0,V1 = V32]). eq(fun3(Out),0,[],[Out = 0]). eq(fun4(Out),0,[],[Out = 0]). eq(fun5(V1, V, Out),0,[],[Out = 0,V33 >= 0,V34 >= 0,V1 = V33,V = V34]). eq(fun6(V1, V, V10, Out),0,[],[Out = 0,V35 >= 0,V10 = V37,V36 >= 0,V1 = V35,V = V36,V37 >= 0]). eq(lt(V1, V, Out),0,[],[Out = 0,V38 >= 0,V39 >= 0,V1 = V38,V = V39]). eq(help(V1, V, V10, Out),0,[],[Out = 0,V41 >= 0,V10 = V42,V40 >= 0,V1 = V41,V = V40,V42 >= 0]). input_output_vars(lt(V1,V,Out),[V1,V],[Out]). input_output_vars(minus(V1,V,Out),[V1,V],[Out]). input_output_vars(help(V1,V,V10,Out),[V1,V,V10],[Out]). input_output_vars(encArg(V1,Out),[V1],[Out]). input_output_vars(fun(V1,V,Out),[V1,V],[Out]). input_output_vars(fun1(Out),[],[Out]). input_output_vars(fun2(V1,Out),[V1],[Out]). input_output_vars(fun3(Out),[],[Out]). input_output_vars(fun4(Out),[],[Out]). input_output_vars(fun5(V1,V,Out),[V1,V],[Out]). input_output_vars(fun6(V1,V,V10,Out),[V1,V,V10],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [lt/3] 1. recursive : [help/4,minus/3] 2. recursive [non_tail,multiple] : [encArg/2] 3. non_recursive : [fun/3] 4. non_recursive : [fun1/1] 5. non_recursive : [fun2/2] 6. non_recursive : [fun3/1] 7. non_recursive : [fun4/1] 8. non_recursive : [fun5/3] 9. non_recursive : [fun6/4] 10. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into lt/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 completely evaluated into other SCCs 5. SCC is partially evaluated into fun2/2 6. SCC is partially evaluated into fun3/1 7. SCC is partially evaluated into fun4/1 8. SCC is partially evaluated into fun5/3 9. SCC is partially evaluated into fun6/4 10. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations lt/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 lt/3 * CEs [46] --> Loop 23 * CEs [43] --> Loop 24 * CEs [44] --> Loop 25 * CEs [45] --> Loop 26 ### Ranking functions of CR lt(V1,V,Out) * RF of phase [23]: [V,V1] #### Partial ranking functions of CR lt(V1,V,Out) * Partial RF of phase [23]: - RF of loop [23:1]: V V1 ### Specialization of cost equations minus/3 * CE 15 is refined into CE [47,48] * CE 13 is refined into CE [49,50,51,52,53] * CE 14 is refined into CE [54,55] ### Cost equations --> "Loop" of minus/3 * CEs [49] --> Loop 27 * CEs [50,51,52,53,54,55] --> Loop 28 * CEs [48] --> Loop 29 * CEs [47] --> Loop 30 ### Ranking functions of CR minus(V1,V,Out) * RF of phase [29]: [V1-V] #### Partial ranking functions of CR minus(V1,V,Out) * Partial RF of phase [29]: - RF of loop [29:1]: V1-V ### Specialization of cost equations encArg/2 * CE 23 is refined into CE [56] * CE 25 is refined into CE [57] * CE 26 is refined into CE [58] * CE 27 is refined into CE [59,60,61,62,63] * CE 28 is refined into CE [64,65,66,67] * CE 24 is refined into CE [68] * CE 22 is refined into CE [69,70] * CE 20 is refined into CE [71] * CE 21 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 [67] --> Loop 35 * CEs [66] --> Loop 36 * CEs [63] --> Loop 37 * CEs [59] --> Loop 38 * CEs [62] --> Loop 39 * CEs [60,65] --> Loop 40 * CEs [61,64] --> Loop 41 * CEs [56] --> Loop 42 * CEs [57] --> Loop 43 * CEs [58] --> Loop 44 ### Ranking functions of CR encArg(V1,Out) * RF of phase [31,32,33,34,35,36,37,38,39,40,41]: [V1] #### Partial ranking functions of CR encArg(V1,Out) * Partial RF of phase [31,32,33,34,35,36,37,38,39,40,41]: - 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]: V1 ### Specialization of cost equations fun/3 * CE 29 is refined into CE [73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98] * CE 30 is refined into CE [99] ### Cost equations --> "Loop" of fun/3 * CEs [78,81,95] --> Loop 45 * CEs [80] --> Loop 46 * CEs [79,96] --> Loop 47 * CEs [73,77,87,92] --> Loop 48 * CEs [74,76,82,84,86,89,90,93,97] --> Loop 49 * CEs [75,83,85,88,91,94,98,99] --> Loop 50 ### Ranking functions of CR fun(V1,V,Out) #### Partial ranking functions of CR fun(V1,V,Out) ### Specialization of cost equations fun2/2 * CE 31 is refined into CE [100,101,102] * CE 32 is refined into CE [103] ### Cost equations --> "Loop" of fun2/2 * CEs [102] --> Loop 51 * CEs [103] --> Loop 52 * CEs [100,101] --> Loop 53 ### Ranking functions of CR fun2(V1,Out) #### Partial ranking functions of CR fun2(V1,Out) ### Specialization of cost equations fun3/1 * CE 33 is refined into CE [104] * CE 34 is refined into CE [105] ### Cost equations --> "Loop" of fun3/1 * CEs [104] --> Loop 54 * CEs [105] --> Loop 55 ### Ranking functions of CR fun3(Out) #### Partial ranking functions of CR fun3(Out) ### Specialization of cost equations fun4/1 * CE 35 is refined into CE [106] * CE 36 is refined into CE [107] ### Cost equations --> "Loop" of fun4/1 * CEs [106] --> Loop 56 * CEs [107] --> Loop 57 ### Ranking functions of CR fun4(Out) #### Partial ranking functions of CR fun4(Out) ### Specialization of cost equations fun5/3 * CE 37 is refined into CE [108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127] * CE 38 is refined into CE [128] ### Cost equations --> "Loop" of fun5/3 * CEs [111,113] --> Loop 58 * CEs [112,126] --> Loop 59 * CEs [110,116,119,124] --> Loop 60 * CEs [109,115,118,120,123] --> Loop 61 * CEs [108,114,117,121,122,125,127,128] --> Loop 62 ### Ranking functions of CR fun5(V1,V,Out) #### Partial ranking functions of CR fun5(V1,V,Out) ### Specialization of cost equations fun6/4 * CE 39 is refined into CE [129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155] * CE 40 is refined into CE [156,157,158,159,160,161,162,163,164] * CE 41 is refined into CE [165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192] * CE 42 is refined into CE [193] ### Cost equations --> "Loop" of fun6/4 * CEs [172,175] --> Loop 63 * CEs [171,173,174] --> Loop 64 * CEs [132,133,134,150,151,152,159,160,161] --> Loop 65 * CEs [168,182] --> Loop 66 * CEs [167,177,181,191] --> Loop 67 * CEs [130,136,139,145,148,154,157,163] --> Loop 68 * CEs [166,170,180,184,186,189] --> Loop 69 * CEs [165,169,176,178,179,183,185,187,188,190,192] --> Loop 70 * CEs [129,131,135,137,138,140,141,142,143,144,146,147,149,153,155,156,158,162,164,193] --> Loop 71 ### Ranking functions of CR fun6(V1,V,V10,Out) #### Partial ranking functions of CR fun6(V1,V,V10,Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [194] * CE 2 is refined into CE [195] * CE 3 is refined into CE [196,197] * CE 4 is refined into CE [198,199,200,201,202] * CE 5 is refined into CE [203,204,205,206] * CE 6 is refined into CE [207,208,209] * CE 7 is refined into CE [210,211,212] * CE 8 is refined into CE [213,214,215] * CE 9 is refined into CE [216,217] * CE 10 is refined into CE [218,219] * CE 11 is refined into CE [220,221,222,223] * CE 12 is refined into CE [224,225,226,227,228,229] ### 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 72 ### Ranking functions of CR start(V1,V,V10) #### Partial ranking functions of CR start(V1,V,V10) Computing Bounds ===================================== #### Cost of chains of lt(V1,V,Out): * Chain [[23],26]: 1*it(23)+1 Such that:it(23) =< V1 with precondition: [Out=2,V1>=1,V>=V1+1] * Chain [[23],25]: 1*it(23)+1 Such that:it(23) =< V with precondition: [Out=1,V>=1,V1>=V] * 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=2,V>=1] * Chain [25]: 1 with precondition: [V=0,Out=1,V1>=0] * Chain [24]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of minus(V1,V,Out): * Chain [[29],28]: 3*it(29)+3*s(2)+1*s(4)+1*s(8)+3 Such that:s(4) =< V+Out it(29) =< Out aux(3) =< V1 s(2) =< aux(3) s(8) =< it(29)*aux(3) with precondition: [V>=1,Out>=1,V1>=Out+V] * Chain [30,[29],28]: 4*it(29)+3*s(2)+1*s(8)+6 Such that:aux(3) =< V1 aux(4) =< Out it(29) =< aux(4) s(2) =< aux(3) s(8) =< it(29)*aux(3) with precondition: [V=0,Out>=2,V1>=Out] * Chain [30,28]: 3*s(2)+1*s(4)+6 Such that:s(4) =< 1 aux(1) =< V1 s(2) =< aux(1) with precondition: [V=0,Out=1,V1>=1] * Chain [28]: 3*s(2)+1*s(4)+3 Such that:s(4) =< V aux(1) =< V1 s(2) =< aux(1) with precondition: [Out=0,V1>=0,V>=0] * Chain [27]: 2 with precondition: [V=0,Out=0,V1>=1] #### Cost of chains of encArg(V1,Out): * Chain [44]: 0 with precondition: [V1=1,Out=1] * Chain [43]: 0 with precondition: [V1=2,Out=2] * Chain [42]: 0 with precondition: [Out=0,V1>=0] * Chain [multiple([31,32,33,34,35,36,37,38,39,40,41],[[44],[43],[42]])]: 4*it(31)+4*it(32)+1*it(33)+3*it(35)+6*it(36)+1*it(37)+1*it(38)+1*it(39)+9*it(40)+7*s(60)+1*s(61)+1*s(63)+3*s(64)+7*s(66)+1*s(67)+7*s(69)+1*s(70)+1*s(72)+1*s(73)+1*s(74)+3*s(75)+1*s(77)+1*s(78)+3*s(79)+0 Such that:it([44]) =< 2/3*V1+1/3 aux(27) =< V1 aux(28) =< 2*V1+1 aux(29) =< V1/2 aux(30) =< 2/3*V1 aux(31) =< 2/5*V1 aux(32) =< 3/7*V1 aux(33) =< 3/11*V1 it(33) =< aux(27) it(35) =< aux(27) it(36) =< aux(27) it(37) =< aux(27) it(38) =< aux(27) it(39) =< aux(27) it(40) =< aux(27) it([44]) =< aux(27) it([42]) =< aux(28) it([44]) =< aux(28) it(36) =< aux(29) it(37) =< aux(29) it(39) =< aux(29) it(38) =< aux(30) it(39) =< aux(30) it(35) =< aux(31) it(37) =< aux(31) it(32) =< aux(32) it(31) =< aux(33) aux(14) =< aux(27)+1 aux(16) =< aux(27)+2 aux(9) =< aux(27) aux(11) =< aux(27)-1 s(74) =< aux(27) it(36) =< it([42])*(1/2)+aux(29) it(37) =< it([42])*(1/2)+aux(29) it(38) =< it([42])*(1/2)+aux(29) it(39) =< it([42])*(1/2)+aux(29) it(40) =< it([42])*(1/2)+aux(29) it(38) =< it([42])*(1/3)+aux(30) it(39) =< it([42])*(1/3)+aux(30) it(40) =< it([42])*(1/3)+aux(30) it(35) =< it([42])*(3/5)+it([44])*(1/5)+aux(31) it(36) =< it([42])*(3/5)+it([44])*(1/5)+aux(31) it(37) =< it([42])*(3/5)+it([44])*(1/5)+aux(31) it(38) =< it([42])*(3/5)+it([44])*(1/5)+aux(31) it(39) =< it([42])*(3/5)+it([44])*(1/5)+aux(31) it(40) =< it([42])*(3/5)+it([44])*(1/5)+aux(31) it(32) =< it([42])*(2/7)+aux(32) it(33) =< it([42])*(2/7)+aux(32) it(31) =< it([42])*(4/11)+it([44])*(1/11)+aux(33) it(32) =< it([42])*(4/11)+it([44])*(1/11)+aux(33) it(33) =< it([42])*(4/11)+it([44])*(1/11)+aux(33) s(77) =< it(40)*aux(14) s(80) =< it(40)*aux(14) s(78) =< it(40)*aux(16) s(76) =< it(40)*aux(16) s(73) =< it(39)*aux(9) s(72) =< it(37)*aux(9) s(71) =< it(36)*aux(16) s(68) =< it(35)*aux(14) s(63) =< it(32)*aux(9) s(65) =< it(32)*aux(11) s(62) =< it(31)*aux(9) s(79) =< s(80) s(75) =< s(76) s(69) =< s(71) s(70) =< s(69)*aux(16) s(66) =< s(68) s(67) =< s(66)*aux(14) s(64) =< s(65) s(60) =< s(62) s(61) =< s(60)*aux(27) with precondition: [V1>=1,Out>=0,V1>=Out] #### Cost of chains of fun(V1,V,Out): * Chain [50]: 2*s(132)+6*s(133)+12*s(134)+2*s(135)+2*s(136)+2*s(137)+18*s(138)+8*s(139)+8*s(140)+2*s(145)+2*s(146)+2*s(148)+2*s(150)+2*s(151)+2*s(154)+6*s(157)+6*s(158)+14*s(159)+2*s(160)+14*s(161)+2*s(162)+6*s(163)+14*s(164)+2*s(165)+3*s(174)+9*s(175)+18*s(176)+3*s(177)+3*s(178)+3*s(179)+27*s(180)+12*s(181)+12*s(182)+6*s(187)+3*s(188)+3*s(190)+3*s(192)+3*s(193)+3*s(196)+9*s(199)+9*s(200)+21*s(201)+3*s(202)+21*s(203)+3*s(204)+9*s(205)+21*s(206)+3*s(207)+1*s(295)+0 Such that:s(295) =< 2 aux(37) =< V1 aux(38) =< 2*V1+1 aux(39) =< V1/2 aux(40) =< 2/3*V1 aux(41) =< 2/3*V1+1/3 aux(42) =< 2/5*V1 aux(43) =< 3/7*V1 aux(44) =< 3/11*V1 aux(45) =< V aux(46) =< 2*V+1 aux(47) =< V/2 aux(48) =< 2/3*V aux(49) =< 2/3*V+1/3 aux(50) =< 2/5*V aux(51) =< 3/7*V aux(52) =< 3/11*V s(128) =< aux(41) s(170) =< aux(49) s(187) =< aux(45) s(174) =< aux(45) s(175) =< aux(45) s(176) =< aux(45) s(177) =< aux(45) s(178) =< aux(45) s(179) =< aux(45) s(180) =< aux(45) s(170) =< aux(45) s(170) =< aux(46) s(176) =< aux(47) s(177) =< aux(47) s(179) =< aux(47) s(178) =< aux(48) s(179) =< aux(48) s(175) =< aux(50) s(177) =< aux(50) s(181) =< aux(51) s(182) =< aux(52) s(183) =< aux(45)+1 s(184) =< aux(45)+2 s(185) =< aux(45) s(186) =< aux(45)-1 s(176) =< aux(46)*(1/2)+aux(47) s(177) =< aux(46)*(1/2)+aux(47) s(178) =< aux(46)*(1/2)+aux(47) s(179) =< aux(46)*(1/2)+aux(47) s(180) =< aux(46)*(1/2)+aux(47) s(178) =< aux(46)*(1/3)+aux(48) s(179) =< aux(46)*(1/3)+aux(48) s(180) =< aux(46)*(1/3)+aux(48) s(175) =< aux(46)*(3/5)+s(170)*(1/5)+aux(50) s(176) =< aux(46)*(3/5)+s(170)*(1/5)+aux(50) s(177) =< aux(46)*(3/5)+s(170)*(1/5)+aux(50) s(178) =< aux(46)*(3/5)+s(170)*(1/5)+aux(50) s(179) =< aux(46)*(3/5)+s(170)*(1/5)+aux(50) s(180) =< aux(46)*(3/5)+s(170)*(1/5)+aux(50) s(181) =< aux(46)*(2/7)+aux(51) s(174) =< aux(46)*(2/7)+aux(51) s(182) =< aux(46)*(4/11)+s(170)*(1/11)+aux(52) s(181) =< aux(46)*(4/11)+s(170)*(1/11)+aux(52) s(174) =< aux(46)*(4/11)+s(170)*(1/11)+aux(52) s(188) =< s(180)*s(183) s(189) =< s(180)*s(183) s(190) =< s(180)*s(184) s(191) =< s(180)*s(184) s(192) =< s(179)*s(185) s(193) =< s(177)*s(185) s(194) =< s(176)*s(184) s(195) =< s(175)*s(183) s(196) =< s(181)*s(185) s(197) =< s(181)*s(186) s(198) =< s(182)*s(185) s(199) =< s(189) s(200) =< s(191) s(201) =< s(194) s(202) =< s(201)*s(184) s(203) =< s(195) s(204) =< s(203)*s(183) s(205) =< s(197) s(206) =< s(198) s(207) =< s(206)*aux(45) s(132) =< aux(37) s(133) =< aux(37) s(134) =< aux(37) s(135) =< aux(37) s(136) =< aux(37) s(137) =< aux(37) s(138) =< aux(37) s(128) =< aux(37) s(128) =< aux(38) s(134) =< aux(39) s(135) =< aux(39) s(137) =< aux(39) s(136) =< aux(40) s(137) =< aux(40) s(133) =< aux(42) s(135) =< aux(42) s(139) =< aux(43) s(140) =< aux(44) s(141) =< aux(37)+1 s(142) =< aux(37)+2 s(143) =< aux(37) s(144) =< aux(37)-1 s(145) =< aux(37) s(134) =< aux(38)*(1/2)+aux(39) s(135) =< aux(38)*(1/2)+aux(39) s(136) =< aux(38)*(1/2)+aux(39) s(137) =< aux(38)*(1/2)+aux(39) s(138) =< aux(38)*(1/2)+aux(39) s(136) =< aux(38)*(1/3)+aux(40) s(137) =< aux(38)*(1/3)+aux(40) s(138) =< aux(38)*(1/3)+aux(40) s(133) =< aux(38)*(3/5)+s(128)*(1/5)+aux(42) s(134) =< aux(38)*(3/5)+s(128)*(1/5)+aux(42) s(135) =< aux(38)*(3/5)+s(128)*(1/5)+aux(42) s(136) =< aux(38)*(3/5)+s(128)*(1/5)+aux(42) s(137) =< aux(38)*(3/5)+s(128)*(1/5)+aux(42) s(138) =< aux(38)*(3/5)+s(128)*(1/5)+aux(42) s(139) =< aux(38)*(2/7)+aux(43) s(132) =< aux(38)*(2/7)+aux(43) s(140) =< aux(38)*(4/11)+s(128)*(1/11)+aux(44) s(139) =< aux(38)*(4/11)+s(128)*(1/11)+aux(44) s(132) =< aux(38)*(4/11)+s(128)*(1/11)+aux(44) s(146) =< s(138)*s(141) s(147) =< s(138)*s(141) s(148) =< s(138)*s(142) s(149) =< s(138)*s(142) s(150) =< s(137)*s(143) s(151) =< s(135)*s(143) s(152) =< s(134)*s(142) s(153) =< s(133)*s(141) s(154) =< s(139)*s(143) s(155) =< s(139)*s(144) s(156) =< s(140)*s(143) s(157) =< s(147) s(158) =< s(149) s(159) =< s(152) s(160) =< s(159)*s(142) s(161) =< s(153) s(162) =< s(161)*s(141) s(163) =< s(155) s(164) =< s(156) s(165) =< s(164)*aux(37) with precondition: [Out=0,V1>=0,V>=0] * Chain [49]: 3*s(349)+9*s(350)+18*s(351)+3*s(352)+3*s(353)+3*s(354)+27*s(355)+12*s(356)+12*s(357)+3*s(362)+3*s(363)+3*s(365)+3*s(367)+3*s(368)+3*s(371)+9*s(374)+9*s(375)+21*s(376)+3*s(377)+21*s(378)+3*s(379)+9*s(380)+21*s(381)+3*s(382)+5*s(391)+15*s(392)+30*s(393)+5*s(394)+5*s(395)+5*s(396)+45*s(397)+20*s(398)+20*s(399)+7*s(404)+5*s(405)+5*s(407)+5*s(409)+5*s(410)+5*s(413)+15*s(416)+15*s(417)+35*s(418)+5*s(419)+35*s(420)+5*s(421)+15*s(422)+35*s(423)+5*s(424)+1*s(637)+1 Such that:s(637) =< 2 aux(55) =< V1 aux(56) =< 2*V1+1 aux(57) =< V1/2 aux(58) =< 2/3*V1 aux(59) =< 2/3*V1+1/3 aux(60) =< 2/5*V1 aux(61) =< 3/7*V1 aux(62) =< 3/11*V1 aux(63) =< V aux(64) =< 2*V+1 aux(65) =< V/2 aux(66) =< 2/3*V aux(67) =< 2/3*V+1/3 aux(68) =< 2/5*V aux(69) =< 3/7*V aux(70) =< 3/11*V s(345) =< aux(59) s(387) =< aux(67) s(391) =< aux(63) s(392) =< aux(63) s(393) =< aux(63) s(394) =< aux(63) s(395) =< aux(63) s(396) =< aux(63) s(397) =< aux(63) s(387) =< aux(63) s(387) =< aux(64) s(393) =< aux(65) s(394) =< aux(65) s(396) =< aux(65) s(395) =< aux(66) s(396) =< aux(66) s(392) =< aux(68) s(394) =< aux(68) s(398) =< aux(69) s(399) =< aux(70) s(400) =< aux(63)+1 s(401) =< aux(63)+2 s(402) =< aux(63) s(403) =< aux(63)-1 s(404) =< aux(63) s(393) =< aux(64)*(1/2)+aux(65) s(394) =< aux(64)*(1/2)+aux(65) s(395) =< aux(64)*(1/2)+aux(65) s(396) =< aux(64)*(1/2)+aux(65) s(397) =< aux(64)*(1/2)+aux(65) s(395) =< aux(64)*(1/3)+aux(66) s(396) =< aux(64)*(1/3)+aux(66) s(397) =< aux(64)*(1/3)+aux(66) s(392) =< aux(64)*(3/5)+s(387)*(1/5)+aux(68) s(393) =< aux(64)*(3/5)+s(387)*(1/5)+aux(68) s(394) =< aux(64)*(3/5)+s(387)*(1/5)+aux(68) s(395) =< aux(64)*(3/5)+s(387)*(1/5)+aux(68) s(396) =< aux(64)*(3/5)+s(387)*(1/5)+aux(68) s(397) =< aux(64)*(3/5)+s(387)*(1/5)+aux(68) s(398) =< aux(64)*(2/7)+aux(69) s(391) =< aux(64)*(2/7)+aux(69) s(399) =< aux(64)*(4/11)+s(387)*(1/11)+aux(70) s(398) =< aux(64)*(4/11)+s(387)*(1/11)+aux(70) s(391) =< aux(64)*(4/11)+s(387)*(1/11)+aux(70) s(405) =< s(397)*s(400) s(406) =< s(397)*s(400) s(407) =< s(397)*s(401) s(408) =< s(397)*s(401) s(409) =< s(396)*s(402) s(410) =< s(394)*s(402) s(411) =< s(393)*s(401) s(412) =< s(392)*s(400) s(413) =< s(398)*s(402) s(414) =< s(398)*s(403) s(415) =< s(399)*s(402) s(416) =< s(406) s(417) =< s(408) s(418) =< s(411) s(419) =< s(418)*s(401) s(420) =< s(412) s(421) =< s(420)*s(400) s(422) =< s(414) s(423) =< s(415) s(424) =< s(423)*aux(63) s(349) =< aux(55) s(350) =< aux(55) s(351) =< aux(55) s(352) =< aux(55) s(353) =< aux(55) s(354) =< aux(55) s(355) =< aux(55) s(345) =< aux(55) s(345) =< aux(56) s(351) =< aux(57) s(352) =< aux(57) s(354) =< aux(57) s(353) =< aux(58) s(354) =< aux(58) s(350) =< aux(60) s(352) =< aux(60) s(356) =< aux(61) s(357) =< aux(62) s(358) =< aux(55)+1 s(359) =< aux(55)+2 s(360) =< aux(55) s(361) =< aux(55)-1 s(362) =< aux(55) s(351) =< aux(56)*(1/2)+aux(57) s(352) =< aux(56)*(1/2)+aux(57) s(353) =< aux(56)*(1/2)+aux(57) s(354) =< aux(56)*(1/2)+aux(57) s(355) =< aux(56)*(1/2)+aux(57) s(353) =< aux(56)*(1/3)+aux(58) s(354) =< aux(56)*(1/3)+aux(58) s(355) =< aux(56)*(1/3)+aux(58) s(350) =< aux(56)*(3/5)+s(345)*(1/5)+aux(60) s(351) =< aux(56)*(3/5)+s(345)*(1/5)+aux(60) s(352) =< aux(56)*(3/5)+s(345)*(1/5)+aux(60) s(353) =< aux(56)*(3/5)+s(345)*(1/5)+aux(60) s(354) =< aux(56)*(3/5)+s(345)*(1/5)+aux(60) s(355) =< aux(56)*(3/5)+s(345)*(1/5)+aux(60) s(356) =< aux(56)*(2/7)+aux(61) s(349) =< aux(56)*(2/7)+aux(61) s(357) =< aux(56)*(4/11)+s(345)*(1/11)+aux(62) s(356) =< aux(56)*(4/11)+s(345)*(1/11)+aux(62) s(349) =< aux(56)*(4/11)+s(345)*(1/11)+aux(62) s(363) =< s(355)*s(358) s(364) =< s(355)*s(358) s(365) =< s(355)*s(359) s(366) =< s(355)*s(359) s(367) =< s(354)*s(360) s(368) =< s(352)*s(360) s(369) =< s(351)*s(359) s(370) =< s(350)*s(358) s(371) =< s(356)*s(360) s(372) =< s(356)*s(361) s(373) =< s(357)*s(360) s(374) =< s(364) s(375) =< s(366) s(376) =< s(369) s(377) =< s(376)*s(359) s(378) =< s(370) s(379) =< s(378)*s(358) s(380) =< s(372) s(381) =< s(373) s(382) =< s(381)*aux(55) with precondition: [Out=1,V1>=0,V>=0] * Chain [48]: 2*s(688)+6*s(689)+12*s(690)+2*s(691)+2*s(692)+2*s(693)+18*s(694)+8*s(695)+8*s(696)+2*s(701)+2*s(702)+2*s(704)+2*s(706)+2*s(707)+2*s(710)+6*s(713)+6*s(714)+14*s(715)+2*s(716)+14*s(717)+2*s(718)+6*s(719)+14*s(720)+2*s(721)+4*s(730)+12*s(731)+24*s(732)+4*s(733)+4*s(734)+4*s(735)+36*s(736)+16*s(737)+16*s(738)+5*s(743)+4*s(744)+4*s(746)+4*s(748)+4*s(749)+4*s(752)+12*s(755)+12*s(756)+28*s(757)+4*s(758)+28*s(759)+4*s(760)+12*s(761)+28*s(762)+4*s(763)+1*s(891)+1 Such that:s(891) =< 2 aux(72) =< V1 aux(73) =< 2*V1+1 aux(74) =< V1/2 aux(75) =< 2/3*V1 aux(76) =< 2/3*V1+1/3 aux(77) =< 2/5*V1 aux(78) =< 3/7*V1 aux(79) =< 3/11*V1 aux(80) =< V aux(81) =< 2*V+1 aux(82) =< V/2 aux(83) =< 2/3*V aux(84) =< 2/3*V+1/3 aux(85) =< 2/5*V aux(86) =< 3/7*V aux(87) =< 3/11*V s(684) =< aux(76) s(726) =< aux(84) s(730) =< aux(80) s(731) =< aux(80) s(732) =< aux(80) s(733) =< aux(80) s(734) =< aux(80) s(735) =< aux(80) s(736) =< aux(80) s(726) =< aux(80) s(726) =< aux(81) s(732) =< aux(82) s(733) =< aux(82) s(735) =< aux(82) s(734) =< aux(83) s(735) =< aux(83) s(731) =< aux(85) s(733) =< aux(85) s(737) =< aux(86) s(738) =< aux(87) s(739) =< aux(80)+1 s(740) =< aux(80)+2 s(741) =< aux(80) s(742) =< aux(80)-1 s(743) =< aux(80) s(732) =< aux(81)*(1/2)+aux(82) s(733) =< aux(81)*(1/2)+aux(82) s(734) =< aux(81)*(1/2)+aux(82) s(735) =< aux(81)*(1/2)+aux(82) s(736) =< aux(81)*(1/2)+aux(82) s(734) =< aux(81)*(1/3)+aux(83) s(735) =< aux(81)*(1/3)+aux(83) s(736) =< aux(81)*(1/3)+aux(83) s(731) =< aux(81)*(3/5)+s(726)*(1/5)+aux(85) s(732) =< aux(81)*(3/5)+s(726)*(1/5)+aux(85) s(733) =< aux(81)*(3/5)+s(726)*(1/5)+aux(85) s(734) =< aux(81)*(3/5)+s(726)*(1/5)+aux(85) s(735) =< aux(81)*(3/5)+s(726)*(1/5)+aux(85) s(736) =< aux(81)*(3/5)+s(726)*(1/5)+aux(85) s(737) =< aux(81)*(2/7)+aux(86) s(730) =< aux(81)*(2/7)+aux(86) s(738) =< aux(81)*(4/11)+s(726)*(1/11)+aux(87) s(737) =< aux(81)*(4/11)+s(726)*(1/11)+aux(87) s(730) =< aux(81)*(4/11)+s(726)*(1/11)+aux(87) s(744) =< s(736)*s(739) s(745) =< s(736)*s(739) s(746) =< s(736)*s(740) s(747) =< s(736)*s(740) s(748) =< s(735)*s(741) s(749) =< s(733)*s(741) s(750) =< s(732)*s(740) s(751) =< s(731)*s(739) s(752) =< s(737)*s(741) s(753) =< s(737)*s(742) s(754) =< s(738)*s(741) s(755) =< s(745) s(756) =< s(747) s(757) =< s(750) s(758) =< s(757)*s(740) s(759) =< s(751) s(760) =< s(759)*s(739) s(761) =< s(753) s(762) =< s(754) s(763) =< s(762)*aux(80) s(688) =< aux(72) s(689) =< aux(72) s(690) =< aux(72) s(691) =< aux(72) s(692) =< aux(72) s(693) =< aux(72) s(694) =< aux(72) s(684) =< aux(72) s(684) =< aux(73) s(690) =< aux(74) s(691) =< aux(74) s(693) =< aux(74) s(692) =< aux(75) s(693) =< aux(75) s(689) =< aux(77) s(691) =< aux(77) s(695) =< aux(78) s(696) =< aux(79) s(697) =< aux(72)+1 s(698) =< aux(72)+2 s(699) =< aux(72) s(700) =< aux(72)-1 s(701) =< aux(72) s(690) =< aux(73)*(1/2)+aux(74) s(691) =< aux(73)*(1/2)+aux(74) s(692) =< aux(73)*(1/2)+aux(74) s(693) =< aux(73)*(1/2)+aux(74) s(694) =< aux(73)*(1/2)+aux(74) s(692) =< aux(73)*(1/3)+aux(75) s(693) =< aux(73)*(1/3)+aux(75) s(694) =< aux(73)*(1/3)+aux(75) s(689) =< aux(73)*(3/5)+s(684)*(1/5)+aux(77) s(690) =< aux(73)*(3/5)+s(684)*(1/5)+aux(77) s(691) =< aux(73)*(3/5)+s(684)*(1/5)+aux(77) s(692) =< aux(73)*(3/5)+s(684)*(1/5)+aux(77) s(693) =< aux(73)*(3/5)+s(684)*(1/5)+aux(77) s(694) =< aux(73)*(3/5)+s(684)*(1/5)+aux(77) s(695) =< aux(73)*(2/7)+aux(78) s(688) =< aux(73)*(2/7)+aux(78) s(696) =< aux(73)*(4/11)+s(684)*(1/11)+aux(79) s(695) =< aux(73)*(4/11)+s(684)*(1/11)+aux(79) s(688) =< aux(73)*(4/11)+s(684)*(1/11)+aux(79) s(702) =< s(694)*s(697) s(703) =< s(694)*s(697) s(704) =< s(694)*s(698) s(705) =< s(694)*s(698) s(706) =< s(693)*s(699) s(707) =< s(691)*s(699) s(708) =< s(690)*s(698) s(709) =< s(689)*s(697) s(710) =< s(695)*s(699) s(711) =< s(695)*s(700) s(712) =< s(696)*s(699) s(713) =< s(703) s(714) =< s(705) s(715) =< s(708) s(716) =< s(715)*s(698) s(717) =< s(709) s(718) =< s(717)*s(697) s(719) =< s(711) s(720) =< s(712) s(721) =< s(720)*aux(72) with precondition: [Out=2,V1>=0,V>=1] * Chain [47]: 1*s(942)+3*s(943)+6*s(944)+1*s(945)+1*s(946)+1*s(947)+9*s(948)+4*s(949)+4*s(950)+1*s(955)+1*s(956)+1*s(958)+1*s(960)+1*s(961)+1*s(964)+3*s(967)+3*s(968)+7*s(969)+1*s(970)+7*s(971)+1*s(972)+3*s(973)+7*s(974)+1*s(975)+2*s(976)+0 Such that:s(934) =< V1 s(935) =< 2*V1+1 s(936) =< V1/2 s(937) =< 2/3*V1 s(938) =< 2/3*V1+1/3 s(939) =< 2/5*V1 s(940) =< 3/7*V1 s(941) =< 3/11*V1 aux(88) =< 2 s(976) =< aux(88) s(942) =< s(934) s(943) =< s(934) s(944) =< s(934) s(945) =< s(934) s(946) =< s(934) s(947) =< s(934) s(948) =< s(934) s(938) =< s(934) s(938) =< s(935) s(944) =< s(936) s(945) =< s(936) s(947) =< s(936) s(946) =< s(937) s(947) =< s(937) s(943) =< s(939) s(945) =< s(939) s(949) =< s(940) s(950) =< s(941) s(951) =< s(934)+1 s(952) =< s(934)+2 s(953) =< s(934) s(954) =< s(934)-1 s(955) =< s(934) s(944) =< s(935)*(1/2)+s(936) s(945) =< s(935)*(1/2)+s(936) s(946) =< s(935)*(1/2)+s(936) s(947) =< s(935)*(1/2)+s(936) s(948) =< s(935)*(1/2)+s(936) s(946) =< s(935)*(1/3)+s(937) s(947) =< s(935)*(1/3)+s(937) s(948) =< s(935)*(1/3)+s(937) s(943) =< s(935)*(3/5)+s(938)*(1/5)+s(939) s(944) =< s(935)*(3/5)+s(938)*(1/5)+s(939) s(945) =< s(935)*(3/5)+s(938)*(1/5)+s(939) s(946) =< s(935)*(3/5)+s(938)*(1/5)+s(939) s(947) =< s(935)*(3/5)+s(938)*(1/5)+s(939) s(948) =< s(935)*(3/5)+s(938)*(1/5)+s(939) s(949) =< s(935)*(2/7)+s(940) s(942) =< s(935)*(2/7)+s(940) s(950) =< s(935)*(4/11)+s(938)*(1/11)+s(941) s(949) =< s(935)*(4/11)+s(938)*(1/11)+s(941) s(942) =< s(935)*(4/11)+s(938)*(1/11)+s(941) s(956) =< s(948)*s(951) s(957) =< s(948)*s(951) s(958) =< s(948)*s(952) s(959) =< s(948)*s(952) s(960) =< s(947)*s(953) s(961) =< s(945)*s(953) s(962) =< s(944)*s(952) s(963) =< s(943)*s(951) s(964) =< s(949)*s(953) s(965) =< s(949)*s(954) s(966) =< s(950)*s(953) s(967) =< s(957) s(968) =< s(959) s(969) =< s(962) s(970) =< s(969)*s(952) s(971) =< s(963) s(972) =< s(971)*s(951) s(973) =< s(965) s(974) =< s(966) s(975) =< s(974)*s(934) with precondition: [V=2,Out=0,V1>=0] * Chain [46]: 1*s(986)+3*s(987)+6*s(988)+1*s(989)+1*s(990)+1*s(991)+9*s(992)+4*s(993)+4*s(994)+1*s(999)+1*s(1000)+1*s(1002)+1*s(1004)+1*s(1005)+1*s(1008)+3*s(1011)+3*s(1012)+7*s(1013)+1*s(1014)+7*s(1015)+1*s(1016)+3*s(1017)+7*s(1018)+1*s(1019)+1*s(1020)+1 Such that:s(1020) =< 2 s(978) =< V1 s(979) =< 2*V1+1 s(980) =< V1/2 s(981) =< 2/3*V1 s(982) =< 2/3*V1+1/3 s(983) =< 2/5*V1 s(984) =< 3/7*V1 s(985) =< 3/11*V1 s(986) =< s(978) s(987) =< s(978) s(988) =< s(978) s(989) =< s(978) s(990) =< s(978) s(991) =< s(978) s(992) =< s(978) s(982) =< s(978) s(982) =< s(979) s(988) =< s(980) s(989) =< s(980) s(991) =< s(980) s(990) =< s(981) s(991) =< s(981) s(987) =< s(983) s(989) =< s(983) s(993) =< s(984) s(994) =< s(985) s(995) =< s(978)+1 s(996) =< s(978)+2 s(997) =< s(978) s(998) =< s(978)-1 s(999) =< s(978) s(988) =< s(979)*(1/2)+s(980) s(989) =< s(979)*(1/2)+s(980) s(990) =< s(979)*(1/2)+s(980) s(991) =< s(979)*(1/2)+s(980) s(992) =< s(979)*(1/2)+s(980) s(990) =< s(979)*(1/3)+s(981) s(991) =< s(979)*(1/3)+s(981) s(992) =< s(979)*(1/3)+s(981) s(987) =< s(979)*(3/5)+s(982)*(1/5)+s(983) s(988) =< s(979)*(3/5)+s(982)*(1/5)+s(983) s(989) =< s(979)*(3/5)+s(982)*(1/5)+s(983) s(990) =< s(979)*(3/5)+s(982)*(1/5)+s(983) s(991) =< s(979)*(3/5)+s(982)*(1/5)+s(983) s(992) =< s(979)*(3/5)+s(982)*(1/5)+s(983) s(993) =< s(979)*(2/7)+s(984) s(986) =< s(979)*(2/7)+s(984) s(994) =< s(979)*(4/11)+s(982)*(1/11)+s(985) s(993) =< s(979)*(4/11)+s(982)*(1/11)+s(985) s(986) =< s(979)*(4/11)+s(982)*(1/11)+s(985) s(1000) =< s(992)*s(995) s(1001) =< s(992)*s(995) s(1002) =< s(992)*s(996) s(1003) =< s(992)*s(996) s(1004) =< s(991)*s(997) s(1005) =< s(989)*s(997) s(1006) =< s(988)*s(996) s(1007) =< s(987)*s(995) s(1008) =< s(993)*s(997) s(1009) =< s(993)*s(998) s(1010) =< s(994)*s(997) s(1011) =< s(1001) s(1012) =< s(1003) s(1013) =< s(1006) s(1014) =< s(1013)*s(996) s(1015) =< s(1007) s(1016) =< s(1015)*s(995) s(1017) =< s(1009) s(1018) =< s(1010) s(1019) =< s(1018)*s(978) with precondition: [V=2,Out=1,V1>=2] * Chain [45]: 2*s(1029)+6*s(1030)+12*s(1031)+2*s(1032)+2*s(1033)+2*s(1034)+18*s(1035)+8*s(1036)+8*s(1037)+2*s(1042)+2*s(1043)+2*s(1045)+2*s(1047)+2*s(1048)+2*s(1051)+6*s(1054)+6*s(1055)+14*s(1056)+2*s(1057)+14*s(1058)+2*s(1059)+6*s(1060)+14*s(1061)+2*s(1062)+1*s(1105)+1 Such that:s(1105) =< 1 aux(89) =< V1 aux(90) =< 2*V1+1 aux(91) =< V1/2 aux(92) =< 2/3*V1 aux(93) =< 2/3*V1+1/3 aux(94) =< 2/5*V1 aux(95) =< 3/7*V1 aux(96) =< 3/11*V1 s(1025) =< aux(93) s(1029) =< aux(89) s(1030) =< aux(89) s(1031) =< aux(89) s(1032) =< aux(89) s(1033) =< aux(89) s(1034) =< aux(89) s(1035) =< aux(89) s(1025) =< aux(89) s(1025) =< aux(90) s(1031) =< aux(91) s(1032) =< aux(91) s(1034) =< aux(91) s(1033) =< aux(92) s(1034) =< aux(92) s(1030) =< aux(94) s(1032) =< aux(94) s(1036) =< aux(95) s(1037) =< aux(96) s(1038) =< aux(89)+1 s(1039) =< aux(89)+2 s(1040) =< aux(89) s(1041) =< aux(89)-1 s(1042) =< aux(89) s(1031) =< aux(90)*(1/2)+aux(91) s(1032) =< aux(90)*(1/2)+aux(91) s(1033) =< aux(90)*(1/2)+aux(91) s(1034) =< aux(90)*(1/2)+aux(91) s(1035) =< aux(90)*(1/2)+aux(91) s(1033) =< aux(90)*(1/3)+aux(92) s(1034) =< aux(90)*(1/3)+aux(92) s(1035) =< aux(90)*(1/3)+aux(92) s(1030) =< aux(90)*(3/5)+s(1025)*(1/5)+aux(94) s(1031) =< aux(90)*(3/5)+s(1025)*(1/5)+aux(94) s(1032) =< aux(90)*(3/5)+s(1025)*(1/5)+aux(94) s(1033) =< aux(90)*(3/5)+s(1025)*(1/5)+aux(94) s(1034) =< aux(90)*(3/5)+s(1025)*(1/5)+aux(94) s(1035) =< aux(90)*(3/5)+s(1025)*(1/5)+aux(94) s(1036) =< aux(90)*(2/7)+aux(95) s(1029) =< aux(90)*(2/7)+aux(95) s(1037) =< aux(90)*(4/11)+s(1025)*(1/11)+aux(96) s(1036) =< aux(90)*(4/11)+s(1025)*(1/11)+aux(96) s(1029) =< aux(90)*(4/11)+s(1025)*(1/11)+aux(96) s(1043) =< s(1035)*s(1038) s(1044) =< s(1035)*s(1038) s(1045) =< s(1035)*s(1039) s(1046) =< s(1035)*s(1039) s(1047) =< s(1034)*s(1040) s(1048) =< s(1032)*s(1040) s(1049) =< s(1031)*s(1039) s(1050) =< s(1030)*s(1038) s(1051) =< s(1036)*s(1040) s(1052) =< s(1036)*s(1041) s(1053) =< s(1037)*s(1040) s(1054) =< s(1044) s(1055) =< s(1046) s(1056) =< s(1049) s(1057) =< s(1056)*s(1039) s(1058) =< s(1050) s(1059) =< s(1058)*s(1038) s(1060) =< s(1052) s(1061) =< s(1053) s(1062) =< s(1061)*aux(89) with precondition: [V=2,Out=2,V1>=0] #### Cost of chains of fun2(V1,Out): * Chain [53]: 1*s(1506)+3*s(1507)+6*s(1508)+1*s(1509)+1*s(1510)+1*s(1511)+9*s(1512)+4*s(1513)+4*s(1514)+1*s(1519)+1*s(1520)+1*s(1522)+1*s(1524)+1*s(1525)+1*s(1528)+3*s(1531)+3*s(1532)+7*s(1533)+1*s(1534)+7*s(1535)+1*s(1536)+3*s(1537)+7*s(1538)+1*s(1539)+0 Such that:s(1498) =< V1 s(1499) =< 2*V1+1 s(1500) =< V1/2 s(1501) =< 2/3*V1 s(1502) =< 2/3*V1+1/3 s(1503) =< 2/5*V1 s(1504) =< 3/7*V1 s(1505) =< 3/11*V1 s(1506) =< s(1498) s(1507) =< s(1498) s(1508) =< s(1498) s(1509) =< s(1498) s(1510) =< s(1498) s(1511) =< s(1498) s(1512) =< s(1498) s(1502) =< s(1498) s(1502) =< s(1499) s(1508) =< s(1500) s(1509) =< s(1500) s(1511) =< s(1500) s(1510) =< s(1501) s(1511) =< s(1501) s(1507) =< s(1503) s(1509) =< s(1503) s(1513) =< s(1504) s(1514) =< s(1505) s(1515) =< s(1498)+1 s(1516) =< s(1498)+2 s(1517) =< s(1498) s(1518) =< s(1498)-1 s(1519) =< s(1498) s(1508) =< s(1499)*(1/2)+s(1500) s(1509) =< s(1499)*(1/2)+s(1500) s(1510) =< s(1499)*(1/2)+s(1500) s(1511) =< s(1499)*(1/2)+s(1500) s(1512) =< s(1499)*(1/2)+s(1500) s(1510) =< s(1499)*(1/3)+s(1501) s(1511) =< s(1499)*(1/3)+s(1501) s(1512) =< s(1499)*(1/3)+s(1501) s(1507) =< s(1499)*(3/5)+s(1502)*(1/5)+s(1503) s(1508) =< s(1499)*(3/5)+s(1502)*(1/5)+s(1503) s(1509) =< s(1499)*(3/5)+s(1502)*(1/5)+s(1503) s(1510) =< s(1499)*(3/5)+s(1502)*(1/5)+s(1503) s(1511) =< s(1499)*(3/5)+s(1502)*(1/5)+s(1503) s(1512) =< s(1499)*(3/5)+s(1502)*(1/5)+s(1503) s(1513) =< s(1499)*(2/7)+s(1504) s(1506) =< s(1499)*(2/7)+s(1504) s(1514) =< s(1499)*(4/11)+s(1502)*(1/11)+s(1505) s(1513) =< s(1499)*(4/11)+s(1502)*(1/11)+s(1505) s(1506) =< s(1499)*(4/11)+s(1502)*(1/11)+s(1505) s(1520) =< s(1512)*s(1515) s(1521) =< s(1512)*s(1515) s(1522) =< s(1512)*s(1516) s(1523) =< s(1512)*s(1516) s(1524) =< s(1511)*s(1517) s(1525) =< s(1509)*s(1517) s(1526) =< s(1508)*s(1516) s(1527) =< s(1507)*s(1515) s(1528) =< s(1513)*s(1517) s(1529) =< s(1513)*s(1518) s(1530) =< s(1514)*s(1517) s(1531) =< s(1521) s(1532) =< s(1523) s(1533) =< s(1526) s(1534) =< s(1533)*s(1516) s(1535) =< s(1527) s(1536) =< s(1535)*s(1515) s(1537) =< s(1529) s(1538) =< s(1530) s(1539) =< s(1538)*s(1498) with precondition: [V1>=1,Out>=1,V1+1>=Out] * Chain [52]: 0 with precondition: [Out=0,V1>=0] * Chain [51]: 0 with precondition: [Out=1,V1>=0] #### Cost of chains of fun3(Out): * Chain [55]: 0 with precondition: [Out=0] * Chain [54]: 0 with precondition: [Out=2] #### Cost of chains of fun4(Out): * Chain [57]: 0 with precondition: [Out=0] * Chain [56]: 0 with precondition: [Out=1] #### Cost of chains of fun5(V1,V,Out): * Chain [62]: 2*s(1548)+6*s(1549)+12*s(1550)+2*s(1551)+2*s(1552)+2*s(1553)+18*s(1554)+8*s(1555)+8*s(1556)+8*s(1561)+2*s(1562)+2*s(1564)+2*s(1566)+2*s(1567)+2*s(1570)+6*s(1573)+6*s(1574)+14*s(1575)+2*s(1576)+14*s(1577)+2*s(1578)+6*s(1579)+14*s(1580)+2*s(1581)+3*s(1590)+9*s(1591)+18*s(1592)+3*s(1593)+3*s(1594)+3*s(1595)+27*s(1596)+12*s(1597)+12*s(1598)+6*s(1603)+3*s(1604)+3*s(1606)+3*s(1608)+3*s(1609)+3*s(1612)+9*s(1615)+9*s(1616)+21*s(1617)+3*s(1618)+21*s(1619)+3*s(1620)+9*s(1621)+21*s(1622)+3*s(1623)+10*s(1716)+3 Such that:aux(130) =< 2 aux(131) =< V1 aux(132) =< 2*V1+1 aux(133) =< V1/2 aux(134) =< 2/3*V1 aux(135) =< 2/3*V1+1/3 aux(136) =< 2/5*V1 aux(137) =< 3/7*V1 aux(138) =< 3/11*V1 aux(139) =< V aux(140) =< 2*V+1 aux(141) =< V/2 aux(142) =< 2/3*V aux(143) =< 2/3*V+1/3 aux(144) =< 2/5*V aux(145) =< 3/7*V aux(146) =< 3/11*V s(1544) =< aux(135) s(1586) =< aux(143) s(1716) =< aux(130) s(1603) =< aux(139) s(1590) =< aux(139) s(1591) =< aux(139) s(1592) =< aux(139) s(1593) =< aux(139) s(1594) =< aux(139) s(1595) =< aux(139) s(1596) =< aux(139) s(1586) =< aux(139) s(1586) =< aux(140) s(1592) =< aux(141) s(1593) =< aux(141) s(1595) =< aux(141) s(1594) =< aux(142) s(1595) =< aux(142) s(1591) =< aux(144) s(1593) =< aux(144) s(1597) =< aux(145) s(1598) =< aux(146) s(1599) =< aux(139)+1 s(1600) =< aux(139)+2 s(1601) =< aux(139) s(1602) =< aux(139)-1 s(1592) =< aux(140)*(1/2)+aux(141) s(1593) =< aux(140)*(1/2)+aux(141) s(1594) =< aux(140)*(1/2)+aux(141) s(1595) =< aux(140)*(1/2)+aux(141) s(1596) =< aux(140)*(1/2)+aux(141) s(1594) =< aux(140)*(1/3)+aux(142) s(1595) =< aux(140)*(1/3)+aux(142) s(1596) =< aux(140)*(1/3)+aux(142) s(1591) =< aux(140)*(3/5)+s(1586)*(1/5)+aux(144) s(1592) =< aux(140)*(3/5)+s(1586)*(1/5)+aux(144) s(1593) =< aux(140)*(3/5)+s(1586)*(1/5)+aux(144) s(1594) =< aux(140)*(3/5)+s(1586)*(1/5)+aux(144) s(1595) =< aux(140)*(3/5)+s(1586)*(1/5)+aux(144) s(1596) =< aux(140)*(3/5)+s(1586)*(1/5)+aux(144) s(1597) =< aux(140)*(2/7)+aux(145) s(1590) =< aux(140)*(2/7)+aux(145) s(1598) =< aux(140)*(4/11)+s(1586)*(1/11)+aux(146) s(1597) =< aux(140)*(4/11)+s(1586)*(1/11)+aux(146) s(1590) =< aux(140)*(4/11)+s(1586)*(1/11)+aux(146) s(1604) =< s(1596)*s(1599) s(1605) =< s(1596)*s(1599) s(1606) =< s(1596)*s(1600) s(1607) =< s(1596)*s(1600) s(1608) =< s(1595)*s(1601) s(1609) =< s(1593)*s(1601) s(1610) =< s(1592)*s(1600) s(1611) =< s(1591)*s(1599) s(1612) =< s(1597)*s(1601) s(1613) =< s(1597)*s(1602) s(1614) =< s(1598)*s(1601) s(1615) =< s(1605) s(1616) =< s(1607) s(1617) =< s(1610) s(1618) =< s(1617)*s(1600) s(1619) =< s(1611) s(1620) =< s(1619)*s(1599) s(1621) =< s(1613) s(1622) =< s(1614) s(1623) =< s(1622)*aux(139) s(1561) =< aux(131) s(1548) =< aux(131) s(1549) =< aux(131) s(1550) =< aux(131) s(1551) =< aux(131) s(1552) =< aux(131) s(1553) =< aux(131) s(1554) =< aux(131) s(1544) =< aux(131) s(1544) =< aux(132) s(1550) =< aux(133) s(1551) =< aux(133) s(1553) =< aux(133) s(1552) =< aux(134) s(1553) =< aux(134) s(1549) =< aux(136) s(1551) =< aux(136) s(1555) =< aux(137) s(1556) =< aux(138) s(1557) =< aux(131)+1 s(1558) =< aux(131)+2 s(1559) =< aux(131) s(1560) =< aux(131)-1 s(1550) =< aux(132)*(1/2)+aux(133) s(1551) =< aux(132)*(1/2)+aux(133) s(1552) =< aux(132)*(1/2)+aux(133) s(1553) =< aux(132)*(1/2)+aux(133) s(1554) =< aux(132)*(1/2)+aux(133) s(1552) =< aux(132)*(1/3)+aux(134) s(1553) =< aux(132)*(1/3)+aux(134) s(1554) =< aux(132)*(1/3)+aux(134) s(1549) =< aux(132)*(3/5)+s(1544)*(1/5)+aux(136) s(1550) =< aux(132)*(3/5)+s(1544)*(1/5)+aux(136) s(1551) =< aux(132)*(3/5)+s(1544)*(1/5)+aux(136) s(1552) =< aux(132)*(3/5)+s(1544)*(1/5)+aux(136) s(1553) =< aux(132)*(3/5)+s(1544)*(1/5)+aux(136) s(1554) =< aux(132)*(3/5)+s(1544)*(1/5)+aux(136) s(1555) =< aux(132)*(2/7)+aux(137) s(1548) =< aux(132)*(2/7)+aux(137) s(1556) =< aux(132)*(4/11)+s(1544)*(1/11)+aux(138) s(1555) =< aux(132)*(4/11)+s(1544)*(1/11)+aux(138) s(1548) =< aux(132)*(4/11)+s(1544)*(1/11)+aux(138) s(1562) =< s(1554)*s(1557) s(1563) =< s(1554)*s(1557) s(1564) =< s(1554)*s(1558) s(1565) =< s(1554)*s(1558) s(1566) =< s(1553)*s(1559) s(1567) =< s(1551)*s(1559) s(1568) =< s(1550)*s(1558) s(1569) =< s(1549)*s(1557) s(1570) =< s(1555)*s(1559) s(1571) =< s(1555)*s(1560) s(1572) =< s(1556)*s(1559) s(1573) =< s(1563) s(1574) =< s(1565) s(1575) =< s(1568) s(1576) =< s(1575)*s(1558) s(1577) =< s(1569) s(1578) =< s(1577)*s(1557) s(1579) =< s(1571) s(1580) =< s(1572) s(1581) =< s(1580)*aux(131) with precondition: [Out=0,V1>=0,V>=0] * Chain [61]: 2*s(1779)+6*s(1780)+12*s(1781)+2*s(1782)+2*s(1783)+2*s(1784)+18*s(1785)+8*s(1786)+8*s(1787)+8*s(1792)+2*s(1793)+2*s(1795)+2*s(1797)+2*s(1798)+2*s(1801)+6*s(1804)+6*s(1805)+14*s(1806)+2*s(1807)+14*s(1808)+2*s(1809)+6*s(1810)+14*s(1811)+2*s(1812)+3*s(1821)+9*s(1822)+18*s(1823)+3*s(1824)+3*s(1825)+3*s(1826)+27*s(1827)+12*s(1828)+12*s(1829)+3*s(1834)+3*s(1835)+3*s(1837)+3*s(1839)+3*s(1840)+3*s(1843)+9*s(1846)+9*s(1847)+21*s(1848)+3*s(1849)+21*s(1850)+3*s(1851)+9*s(1852)+21*s(1853)+3*s(1854)+7*s(1855)+10*s(1947)+1*s(1994)+6 Such that:aux(150) =< 1 aux(151) =< 2 aux(152) =< V1 aux(153) =< 2*V1+1 aux(154) =< V1/2 aux(155) =< 2/3*V1 aux(156) =< 2/3*V1+1/3 aux(157) =< 2/5*V1 aux(158) =< 3/7*V1 aux(159) =< 3/11*V1 aux(160) =< V aux(161) =< 2*V+1 aux(162) =< V/2 aux(163) =< 2/3*V aux(164) =< 2/3*V+1/3 aux(165) =< 2/5*V aux(166) =< 3/7*V aux(167) =< 3/11*V s(1855) =< aux(150) s(1775) =< aux(156) s(1817) =< aux(164) s(1792) =< aux(152) s(1821) =< aux(160) s(1822) =< aux(160) s(1823) =< aux(160) s(1824) =< aux(160) s(1825) =< aux(160) s(1826) =< aux(160) s(1827) =< aux(160) s(1817) =< aux(160) s(1817) =< aux(161) s(1823) =< aux(162) s(1824) =< aux(162) s(1826) =< aux(162) s(1825) =< aux(163) s(1826) =< aux(163) s(1822) =< aux(165) s(1824) =< aux(165) s(1828) =< aux(166) s(1829) =< aux(167) s(1830) =< aux(160)+1 s(1831) =< aux(160)+2 s(1832) =< aux(160) s(1833) =< aux(160)-1 s(1834) =< aux(160) s(1823) =< aux(161)*(1/2)+aux(162) s(1824) =< aux(161)*(1/2)+aux(162) s(1825) =< aux(161)*(1/2)+aux(162) s(1826) =< aux(161)*(1/2)+aux(162) s(1827) =< aux(161)*(1/2)+aux(162) s(1825) =< aux(161)*(1/3)+aux(163) s(1826) =< aux(161)*(1/3)+aux(163) s(1827) =< aux(161)*(1/3)+aux(163) s(1822) =< aux(161)*(3/5)+s(1817)*(1/5)+aux(165) s(1823) =< aux(161)*(3/5)+s(1817)*(1/5)+aux(165) s(1824) =< aux(161)*(3/5)+s(1817)*(1/5)+aux(165) s(1825) =< aux(161)*(3/5)+s(1817)*(1/5)+aux(165) s(1826) =< aux(161)*(3/5)+s(1817)*(1/5)+aux(165) s(1827) =< aux(161)*(3/5)+s(1817)*(1/5)+aux(165) s(1828) =< aux(161)*(2/7)+aux(166) s(1821) =< aux(161)*(2/7)+aux(166) s(1829) =< aux(161)*(4/11)+s(1817)*(1/11)+aux(167) s(1828) =< aux(161)*(4/11)+s(1817)*(1/11)+aux(167) s(1821) =< aux(161)*(4/11)+s(1817)*(1/11)+aux(167) s(1835) =< s(1827)*s(1830) s(1836) =< s(1827)*s(1830) s(1837) =< s(1827)*s(1831) s(1838) =< s(1827)*s(1831) s(1839) =< s(1826)*s(1832) s(1840) =< s(1824)*s(1832) s(1841) =< s(1823)*s(1831) s(1842) =< s(1822)*s(1830) s(1843) =< s(1828)*s(1832) s(1844) =< s(1828)*s(1833) s(1845) =< s(1829)*s(1832) s(1846) =< s(1836) s(1847) =< s(1838) s(1848) =< s(1841) s(1849) =< s(1848)*s(1831) s(1850) =< s(1842) s(1851) =< s(1850)*s(1830) s(1852) =< s(1844) s(1853) =< s(1845) s(1854) =< s(1853)*aux(160) s(1779) =< aux(152) s(1780) =< aux(152) s(1781) =< aux(152) s(1782) =< aux(152) s(1783) =< aux(152) s(1784) =< aux(152) s(1785) =< aux(152) s(1775) =< aux(152) s(1775) =< aux(153) s(1781) =< aux(154) s(1782) =< aux(154) s(1784) =< aux(154) s(1783) =< aux(155) s(1784) =< aux(155) s(1780) =< aux(157) s(1782) =< aux(157) s(1786) =< aux(158) s(1787) =< aux(159) s(1788) =< aux(152)+1 s(1789) =< aux(152)+2 s(1790) =< aux(152) s(1791) =< aux(152)-1 s(1781) =< aux(153)*(1/2)+aux(154) s(1782) =< aux(153)*(1/2)+aux(154) s(1783) =< aux(153)*(1/2)+aux(154) s(1784) =< aux(153)*(1/2)+aux(154) s(1785) =< aux(153)*(1/2)+aux(154) s(1783) =< aux(153)*(1/3)+aux(155) s(1784) =< aux(153)*(1/3)+aux(155) s(1785) =< aux(153)*(1/3)+aux(155) s(1780) =< aux(153)*(3/5)+s(1775)*(1/5)+aux(157) s(1781) =< aux(153)*(3/5)+s(1775)*(1/5)+aux(157) s(1782) =< aux(153)*(3/5)+s(1775)*(1/5)+aux(157) s(1783) =< aux(153)*(3/5)+s(1775)*(1/5)+aux(157) s(1784) =< aux(153)*(3/5)+s(1775)*(1/5)+aux(157) s(1785) =< aux(153)*(3/5)+s(1775)*(1/5)+aux(157) s(1786) =< aux(153)*(2/7)+aux(158) s(1779) =< aux(153)*(2/7)+aux(158) s(1787) =< aux(153)*(4/11)+s(1775)*(1/11)+aux(159) s(1786) =< aux(153)*(4/11)+s(1775)*(1/11)+aux(159) s(1779) =< aux(153)*(4/11)+s(1775)*(1/11)+aux(159) s(1793) =< s(1785)*s(1788) s(1794) =< s(1785)*s(1788) s(1795) =< s(1785)*s(1789) s(1796) =< s(1785)*s(1789) s(1797) =< s(1784)*s(1790) s(1798) =< s(1782)*s(1790) s(1799) =< s(1781)*s(1789) s(1800) =< s(1780)*s(1788) s(1801) =< s(1786)*s(1790) s(1802) =< s(1786)*s(1791) s(1803) =< s(1787)*s(1790) s(1804) =< s(1794) s(1805) =< s(1796) s(1806) =< s(1799) s(1807) =< s(1806)*s(1789) s(1808) =< s(1800) s(1809) =< s(1808)*s(1788) s(1810) =< s(1802) s(1811) =< s(1803) s(1812) =< s(1811)*aux(152) s(1947) =< aux(151) s(1994) =< s(1855)*aux(151) with precondition: [Out=1,V1>=1,V>=0] * Chain [60]: 2*s(2006)+6*s(2007)+12*s(2008)+2*s(2009)+2*s(2010)+2*s(2011)+18*s(2012)+8*s(2013)+8*s(2014)+16*s(2019)+2*s(2020)+2*s(2022)+2*s(2024)+2*s(2025)+2*s(2028)+6*s(2031)+6*s(2032)+14*s(2033)+2*s(2034)+14*s(2035)+2*s(2036)+6*s(2037)+14*s(2038)+2*s(2039)+2*s(2048)+6*s(2049)+12*s(2050)+2*s(2051)+2*s(2052)+2*s(2053)+18*s(2054)+8*s(2055)+8*s(2056)+2*s(2061)+2*s(2062)+2*s(2064)+2*s(2066)+2*s(2067)+2*s(2070)+6*s(2073)+6*s(2074)+14*s(2075)+2*s(2076)+14*s(2077)+2*s(2078)+6*s(2079)+14*s(2080)+2*s(2081)+2*s(2086)+14*s(2178)+2*s(2180)+6 Such that:aux(172) =< 2 aux(173) =< V1 aux(174) =< 2*V1+1 aux(175) =< V1/2 aux(176) =< 2/3*V1 aux(177) =< 2/3*V1+1/3 aux(178) =< 2/5*V1 aux(179) =< 3/7*V1 aux(180) =< 3/11*V1 aux(181) =< V aux(182) =< 2*V+1 aux(183) =< V/2 aux(184) =< 2/3*V aux(185) =< 2/3*V+1/3 aux(186) =< 2/5*V aux(187) =< 3/7*V aux(188) =< 3/11*V s(2002) =< aux(177) s(2044) =< aux(185) s(2178) =< aux(172) s(2180) =< s(2178)*aux(172) s(2019) =< aux(173) s(2086) =< s(2019)*aux(173) s(2048) =< aux(181) s(2049) =< aux(181) s(2050) =< aux(181) s(2051) =< aux(181) s(2052) =< aux(181) s(2053) =< aux(181) s(2054) =< aux(181) s(2044) =< aux(181) s(2044) =< aux(182) s(2050) =< aux(183) s(2051) =< aux(183) s(2053) =< aux(183) s(2052) =< aux(184) s(2053) =< aux(184) s(2049) =< aux(186) s(2051) =< aux(186) s(2055) =< aux(187) s(2056) =< aux(188) s(2057) =< aux(181)+1 s(2058) =< aux(181)+2 s(2059) =< aux(181) s(2060) =< aux(181)-1 s(2061) =< aux(181) s(2050) =< aux(182)*(1/2)+aux(183) s(2051) =< aux(182)*(1/2)+aux(183) s(2052) =< aux(182)*(1/2)+aux(183) s(2053) =< aux(182)*(1/2)+aux(183) s(2054) =< aux(182)*(1/2)+aux(183) s(2052) =< aux(182)*(1/3)+aux(184) s(2053) =< aux(182)*(1/3)+aux(184) s(2054) =< aux(182)*(1/3)+aux(184) s(2049) =< aux(182)*(3/5)+s(2044)*(1/5)+aux(186) s(2050) =< aux(182)*(3/5)+s(2044)*(1/5)+aux(186) s(2051) =< aux(182)*(3/5)+s(2044)*(1/5)+aux(186) s(2052) =< aux(182)*(3/5)+s(2044)*(1/5)+aux(186) s(2053) =< aux(182)*(3/5)+s(2044)*(1/5)+aux(186) s(2054) =< aux(182)*(3/5)+s(2044)*(1/5)+aux(186) s(2055) =< aux(182)*(2/7)+aux(187) s(2048) =< aux(182)*(2/7)+aux(187) s(2056) =< aux(182)*(4/11)+s(2044)*(1/11)+aux(188) s(2055) =< aux(182)*(4/11)+s(2044)*(1/11)+aux(188) s(2048) =< aux(182)*(4/11)+s(2044)*(1/11)+aux(188) s(2062) =< s(2054)*s(2057) s(2063) =< s(2054)*s(2057) s(2064) =< s(2054)*s(2058) s(2065) =< s(2054)*s(2058) s(2066) =< s(2053)*s(2059) s(2067) =< s(2051)*s(2059) s(2068) =< s(2050)*s(2058) s(2069) =< s(2049)*s(2057) s(2070) =< s(2055)*s(2059) s(2071) =< s(2055)*s(2060) s(2072) =< s(2056)*s(2059) s(2073) =< s(2063) s(2074) =< s(2065) s(2075) =< s(2068) s(2076) =< s(2075)*s(2058) s(2077) =< s(2069) s(2078) =< s(2077)*s(2057) s(2079) =< s(2071) s(2080) =< s(2072) s(2081) =< s(2080)*aux(181) s(2006) =< aux(173) s(2007) =< aux(173) s(2008) =< aux(173) s(2009) =< aux(173) s(2010) =< aux(173) s(2011) =< aux(173) s(2012) =< aux(173) s(2002) =< aux(173) s(2002) =< aux(174) s(2008) =< aux(175) s(2009) =< aux(175) s(2011) =< aux(175) s(2010) =< aux(176) s(2011) =< aux(176) s(2007) =< aux(178) s(2009) =< aux(178) s(2013) =< aux(179) s(2014) =< aux(180) s(2015) =< aux(173)+1 s(2016) =< aux(173)+2 s(2017) =< aux(173) s(2018) =< aux(173)-1 s(2008) =< aux(174)*(1/2)+aux(175) s(2009) =< aux(174)*(1/2)+aux(175) s(2010) =< aux(174)*(1/2)+aux(175) s(2011) =< aux(174)*(1/2)+aux(175) s(2012) =< aux(174)*(1/2)+aux(175) s(2010) =< aux(174)*(1/3)+aux(176) s(2011) =< aux(174)*(1/3)+aux(176) s(2012) =< aux(174)*(1/3)+aux(176) s(2007) =< aux(174)*(3/5)+s(2002)*(1/5)+aux(178) s(2008) =< aux(174)*(3/5)+s(2002)*(1/5)+aux(178) s(2009) =< aux(174)*(3/5)+s(2002)*(1/5)+aux(178) s(2010) =< aux(174)*(3/5)+s(2002)*(1/5)+aux(178) s(2011) =< aux(174)*(3/5)+s(2002)*(1/5)+aux(178) s(2012) =< aux(174)*(3/5)+s(2002)*(1/5)+aux(178) s(2013) =< aux(174)*(2/7)+aux(179) s(2006) =< aux(174)*(2/7)+aux(179) s(2014) =< aux(174)*(4/11)+s(2002)*(1/11)+aux(180) s(2013) =< aux(174)*(4/11)+s(2002)*(1/11)+aux(180) s(2006) =< aux(174)*(4/11)+s(2002)*(1/11)+aux(180) s(2020) =< s(2012)*s(2015) s(2021) =< s(2012)*s(2015) s(2022) =< s(2012)*s(2016) s(2023) =< s(2012)*s(2016) s(2024) =< s(2011)*s(2017) s(2025) =< s(2009)*s(2017) s(2026) =< s(2008)*s(2016) s(2027) =< s(2007)*s(2015) s(2028) =< s(2013)*s(2017) s(2029) =< s(2013)*s(2018) s(2030) =< s(2014)*s(2017) s(2031) =< s(2021) s(2032) =< s(2023) s(2033) =< s(2026) s(2034) =< s(2033)*s(2016) s(2035) =< s(2027) s(2036) =< s(2035)*s(2015) s(2037) =< s(2029) s(2038) =< s(2030) s(2039) =< s(2038)*aux(173) with precondition: [V>=0,Out>=2,V1>=Out] * Chain [59]: 1*s(2194)+3*s(2195)+6*s(2196)+1*s(2197)+1*s(2198)+1*s(2199)+9*s(2200)+4*s(2201)+4*s(2202)+4*s(2207)+1*s(2208)+1*s(2210)+1*s(2212)+1*s(2213)+1*s(2216)+3*s(2219)+3*s(2220)+7*s(2221)+1*s(2222)+7*s(2223)+1*s(2224)+3*s(2225)+7*s(2226)+1*s(2227)+2*s(2229)+3 Such that:aux(189) =< V1 s(2187) =< 2*V1+1 s(2188) =< V1/2 s(2189) =< 2/3*V1 s(2190) =< 2/3*V1+1/3 s(2191) =< 2/5*V1 s(2192) =< 3/7*V1 s(2193) =< 3/11*V1 aux(190) =< 2 s(2229) =< aux(190) s(2207) =< aux(189) s(2194) =< aux(189) s(2195) =< aux(189) s(2196) =< aux(189) s(2197) =< aux(189) s(2198) =< aux(189) s(2199) =< aux(189) s(2200) =< aux(189) s(2190) =< aux(189) s(2190) =< s(2187) s(2196) =< s(2188) s(2197) =< s(2188) s(2199) =< s(2188) s(2198) =< s(2189) s(2199) =< s(2189) s(2195) =< s(2191) s(2197) =< s(2191) s(2201) =< s(2192) s(2202) =< s(2193) s(2203) =< aux(189)+1 s(2204) =< aux(189)+2 s(2205) =< aux(189) s(2206) =< aux(189)-1 s(2196) =< s(2187)*(1/2)+s(2188) s(2197) =< s(2187)*(1/2)+s(2188) s(2198) =< s(2187)*(1/2)+s(2188) s(2199) =< s(2187)*(1/2)+s(2188) s(2200) =< s(2187)*(1/2)+s(2188) s(2198) =< s(2187)*(1/3)+s(2189) s(2199) =< s(2187)*(1/3)+s(2189) s(2200) =< s(2187)*(1/3)+s(2189) s(2195) =< s(2187)*(3/5)+s(2190)*(1/5)+s(2191) s(2196) =< s(2187)*(3/5)+s(2190)*(1/5)+s(2191) s(2197) =< s(2187)*(3/5)+s(2190)*(1/5)+s(2191) s(2198) =< s(2187)*(3/5)+s(2190)*(1/5)+s(2191) s(2199) =< s(2187)*(3/5)+s(2190)*(1/5)+s(2191) s(2200) =< s(2187)*(3/5)+s(2190)*(1/5)+s(2191) s(2201) =< s(2187)*(2/7)+s(2192) s(2194) =< s(2187)*(2/7)+s(2192) s(2202) =< s(2187)*(4/11)+s(2190)*(1/11)+s(2193) s(2201) =< s(2187)*(4/11)+s(2190)*(1/11)+s(2193) s(2194) =< s(2187)*(4/11)+s(2190)*(1/11)+s(2193) s(2208) =< s(2200)*s(2203) s(2209) =< s(2200)*s(2203) s(2210) =< s(2200)*s(2204) s(2211) =< s(2200)*s(2204) s(2212) =< s(2199)*s(2205) s(2213) =< s(2197)*s(2205) s(2214) =< s(2196)*s(2204) s(2215) =< s(2195)*s(2203) s(2216) =< s(2201)*s(2205) s(2217) =< s(2201)*s(2206) s(2218) =< s(2202)*s(2205) s(2219) =< s(2209) s(2220) =< s(2211) s(2221) =< s(2214) s(2222) =< s(2221)*s(2204) s(2223) =< s(2215) s(2224) =< s(2223)*s(2203) s(2225) =< s(2217) s(2226) =< s(2218) s(2227) =< s(2226)*aux(189) with precondition: [V=2,Out=0,V1>=0] * Chain [58]: 2*s(2242)+6*s(2243)+12*s(2244)+2*s(2245)+2*s(2246)+2*s(2247)+18*s(2248)+8*s(2249)+8*s(2250)+16*s(2255)+2*s(2256)+2*s(2258)+2*s(2260)+2*s(2261)+2*s(2264)+6*s(2267)+6*s(2268)+14*s(2269)+2*s(2270)+14*s(2271)+2*s(2272)+6*s(2273)+14*s(2274)+2*s(2275)+1*s(2284)+3*s(2285)+6*s(2286)+1*s(2287)+1*s(2288)+1*s(2289)+9*s(2290)+4*s(2291)+4*s(2292)+1*s(2297)+1*s(2298)+1*s(2300)+1*s(2302)+1*s(2303)+1*s(2306)+3*s(2309)+3*s(2310)+7*s(2311)+1*s(2312)+7*s(2313)+1*s(2314)+3*s(2315)+7*s(2316)+1*s(2317)+2*s(2322)+3 Such that:s(2276) =< V s(2277) =< 2*V+1 s(2278) =< V/2 s(2279) =< 2/3*V s(2280) =< 2/3*V+1/3 s(2281) =< 2/5*V s(2282) =< 3/7*V s(2283) =< 3/11*V aux(193) =< V1 aux(194) =< 2*V1+1 aux(195) =< V1/2 aux(196) =< 2/3*V1 aux(197) =< 2/3*V1+1/3 aux(198) =< 2/5*V1 aux(199) =< 3/7*V1 aux(200) =< 3/11*V1 s(2238) =< aux(197) s(2255) =< aux(193) s(2322) =< s(2255)*aux(193) s(2284) =< s(2276) s(2285) =< s(2276) s(2286) =< s(2276) s(2287) =< s(2276) s(2288) =< s(2276) s(2289) =< s(2276) s(2290) =< s(2276) s(2280) =< s(2276) s(2280) =< s(2277) s(2286) =< s(2278) s(2287) =< s(2278) s(2289) =< s(2278) s(2288) =< s(2279) s(2289) =< s(2279) s(2285) =< s(2281) s(2287) =< s(2281) s(2291) =< s(2282) s(2292) =< s(2283) s(2293) =< s(2276)+1 s(2294) =< s(2276)+2 s(2295) =< s(2276) s(2296) =< s(2276)-1 s(2297) =< s(2276) s(2286) =< s(2277)*(1/2)+s(2278) s(2287) =< s(2277)*(1/2)+s(2278) s(2288) =< s(2277)*(1/2)+s(2278) s(2289) =< s(2277)*(1/2)+s(2278) s(2290) =< s(2277)*(1/2)+s(2278) s(2288) =< s(2277)*(1/3)+s(2279) s(2289) =< s(2277)*(1/3)+s(2279) s(2290) =< s(2277)*(1/3)+s(2279) s(2285) =< s(2277)*(3/5)+s(2280)*(1/5)+s(2281) s(2286) =< s(2277)*(3/5)+s(2280)*(1/5)+s(2281) s(2287) =< s(2277)*(3/5)+s(2280)*(1/5)+s(2281) s(2288) =< s(2277)*(3/5)+s(2280)*(1/5)+s(2281) s(2289) =< s(2277)*(3/5)+s(2280)*(1/5)+s(2281) s(2290) =< s(2277)*(3/5)+s(2280)*(1/5)+s(2281) s(2291) =< s(2277)*(2/7)+s(2282) s(2284) =< s(2277)*(2/7)+s(2282) s(2292) =< s(2277)*(4/11)+s(2280)*(1/11)+s(2283) s(2291) =< s(2277)*(4/11)+s(2280)*(1/11)+s(2283) s(2284) =< s(2277)*(4/11)+s(2280)*(1/11)+s(2283) s(2298) =< s(2290)*s(2293) s(2299) =< s(2290)*s(2293) s(2300) =< s(2290)*s(2294) s(2301) =< s(2290)*s(2294) s(2302) =< s(2289)*s(2295) s(2303) =< s(2287)*s(2295) s(2304) =< s(2286)*s(2294) s(2305) =< s(2285)*s(2293) s(2306) =< s(2291)*s(2295) s(2307) =< s(2291)*s(2296) s(2308) =< s(2292)*s(2295) s(2309) =< s(2299) s(2310) =< s(2301) s(2311) =< s(2304) s(2312) =< s(2311)*s(2294) s(2313) =< s(2305) s(2314) =< s(2313)*s(2293) s(2315) =< s(2307) s(2316) =< s(2308) s(2317) =< s(2316)*s(2276) s(2242) =< aux(193) s(2243) =< aux(193) s(2244) =< aux(193) s(2245) =< aux(193) s(2246) =< aux(193) s(2247) =< aux(193) s(2248) =< aux(193) s(2238) =< aux(193) s(2238) =< aux(194) s(2244) =< aux(195) s(2245) =< aux(195) s(2247) =< aux(195) s(2246) =< aux(196) s(2247) =< aux(196) s(2243) =< aux(198) s(2245) =< aux(198) s(2249) =< aux(199) s(2250) =< aux(200) s(2251) =< aux(193)+1 s(2252) =< aux(193)+2 s(2253) =< aux(193) s(2254) =< aux(193)-1 s(2244) =< aux(194)*(1/2)+aux(195) s(2245) =< aux(194)*(1/2)+aux(195) s(2246) =< aux(194)*(1/2)+aux(195) s(2247) =< aux(194)*(1/2)+aux(195) s(2248) =< aux(194)*(1/2)+aux(195) s(2246) =< aux(194)*(1/3)+aux(196) s(2247) =< aux(194)*(1/3)+aux(196) s(2248) =< aux(194)*(1/3)+aux(196) s(2243) =< aux(194)*(3/5)+s(2238)*(1/5)+aux(198) s(2244) =< aux(194)*(3/5)+s(2238)*(1/5)+aux(198) s(2245) =< aux(194)*(3/5)+s(2238)*(1/5)+aux(198) s(2246) =< aux(194)*(3/5)+s(2238)*(1/5)+aux(198) s(2247) =< aux(194)*(3/5)+s(2238)*(1/5)+aux(198) s(2248) =< aux(194)*(3/5)+s(2238)*(1/5)+aux(198) s(2249) =< aux(194)*(2/7)+aux(199) s(2242) =< aux(194)*(2/7)+aux(199) s(2250) =< aux(194)*(4/11)+s(2238)*(1/11)+aux(200) s(2249) =< aux(194)*(4/11)+s(2238)*(1/11)+aux(200) s(2242) =< aux(194)*(4/11)+s(2238)*(1/11)+aux(200) s(2256) =< s(2248)*s(2251) s(2257) =< s(2248)*s(2251) s(2258) =< s(2248)*s(2252) s(2259) =< s(2248)*s(2252) s(2260) =< s(2247)*s(2253) s(2261) =< s(2245)*s(2253) s(2262) =< s(2244)*s(2252) s(2263) =< s(2243)*s(2251) s(2264) =< s(2249)*s(2253) s(2265) =< s(2249)*s(2254) s(2266) =< s(2250)*s(2253) s(2267) =< s(2257) s(2268) =< s(2259) s(2269) =< s(2262) s(2270) =< s(2269)*s(2252) s(2271) =< s(2263) s(2272) =< s(2271)*s(2251) s(2273) =< s(2265) s(2274) =< s(2266) s(2275) =< s(2274)*aux(193) with precondition: [V>=1,Out>=1,V1>=Out+1] #### Cost of chains of fun6(V1,V,V10,Out): * Chain [71]: 8*s(2510)+24*s(2511)+48*s(2512)+8*s(2513)+8*s(2514)+8*s(2515)+72*s(2516)+32*s(2517)+32*s(2518)+8*s(2523)+8*s(2524)+8*s(2526)+8*s(2528)+8*s(2529)+8*s(2532)+24*s(2535)+24*s(2536)+56*s(2537)+8*s(2538)+56*s(2539)+8*s(2540)+24*s(2541)+56*s(2542)+8*s(2543)+8*s(2552)+24*s(2553)+48*s(2554)+8*s(2555)+8*s(2556)+8*s(2557)+72*s(2558)+32*s(2559)+32*s(2560)+8*s(2565)+8*s(2566)+8*s(2568)+8*s(2570)+8*s(2571)+8*s(2574)+24*s(2577)+24*s(2578)+56*s(2579)+8*s(2580)+56*s(2581)+8*s(2582)+24*s(2583)+56*s(2584)+8*s(2585)+9*s(2594)+27*s(2595)+54*s(2596)+9*s(2597)+9*s(2598)+9*s(2599)+81*s(2600)+36*s(2601)+36*s(2602)+9*s(2607)+9*s(2608)+9*s(2610)+9*s(2612)+9*s(2613)+9*s(2616)+27*s(2619)+27*s(2620)+63*s(2621)+9*s(2622)+63*s(2623)+9*s(2624)+27*s(2625)+63*s(2626)+9*s(2627)+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 aux(226) =< V10 aux(227) =< 2*V10+1 aux(228) =< V10/2 aux(229) =< 2/3*V10 aux(230) =< 2/3*V10+1/3 aux(231) =< 2/5*V10 aux(232) =< 3/7*V10 aux(233) =< 3/11*V10 s(2506) =< aux(214) s(2548) =< aux(222) s(2590) =< aux(230) s(2594) =< aux(226) s(2595) =< aux(226) s(2596) =< aux(226) s(2597) =< aux(226) s(2598) =< aux(226) s(2599) =< aux(226) s(2600) =< aux(226) s(2590) =< aux(226) s(2590) =< aux(227) s(2596) =< aux(228) s(2597) =< aux(228) s(2599) =< aux(228) s(2598) =< aux(229) s(2599) =< aux(229) s(2595) =< aux(231) s(2597) =< aux(231) s(2601) =< aux(232) s(2602) =< aux(233) s(2603) =< aux(226)+1 s(2604) =< aux(226)+2 s(2605) =< aux(226) s(2606) =< aux(226)-1 s(2607) =< aux(226) s(2596) =< aux(227)*(1/2)+aux(228) s(2597) =< aux(227)*(1/2)+aux(228) s(2598) =< aux(227)*(1/2)+aux(228) s(2599) =< aux(227)*(1/2)+aux(228) s(2600) =< aux(227)*(1/2)+aux(228) s(2598) =< aux(227)*(1/3)+aux(229) s(2599) =< aux(227)*(1/3)+aux(229) s(2600) =< aux(227)*(1/3)+aux(229) s(2595) =< aux(227)*(3/5)+s(2590)*(1/5)+aux(231) s(2596) =< aux(227)*(3/5)+s(2590)*(1/5)+aux(231) s(2597) =< aux(227)*(3/5)+s(2590)*(1/5)+aux(231) s(2598) =< aux(227)*(3/5)+s(2590)*(1/5)+aux(231) s(2599) =< aux(227)*(3/5)+s(2590)*(1/5)+aux(231) s(2600) =< aux(227)*(3/5)+s(2590)*(1/5)+aux(231) s(2601) =< aux(227)*(2/7)+aux(232) s(2594) =< aux(227)*(2/7)+aux(232) s(2602) =< aux(227)*(4/11)+s(2590)*(1/11)+aux(233) s(2601) =< aux(227)*(4/11)+s(2590)*(1/11)+aux(233) s(2594) =< aux(227)*(4/11)+s(2590)*(1/11)+aux(233) s(2608) =< s(2600)*s(2603) s(2609) =< s(2600)*s(2603) s(2610) =< s(2600)*s(2604) s(2611) =< s(2600)*s(2604) s(2612) =< s(2599)*s(2605) s(2613) =< s(2597)*s(2605) s(2614) =< s(2596)*s(2604) s(2615) =< s(2595)*s(2603) s(2616) =< s(2601)*s(2605) s(2617) =< s(2601)*s(2606) s(2618) =< s(2602)*s(2605) s(2619) =< s(2609) s(2620) =< s(2611) s(2621) =< s(2614) s(2622) =< s(2621)*s(2604) s(2623) =< s(2615) s(2624) =< s(2623)*s(2603) s(2625) =< s(2617) s(2626) =< s(2618) s(2627) =< s(2626)*aux(226) s(2552) =< aux(218) s(2553) =< aux(218) s(2554) =< aux(218) s(2555) =< aux(218) s(2556) =< aux(218) s(2557) =< aux(218) s(2558) =< aux(218) s(2548) =< aux(218) s(2548) =< aux(219) s(2554) =< aux(220) s(2555) =< aux(220) s(2557) =< aux(220) s(2556) =< aux(221) s(2557) =< aux(221) s(2553) =< aux(223) s(2555) =< aux(223) s(2559) =< aux(224) s(2560) =< aux(225) s(2561) =< aux(218)+1 s(2562) =< aux(218)+2 s(2563) =< aux(218) s(2564) =< aux(218)-1 s(2565) =< aux(218) s(2554) =< aux(219)*(1/2)+aux(220) s(2555) =< aux(219)*(1/2)+aux(220) s(2556) =< aux(219)*(1/2)+aux(220) s(2557) =< aux(219)*(1/2)+aux(220) s(2558) =< aux(219)*(1/2)+aux(220) s(2556) =< aux(219)*(1/3)+aux(221) s(2557) =< aux(219)*(1/3)+aux(221) s(2558) =< aux(219)*(1/3)+aux(221) s(2553) =< aux(219)*(3/5)+s(2548)*(1/5)+aux(223) s(2554) =< aux(219)*(3/5)+s(2548)*(1/5)+aux(223) s(2555) =< aux(219)*(3/5)+s(2548)*(1/5)+aux(223) s(2556) =< aux(219)*(3/5)+s(2548)*(1/5)+aux(223) s(2557) =< aux(219)*(3/5)+s(2548)*(1/5)+aux(223) s(2558) =< aux(219)*(3/5)+s(2548)*(1/5)+aux(223) s(2559) =< aux(219)*(2/7)+aux(224) s(2552) =< aux(219)*(2/7)+aux(224) s(2560) =< aux(219)*(4/11)+s(2548)*(1/11)+aux(225) s(2559) =< aux(219)*(4/11)+s(2548)*(1/11)+aux(225) s(2552) =< aux(219)*(4/11)+s(2548)*(1/11)+aux(225) s(2566) =< s(2558)*s(2561) s(2567) =< s(2558)*s(2561) s(2568) =< s(2558)*s(2562) s(2569) =< s(2558)*s(2562) s(2570) =< s(2557)*s(2563) s(2571) =< s(2555)*s(2563) s(2572) =< s(2554)*s(2562) s(2573) =< s(2553)*s(2561) s(2574) =< s(2559)*s(2563) s(2575) =< s(2559)*s(2564) s(2576) =< s(2560)*s(2563) s(2577) =< s(2567) s(2578) =< s(2569) s(2579) =< s(2572) s(2580) =< s(2579)*s(2562) s(2581) =< s(2573) s(2582) =< s(2581)*s(2561) s(2583) =< s(2575) s(2584) =< s(2576) s(2585) =< s(2584)*aux(218) s(2510) =< aux(210) s(2511) =< aux(210) s(2512) =< aux(210) s(2513) =< aux(210) s(2514) =< aux(210) s(2515) =< aux(210) s(2516) =< aux(210) s(2506) =< aux(210) s(2506) =< aux(211) s(2512) =< aux(212) s(2513) =< aux(212) s(2515) =< aux(212) s(2514) =< aux(213) s(2515) =< aux(213) s(2511) =< aux(215) s(2513) =< aux(215) s(2517) =< aux(216) s(2518) =< aux(217) s(2519) =< aux(210)+1 s(2520) =< aux(210)+2 s(2521) =< aux(210) s(2522) =< aux(210)-1 s(2523) =< aux(210) s(2512) =< aux(211)*(1/2)+aux(212) s(2513) =< aux(211)*(1/2)+aux(212) s(2514) =< aux(211)*(1/2)+aux(212) s(2515) =< aux(211)*(1/2)+aux(212) s(2516) =< aux(211)*(1/2)+aux(212) s(2514) =< aux(211)*(1/3)+aux(213) s(2515) =< aux(211)*(1/3)+aux(213) s(2516) =< aux(211)*(1/3)+aux(213) s(2511) =< aux(211)*(3/5)+s(2506)*(1/5)+aux(215) s(2512) =< aux(211)*(3/5)+s(2506)*(1/5)+aux(215) s(2513) =< aux(211)*(3/5)+s(2506)*(1/5)+aux(215) s(2514) =< aux(211)*(3/5)+s(2506)*(1/5)+aux(215) s(2515) =< aux(211)*(3/5)+s(2506)*(1/5)+aux(215) s(2516) =< aux(211)*(3/5)+s(2506)*(1/5)+aux(215) s(2517) =< aux(211)*(2/7)+aux(216) s(2510) =< aux(211)*(2/7)+aux(216) s(2518) =< aux(211)*(4/11)+s(2506)*(1/11)+aux(217) s(2517) =< aux(211)*(4/11)+s(2506)*(1/11)+aux(217) s(2510) =< aux(211)*(4/11)+s(2506)*(1/11)+aux(217) s(2524) =< s(2516)*s(2519) s(2525) =< s(2516)*s(2519) s(2526) =< s(2516)*s(2520) s(2527) =< s(2516)*s(2520) s(2528) =< s(2515)*s(2521) s(2529) =< s(2513)*s(2521) s(2530) =< s(2512)*s(2520) s(2531) =< s(2511)*s(2519) s(2532) =< s(2517)*s(2521) s(2533) =< s(2517)*s(2522) s(2534) =< s(2518)*s(2521) s(2535) =< s(2525) s(2536) =< s(2527) s(2537) =< s(2530) s(2538) =< s(2537)*s(2520) s(2539) =< s(2531) s(2540) =< s(2539)*s(2519) s(2541) =< s(2533) s(2542) =< s(2534) s(2543) =< s(2542)*aux(210) with precondition: [Out=0,V1>=0,V>=0,V10>=0] * Chain [70]: 4*s(3560)+12*s(3561)+24*s(3562)+4*s(3563)+4*s(3564)+4*s(3565)+36*s(3566)+16*s(3567)+16*s(3568)+4*s(3573)+4*s(3574)+4*s(3576)+4*s(3578)+4*s(3579)+4*s(3582)+12*s(3585)+12*s(3586)+28*s(3587)+4*s(3588)+28*s(3589)+4*s(3590)+12*s(3591)+28*s(3592)+4*s(3593)+4*s(3602)+12*s(3603)+24*s(3604)+4*s(3605)+4*s(3606)+4*s(3607)+36*s(3608)+16*s(3609)+16*s(3610)+16*s(3615)+4*s(3616)+4*s(3618)+4*s(3620)+4*s(3621)+4*s(3624)+12*s(3627)+12*s(3628)+28*s(3629)+4*s(3630)+28*s(3631)+4*s(3632)+12*s(3633)+28*s(3634)+4*s(3635)+5*s(3644)+15*s(3645)+30*s(3646)+5*s(3647)+5*s(3648)+5*s(3649)+45*s(3650)+20*s(3651)+20*s(3652)+5*s(3657)+5*s(3658)+5*s(3660)+5*s(3662)+5*s(3663)+5*s(3666)+15*s(3669)+15*s(3670)+35*s(3671)+5*s(3672)+35*s(3673)+5*s(3674)+15*s(3675)+35*s(3676)+5*s(3677)+5*s(3679)+5*s(3766)+9*s(4076)+1*s(4078)+4 Such that:s(4078) =< 3 aux(238) =< 1 aux(239) =< 2 aux(240) =< V1 aux(241) =< 2*V1+1 aux(242) =< V1/2 aux(243) =< 2/3*V1 aux(244) =< 2/3*V1+1/3 aux(245) =< 2/5*V1 aux(246) =< 3/7*V1 aux(247) =< 3/11*V1 aux(248) =< V aux(249) =< 2*V+1 aux(250) =< V/2 aux(251) =< 2/3*V aux(252) =< 2/3*V+1/3 aux(253) =< 2/5*V aux(254) =< 3/7*V aux(255) =< 3/11*V aux(256) =< V10 aux(257) =< V10+1 aux(258) =< 2*V10+1 aux(259) =< V10/2 aux(260) =< 2/3*V10 aux(261) =< 2/3*V10+1/3 aux(262) =< 2/5*V10 aux(263) =< 3/7*V10 aux(264) =< 3/11*V10 s(3766) =< aux(238) s(3556) =< aux(244) s(3598) =< aux(252) s(3679) =< aux(257) s(3640) =< aux(261) s(3615) =< aux(248) s(3602) =< aux(248) s(3603) =< aux(248) s(3604) =< aux(248) s(3605) =< aux(248) s(3606) =< aux(248) s(3607) =< aux(248) s(3608) =< aux(248) s(3598) =< aux(248) s(3598) =< aux(249) s(3604) =< aux(250) s(3605) =< aux(250) s(3607) =< aux(250) s(3606) =< aux(251) s(3607) =< aux(251) s(3603) =< aux(253) s(3605) =< aux(253) s(3609) =< aux(254) s(3610) =< aux(255) s(3611) =< aux(248)+1 s(3612) =< aux(248)+2 s(3613) =< aux(248) s(3614) =< aux(248)-1 s(3604) =< aux(249)*(1/2)+aux(250) s(3605) =< aux(249)*(1/2)+aux(250) s(3606) =< aux(249)*(1/2)+aux(250) s(3607) =< aux(249)*(1/2)+aux(250) s(3608) =< aux(249)*(1/2)+aux(250) s(3606) =< aux(249)*(1/3)+aux(251) s(3607) =< aux(249)*(1/3)+aux(251) s(3608) =< aux(249)*(1/3)+aux(251) s(3603) =< aux(249)*(3/5)+s(3598)*(1/5)+aux(253) s(3604) =< aux(249)*(3/5)+s(3598)*(1/5)+aux(253) s(3605) =< aux(249)*(3/5)+s(3598)*(1/5)+aux(253) s(3606) =< aux(249)*(3/5)+s(3598)*(1/5)+aux(253) s(3607) =< aux(249)*(3/5)+s(3598)*(1/5)+aux(253) s(3608) =< aux(249)*(3/5)+s(3598)*(1/5)+aux(253) s(3609) =< aux(249)*(2/7)+aux(254) s(3602) =< aux(249)*(2/7)+aux(254) s(3610) =< aux(249)*(4/11)+s(3598)*(1/11)+aux(255) s(3609) =< aux(249)*(4/11)+s(3598)*(1/11)+aux(255) s(3602) =< aux(249)*(4/11)+s(3598)*(1/11)+aux(255) s(3616) =< s(3608)*s(3611) s(3617) =< s(3608)*s(3611) s(3618) =< s(3608)*s(3612) s(3619) =< s(3608)*s(3612) s(3620) =< s(3607)*s(3613) s(3621) =< s(3605)*s(3613) s(3622) =< s(3604)*s(3612) s(3623) =< s(3603)*s(3611) s(3624) =< s(3609)*s(3613) s(3625) =< s(3609)*s(3614) s(3626) =< s(3610)*s(3613) s(3627) =< s(3617) s(3628) =< s(3619) s(3629) =< s(3622) s(3630) =< s(3629)*s(3612) s(3631) =< s(3623) s(3632) =< s(3631)*s(3611) s(3633) =< s(3625) s(3634) =< s(3626) s(3635) =< s(3634)*aux(248) s(3560) =< aux(240) s(3561) =< aux(240) s(3562) =< aux(240) s(3563) =< aux(240) s(3564) =< aux(240) s(3565) =< aux(240) s(3566) =< aux(240) s(3556) =< aux(240) s(3556) =< aux(241) s(3562) =< aux(242) s(3563) =< aux(242) s(3565) =< aux(242) s(3564) =< aux(243) s(3565) =< aux(243) s(3561) =< aux(245) s(3563) =< aux(245) s(3567) =< aux(246) s(3568) =< aux(247) s(3569) =< aux(240)+1 s(3570) =< aux(240)+2 s(3571) =< aux(240) s(3572) =< aux(240)-1 s(3573) =< aux(240) s(3562) =< aux(241)*(1/2)+aux(242) s(3563) =< aux(241)*(1/2)+aux(242) s(3564) =< aux(241)*(1/2)+aux(242) s(3565) =< aux(241)*(1/2)+aux(242) s(3566) =< aux(241)*(1/2)+aux(242) s(3564) =< aux(241)*(1/3)+aux(243) s(3565) =< aux(241)*(1/3)+aux(243) s(3566) =< aux(241)*(1/3)+aux(243) s(3561) =< aux(241)*(3/5)+s(3556)*(1/5)+aux(245) s(3562) =< aux(241)*(3/5)+s(3556)*(1/5)+aux(245) s(3563) =< aux(241)*(3/5)+s(3556)*(1/5)+aux(245) s(3564) =< aux(241)*(3/5)+s(3556)*(1/5)+aux(245) s(3565) =< aux(241)*(3/5)+s(3556)*(1/5)+aux(245) s(3566) =< aux(241)*(3/5)+s(3556)*(1/5)+aux(245) s(3567) =< aux(241)*(2/7)+aux(246) s(3560) =< aux(241)*(2/7)+aux(246) s(3568) =< aux(241)*(4/11)+s(3556)*(1/11)+aux(247) s(3567) =< aux(241)*(4/11)+s(3556)*(1/11)+aux(247) s(3560) =< aux(241)*(4/11)+s(3556)*(1/11)+aux(247) s(3574) =< s(3566)*s(3569) s(3575) =< s(3566)*s(3569) s(3576) =< s(3566)*s(3570) s(3577) =< s(3566)*s(3570) s(3578) =< s(3565)*s(3571) s(3579) =< s(3563)*s(3571) s(3580) =< s(3562)*s(3570) s(3581) =< s(3561)*s(3569) s(3582) =< s(3567)*s(3571) s(3583) =< s(3567)*s(3572) s(3584) =< s(3568)*s(3571) s(3585) =< s(3575) s(3586) =< s(3577) s(3587) =< s(3580) s(3588) =< s(3587)*s(3570) s(3589) =< s(3581) s(3590) =< s(3589)*s(3569) s(3591) =< s(3583) s(3592) =< s(3584) s(3593) =< s(3592)*aux(240) s(4076) =< aux(239) s(3644) =< aux(256) s(3645) =< aux(256) s(3646) =< aux(256) s(3647) =< aux(256) s(3648) =< aux(256) s(3649) =< aux(256) s(3650) =< aux(256) s(3640) =< aux(256) s(3640) =< aux(258) s(3646) =< aux(259) s(3647) =< aux(259) s(3649) =< aux(259) s(3648) =< aux(260) s(3649) =< aux(260) s(3645) =< aux(262) s(3647) =< aux(262) s(3651) =< aux(263) s(3652) =< aux(264) s(3653) =< aux(256)+1 s(3654) =< aux(256)+2 s(3655) =< aux(256) s(3656) =< aux(256)-1 s(3657) =< aux(256) s(3646) =< aux(258)*(1/2)+aux(259) s(3647) =< aux(258)*(1/2)+aux(259) s(3648) =< aux(258)*(1/2)+aux(259) s(3649) =< aux(258)*(1/2)+aux(259) s(3650) =< aux(258)*(1/2)+aux(259) s(3648) =< aux(258)*(1/3)+aux(260) s(3649) =< aux(258)*(1/3)+aux(260) s(3650) =< aux(258)*(1/3)+aux(260) s(3645) =< aux(258)*(3/5)+s(3640)*(1/5)+aux(262) s(3646) =< aux(258)*(3/5)+s(3640)*(1/5)+aux(262) s(3647) =< aux(258)*(3/5)+s(3640)*(1/5)+aux(262) s(3648) =< aux(258)*(3/5)+s(3640)*(1/5)+aux(262) s(3649) =< aux(258)*(3/5)+s(3640)*(1/5)+aux(262) s(3650) =< aux(258)*(3/5)+s(3640)*(1/5)+aux(262) s(3651) =< aux(258)*(2/7)+aux(263) s(3644) =< aux(258)*(2/7)+aux(263) s(3652) =< aux(258)*(4/11)+s(3640)*(1/11)+aux(264) s(3651) =< aux(258)*(4/11)+s(3640)*(1/11)+aux(264) s(3644) =< aux(258)*(4/11)+s(3640)*(1/11)+aux(264) s(3658) =< s(3650)*s(3653) s(3659) =< s(3650)*s(3653) s(3660) =< s(3650)*s(3654) s(3661) =< s(3650)*s(3654) s(3662) =< s(3649)*s(3655) s(3663) =< s(3647)*s(3655) s(3664) =< s(3646)*s(3654) s(3665) =< s(3645)*s(3653) s(3666) =< s(3651)*s(3655) s(3667) =< s(3651)*s(3656) s(3668) =< s(3652)*s(3655) s(3669) =< s(3659) s(3670) =< s(3661) s(3671) =< s(3664) s(3672) =< s(3671)*s(3654) s(3673) =< s(3665) s(3674) =< s(3673)*s(3653) s(3675) =< s(3667) s(3676) =< s(3668) s(3677) =< s(3676)*aux(256) with precondition: [Out=1,V1>=2,V>=0,V10>=0] * Chain [69]: 2*s(4139)+6*s(4140)+12*s(4141)+2*s(4142)+2*s(4143)+2*s(4144)+18*s(4145)+8*s(4146)+8*s(4147)+2*s(4152)+2*s(4153)+2*s(4155)+2*s(4157)+2*s(4158)+2*s(4161)+6*s(4164)+6*s(4165)+14*s(4166)+2*s(4167)+14*s(4168)+2*s(4169)+6*s(4170)+14*s(4171)+2*s(4172)+4*s(4181)+12*s(4182)+24*s(4183)+4*s(4184)+4*s(4185)+4*s(4186)+36*s(4187)+16*s(4188)+16*s(4189)+32*s(4194)+4*s(4195)+4*s(4197)+4*s(4199)+4*s(4200)+4*s(4203)+12*s(4206)+12*s(4207)+28*s(4208)+4*s(4209)+28*s(4210)+4*s(4211)+12*s(4212)+28*s(4213)+4*s(4214)+3*s(4223)+9*s(4224)+18*s(4225)+3*s(4226)+3*s(4227)+3*s(4228)+27*s(4229)+12*s(4230)+12*s(4231)+3*s(4236)+3*s(4237)+3*s(4239)+3*s(4241)+3*s(4242)+3*s(4245)+9*s(4248)+9*s(4249)+21*s(4250)+3*s(4251)+21*s(4252)+3*s(4253)+9*s(4254)+21*s(4255)+3*s(4256)+4*s(4261)+8*s(4529)+6*s(4530)+2*s(4533)+4 Such that:aux(271) =< 1 aux(272) =< 2 aux(273) =< V1 aux(274) =< 2*V1+1 aux(275) =< V1/2 aux(276) =< 2/3*V1 aux(277) =< 2/3*V1+1/3 aux(278) =< 2/5*V1 aux(279) =< 3/7*V1 aux(280) =< 3/11*V1 aux(281) =< V aux(282) =< 2*V+1 aux(283) =< V/2 aux(284) =< 2/3*V aux(285) =< 2/3*V+1/3 aux(286) =< 2/5*V aux(287) =< 3/7*V aux(288) =< 3/11*V aux(289) =< V10 aux(290) =< 2*V10+1 aux(291) =< V10/2 aux(292) =< 2/3*V10 aux(293) =< 2/3*V10+1/3 aux(294) =< 2/5*V10 aux(295) =< 3/7*V10 aux(296) =< 3/11*V10 s(4530) =< aux(271) s(4135) =< aux(277) s(4177) =< aux(285) s(4219) =< aux(293) s(4529) =< aux(272) s(4533) =< s(4530)*aux(272) s(4223) =< aux(289) s(4224) =< aux(289) s(4225) =< aux(289) s(4226) =< aux(289) s(4227) =< aux(289) s(4228) =< aux(289) s(4229) =< aux(289) s(4219) =< aux(289) s(4219) =< aux(290) s(4225) =< aux(291) s(4226) =< aux(291) s(4228) =< aux(291) s(4227) =< aux(292) s(4228) =< aux(292) s(4224) =< aux(294) s(4226) =< aux(294) s(4230) =< aux(295) s(4231) =< aux(296) s(4232) =< aux(289)+1 s(4233) =< aux(289)+2 s(4234) =< aux(289) s(4235) =< aux(289)-1 s(4236) =< aux(289) s(4225) =< aux(290)*(1/2)+aux(291) s(4226) =< aux(290)*(1/2)+aux(291) s(4227) =< aux(290)*(1/2)+aux(291) s(4228) =< aux(290)*(1/2)+aux(291) s(4229) =< aux(290)*(1/2)+aux(291) s(4227) =< aux(290)*(1/3)+aux(292) s(4228) =< aux(290)*(1/3)+aux(292) s(4229) =< aux(290)*(1/3)+aux(292) s(4224) =< aux(290)*(3/5)+s(4219)*(1/5)+aux(294) s(4225) =< aux(290)*(3/5)+s(4219)*(1/5)+aux(294) s(4226) =< aux(290)*(3/5)+s(4219)*(1/5)+aux(294) s(4227) =< aux(290)*(3/5)+s(4219)*(1/5)+aux(294) s(4228) =< aux(290)*(3/5)+s(4219)*(1/5)+aux(294) s(4229) =< aux(290)*(3/5)+s(4219)*(1/5)+aux(294) s(4230) =< aux(290)*(2/7)+aux(295) s(4223) =< aux(290)*(2/7)+aux(295) s(4231) =< aux(290)*(4/11)+s(4219)*(1/11)+aux(296) s(4230) =< aux(290)*(4/11)+s(4219)*(1/11)+aux(296) s(4223) =< aux(290)*(4/11)+s(4219)*(1/11)+aux(296) s(4237) =< s(4229)*s(4232) s(4238) =< s(4229)*s(4232) s(4239) =< s(4229)*s(4233) s(4240) =< s(4229)*s(4233) s(4241) =< s(4228)*s(4234) s(4242) =< s(4226)*s(4234) s(4243) =< s(4225)*s(4233) s(4244) =< s(4224)*s(4232) s(4245) =< s(4230)*s(4234) s(4246) =< s(4230)*s(4235) s(4247) =< s(4231)*s(4234) s(4248) =< s(4238) s(4249) =< s(4240) s(4250) =< s(4243) s(4251) =< s(4250)*s(4233) s(4252) =< s(4244) s(4253) =< s(4252)*s(4232) s(4254) =< s(4246) s(4255) =< s(4247) s(4256) =< s(4255)*aux(289) s(4194) =< aux(281) s(4261) =< s(4194)*aux(281) s(4181) =< aux(281) s(4182) =< aux(281) s(4183) =< aux(281) s(4184) =< aux(281) s(4185) =< aux(281) s(4186) =< aux(281) s(4187) =< aux(281) s(4177) =< aux(281) s(4177) =< aux(282) s(4183) =< aux(283) s(4184) =< aux(283) s(4186) =< aux(283) s(4185) =< aux(284) s(4186) =< aux(284) s(4182) =< aux(286) s(4184) =< aux(286) s(4188) =< aux(287) s(4189) =< aux(288) s(4190) =< aux(281)+1 s(4191) =< aux(281)+2 s(4192) =< aux(281) s(4193) =< aux(281)-1 s(4183) =< aux(282)*(1/2)+aux(283) s(4184) =< aux(282)*(1/2)+aux(283) s(4185) =< aux(282)*(1/2)+aux(283) s(4186) =< aux(282)*(1/2)+aux(283) s(4187) =< aux(282)*(1/2)+aux(283) s(4185) =< aux(282)*(1/3)+aux(284) s(4186) =< aux(282)*(1/3)+aux(284) s(4187) =< aux(282)*(1/3)+aux(284) s(4182) =< aux(282)*(3/5)+s(4177)*(1/5)+aux(286) s(4183) =< aux(282)*(3/5)+s(4177)*(1/5)+aux(286) s(4184) =< aux(282)*(3/5)+s(4177)*(1/5)+aux(286) s(4185) =< aux(282)*(3/5)+s(4177)*(1/5)+aux(286) s(4186) =< aux(282)*(3/5)+s(4177)*(1/5)+aux(286) s(4187) =< aux(282)*(3/5)+s(4177)*(1/5)+aux(286) s(4188) =< aux(282)*(2/7)+aux(287) s(4181) =< aux(282)*(2/7)+aux(287) s(4189) =< aux(282)*(4/11)+s(4177)*(1/11)+aux(288) s(4188) =< aux(282)*(4/11)+s(4177)*(1/11)+aux(288) s(4181) =< aux(282)*(4/11)+s(4177)*(1/11)+aux(288) s(4195) =< s(4187)*s(4190) s(4196) =< s(4187)*s(4190) s(4197) =< s(4187)*s(4191) s(4198) =< s(4187)*s(4191) s(4199) =< s(4186)*s(4192) s(4200) =< s(4184)*s(4192) s(4201) =< s(4183)*s(4191) s(4202) =< s(4182)*s(4190) s(4203) =< s(4188)*s(4192) s(4204) =< s(4188)*s(4193) s(4205) =< s(4189)*s(4192) s(4206) =< s(4196) s(4207) =< s(4198) s(4208) =< s(4201) s(4209) =< s(4208)*s(4191) s(4210) =< s(4202) s(4211) =< s(4210)*s(4190) s(4212) =< s(4204) s(4213) =< s(4205) s(4214) =< s(4213)*aux(281) s(4139) =< aux(273) s(4140) =< aux(273) s(4141) =< aux(273) s(4142) =< aux(273) s(4143) =< aux(273) s(4144) =< aux(273) s(4145) =< aux(273) s(4135) =< aux(273) s(4135) =< aux(274) s(4141) =< aux(275) s(4142) =< aux(275) s(4144) =< aux(275) s(4143) =< aux(276) s(4144) =< aux(276) s(4140) =< aux(278) s(4142) =< aux(278) s(4146) =< aux(279) s(4147) =< aux(280) s(4148) =< aux(273)+1 s(4149) =< aux(273)+2 s(4150) =< aux(273) s(4151) =< aux(273)-1 s(4152) =< aux(273) s(4141) =< aux(274)*(1/2)+aux(275) s(4142) =< aux(274)*(1/2)+aux(275) s(4143) =< aux(274)*(1/2)+aux(275) s(4144) =< aux(274)*(1/2)+aux(275) s(4145) =< aux(274)*(1/2)+aux(275) s(4143) =< aux(274)*(1/3)+aux(276) s(4144) =< aux(274)*(1/3)+aux(276) s(4145) =< aux(274)*(1/3)+aux(276) s(4140) =< aux(274)*(3/5)+s(4135)*(1/5)+aux(278) s(4141) =< aux(274)*(3/5)+s(4135)*(1/5)+aux(278) s(4142) =< aux(274)*(3/5)+s(4135)*(1/5)+aux(278) s(4143) =< aux(274)*(3/5)+s(4135)*(1/5)+aux(278) s(4144) =< aux(274)*(3/5)+s(4135)*(1/5)+aux(278) s(4145) =< aux(274)*(3/5)+s(4135)*(1/5)+aux(278) s(4146) =< aux(274)*(2/7)+aux(279) s(4139) =< aux(274)*(2/7)+aux(279) s(4147) =< aux(274)*(4/11)+s(4135)*(1/11)+aux(280) s(4146) =< aux(274)*(4/11)+s(4135)*(1/11)+aux(280) s(4139) =< aux(274)*(4/11)+s(4135)*(1/11)+aux(280) s(4153) =< s(4145)*s(4148) s(4154) =< s(4145)*s(4148) s(4155) =< s(4145)*s(4149) s(4156) =< s(4145)*s(4149) s(4157) =< s(4144)*s(4150) s(4158) =< s(4142)*s(4150) s(4159) =< s(4141)*s(4149) s(4160) =< s(4140)*s(4148) s(4161) =< s(4146)*s(4150) s(4162) =< s(4146)*s(4151) s(4163) =< s(4147)*s(4150) s(4164) =< s(4154) s(4165) =< s(4156) s(4166) =< s(4159) s(4167) =< s(4166)*s(4149) s(4168) =< s(4160) s(4169) =< s(4168)*s(4148) s(4170) =< s(4162) s(4171) =< s(4163) s(4172) =< s(4171)*aux(273) with precondition: [V1>=2,V10>=0,Out>=2,V>=Out] * Chain [68]: 4*s(4547)+12*s(4548)+24*s(4549)+4*s(4550)+4*s(4551)+4*s(4552)+36*s(4553)+16*s(4554)+16*s(4555)+4*s(4560)+4*s(4561)+4*s(4563)+4*s(4565)+4*s(4566)+4*s(4569)+12*s(4572)+12*s(4573)+28*s(4574)+4*s(4575)+28*s(4576)+4*s(4577)+12*s(4578)+28*s(4579)+4*s(4580)+4*s(4589)+12*s(4590)+24*s(4591)+4*s(4592)+4*s(4593)+4*s(4594)+36*s(4595)+16*s(4596)+16*s(4597)+4*s(4602)+4*s(4603)+4*s(4605)+4*s(4607)+4*s(4608)+4*s(4611)+12*s(4614)+12*s(4615)+28*s(4616)+4*s(4617)+28*s(4618)+4*s(4619)+12*s(4620)+28*s(4621)+4*s(4622)+1 Such that:aux(297) =< V1 aux(298) =< 2*V1+1 aux(299) =< V1/2 aux(300) =< 2/3*V1 aux(301) =< 2/3*V1+1/3 aux(302) =< 2/5*V1 aux(303) =< 3/7*V1 aux(304) =< 3/11*V1 aux(305) =< V aux(306) =< 2*V+1 aux(307) =< V/2 aux(308) =< 2/3*V aux(309) =< 2/3*V+1/3 aux(310) =< 2/5*V aux(311) =< 3/7*V aux(312) =< 3/11*V s(4543) =< aux(301) s(4585) =< aux(309) s(4589) =< aux(305) s(4590) =< aux(305) s(4591) =< aux(305) s(4592) =< aux(305) s(4593) =< aux(305) s(4594) =< aux(305) s(4595) =< aux(305) s(4585) =< aux(305) s(4585) =< aux(306) s(4591) =< aux(307) s(4592) =< aux(307) s(4594) =< aux(307) s(4593) =< aux(308) s(4594) =< aux(308) s(4590) =< aux(310) s(4592) =< aux(310) s(4596) =< aux(311) s(4597) =< aux(312) s(4598) =< aux(305)+1 s(4599) =< aux(305)+2 s(4600) =< aux(305) s(4601) =< aux(305)-1 s(4602) =< aux(305) s(4591) =< aux(306)*(1/2)+aux(307) s(4592) =< aux(306)*(1/2)+aux(307) s(4593) =< aux(306)*(1/2)+aux(307) s(4594) =< aux(306)*(1/2)+aux(307) s(4595) =< aux(306)*(1/2)+aux(307) s(4593) =< aux(306)*(1/3)+aux(308) s(4594) =< aux(306)*(1/3)+aux(308) s(4595) =< aux(306)*(1/3)+aux(308) s(4590) =< aux(306)*(3/5)+s(4585)*(1/5)+aux(310) s(4591) =< aux(306)*(3/5)+s(4585)*(1/5)+aux(310) s(4592) =< aux(306)*(3/5)+s(4585)*(1/5)+aux(310) s(4593) =< aux(306)*(3/5)+s(4585)*(1/5)+aux(310) s(4594) =< aux(306)*(3/5)+s(4585)*(1/5)+aux(310) s(4595) =< aux(306)*(3/5)+s(4585)*(1/5)+aux(310) s(4596) =< aux(306)*(2/7)+aux(311) s(4589) =< aux(306)*(2/7)+aux(311) s(4597) =< aux(306)*(4/11)+s(4585)*(1/11)+aux(312) s(4596) =< aux(306)*(4/11)+s(4585)*(1/11)+aux(312) s(4589) =< aux(306)*(4/11)+s(4585)*(1/11)+aux(312) s(4603) =< s(4595)*s(4598) s(4604) =< s(4595)*s(4598) s(4605) =< s(4595)*s(4599) s(4606) =< s(4595)*s(4599) s(4607) =< s(4594)*s(4600) s(4608) =< s(4592)*s(4600) s(4609) =< s(4591)*s(4599) s(4610) =< s(4590)*s(4598) s(4611) =< s(4596)*s(4600) s(4612) =< s(4596)*s(4601) s(4613) =< s(4597)*s(4600) s(4614) =< s(4604) s(4615) =< s(4606) s(4616) =< s(4609) s(4617) =< s(4616)*s(4599) s(4618) =< s(4610) s(4619) =< s(4618)*s(4598) s(4620) =< s(4612) s(4621) =< s(4613) s(4622) =< s(4621)*aux(305) s(4547) =< aux(297) s(4548) =< aux(297) s(4549) =< aux(297) s(4550) =< aux(297) s(4551) =< aux(297) s(4552) =< aux(297) s(4553) =< aux(297) s(4543) =< aux(297) s(4543) =< aux(298) s(4549) =< aux(299) s(4550) =< aux(299) s(4552) =< aux(299) s(4551) =< aux(300) s(4552) =< aux(300) s(4548) =< aux(302) s(4550) =< aux(302) s(4554) =< aux(303) s(4555) =< aux(304) s(4556) =< aux(297)+1 s(4557) =< aux(297)+2 s(4558) =< aux(297) s(4559) =< aux(297)-1 s(4560) =< aux(297) s(4549) =< aux(298)*(1/2)+aux(299) s(4550) =< aux(298)*(1/2)+aux(299) s(4551) =< aux(298)*(1/2)+aux(299) s(4552) =< aux(298)*(1/2)+aux(299) s(4553) =< aux(298)*(1/2)+aux(299) s(4551) =< aux(298)*(1/3)+aux(300) s(4552) =< aux(298)*(1/3)+aux(300) s(4553) =< aux(298)*(1/3)+aux(300) s(4548) =< aux(298)*(3/5)+s(4543)*(1/5)+aux(302) s(4549) =< aux(298)*(3/5)+s(4543)*(1/5)+aux(302) s(4550) =< aux(298)*(3/5)+s(4543)*(1/5)+aux(302) s(4551) =< aux(298)*(3/5)+s(4543)*(1/5)+aux(302) s(4552) =< aux(298)*(3/5)+s(4543)*(1/5)+aux(302) s(4553) =< aux(298)*(3/5)+s(4543)*(1/5)+aux(302) s(4554) =< aux(298)*(2/7)+aux(303) s(4547) =< aux(298)*(2/7)+aux(303) s(4555) =< aux(298)*(4/11)+s(4543)*(1/11)+aux(304) s(4554) =< aux(298)*(4/11)+s(4543)*(1/11)+aux(304) s(4547) =< aux(298)*(4/11)+s(4543)*(1/11)+aux(304) s(4561) =< s(4553)*s(4556) s(4562) =< s(4553)*s(4556) s(4563) =< s(4553)*s(4557) s(4564) =< s(4553)*s(4557) s(4565) =< s(4552)*s(4558) s(4566) =< s(4550)*s(4558) s(4567) =< s(4549)*s(4557) s(4568) =< s(4548)*s(4556) s(4569) =< s(4554)*s(4558) s(4570) =< s(4554)*s(4559) s(4571) =< s(4555)*s(4558) s(4572) =< s(4562) s(4573) =< s(4564) s(4574) =< s(4567) s(4575) =< s(4574)*s(4557) s(4576) =< s(4568) s(4577) =< s(4576)*s(4556) s(4578) =< s(4570) s(4579) =< s(4571) s(4580) =< s(4579)*aux(297) with precondition: [V10=2,Out=0,V1>=0,V>=0] * Chain [67]: 2*s(4883)+6*s(4884)+12*s(4885)+2*s(4886)+2*s(4887)+2*s(4888)+18*s(4889)+8*s(4890)+8*s(4891)+2*s(4896)+2*s(4897)+2*s(4899)+2*s(4901)+2*s(4902)+2*s(4905)+6*s(4908)+6*s(4909)+14*s(4910)+2*s(4911)+14*s(4912)+2*s(4913)+6*s(4914)+14*s(4915)+2*s(4916)+2*s(4925)+6*s(4926)+12*s(4927)+2*s(4928)+2*s(4929)+2*s(4930)+18*s(4931)+8*s(4932)+8*s(4933)+8*s(4938)+2*s(4939)+2*s(4941)+2*s(4943)+2*s(4944)+2*s(4947)+6*s(4950)+6*s(4951)+14*s(4952)+2*s(4953)+14*s(4954)+2*s(4955)+6*s(4956)+14*s(4957)+2*s(4958)+4*s(4960)+4 Such that:aux(315) =< 3 aux(316) =< V1 aux(317) =< 2*V1+1 aux(318) =< V1/2 aux(319) =< 2/3*V1 aux(320) =< 2/3*V1+1/3 aux(321) =< 2/5*V1 aux(322) =< 3/7*V1 aux(323) =< 3/11*V1 aux(324) =< V aux(325) =< 2*V+1 aux(326) =< V/2 aux(327) =< 2/3*V aux(328) =< 2/3*V+1/3 aux(329) =< 2/5*V aux(330) =< 3/7*V aux(331) =< 3/11*V s(4960) =< aux(315) s(4879) =< aux(320) s(4921) =< aux(328) s(4938) =< aux(324) s(4925) =< aux(324) s(4926) =< aux(324) s(4927) =< aux(324) s(4928) =< aux(324) s(4929) =< aux(324) s(4930) =< aux(324) s(4931) =< aux(324) s(4921) =< aux(324) s(4921) =< aux(325) s(4927) =< aux(326) s(4928) =< aux(326) s(4930) =< aux(326) s(4929) =< aux(327) s(4930) =< aux(327) s(4926) =< aux(329) s(4928) =< aux(329) s(4932) =< aux(330) s(4933) =< aux(331) s(4934) =< aux(324)+1 s(4935) =< aux(324)+2 s(4936) =< aux(324) s(4937) =< aux(324)-1 s(4927) =< aux(325)*(1/2)+aux(326) s(4928) =< aux(325)*(1/2)+aux(326) s(4929) =< aux(325)*(1/2)+aux(326) s(4930) =< aux(325)*(1/2)+aux(326) s(4931) =< aux(325)*(1/2)+aux(326) s(4929) =< aux(325)*(1/3)+aux(327) s(4930) =< aux(325)*(1/3)+aux(327) s(4931) =< aux(325)*(1/3)+aux(327) s(4926) =< aux(325)*(3/5)+s(4921)*(1/5)+aux(329) s(4927) =< aux(325)*(3/5)+s(4921)*(1/5)+aux(329) s(4928) =< aux(325)*(3/5)+s(4921)*(1/5)+aux(329) s(4929) =< aux(325)*(3/5)+s(4921)*(1/5)+aux(329) s(4930) =< aux(325)*(3/5)+s(4921)*(1/5)+aux(329) s(4931) =< aux(325)*(3/5)+s(4921)*(1/5)+aux(329) s(4932) =< aux(325)*(2/7)+aux(330) s(4925) =< aux(325)*(2/7)+aux(330) s(4933) =< aux(325)*(4/11)+s(4921)*(1/11)+aux(331) s(4932) =< aux(325)*(4/11)+s(4921)*(1/11)+aux(331) s(4925) =< aux(325)*(4/11)+s(4921)*(1/11)+aux(331) s(4939) =< s(4931)*s(4934) s(4940) =< s(4931)*s(4934) s(4941) =< s(4931)*s(4935) s(4942) =< s(4931)*s(4935) s(4943) =< s(4930)*s(4936) s(4944) =< s(4928)*s(4936) s(4945) =< s(4927)*s(4935) s(4946) =< s(4926)*s(4934) s(4947) =< s(4932)*s(4936) s(4948) =< s(4932)*s(4937) s(4949) =< s(4933)*s(4936) s(4950) =< s(4940) s(4951) =< s(4942) s(4952) =< s(4945) s(4953) =< s(4952)*s(4935) s(4954) =< s(4946) s(4955) =< s(4954)*s(4934) s(4956) =< s(4948) s(4957) =< s(4949) s(4958) =< s(4957)*aux(324) s(4883) =< aux(316) s(4884) =< aux(316) s(4885) =< aux(316) s(4886) =< aux(316) s(4887) =< aux(316) s(4888) =< aux(316) s(4889) =< aux(316) s(4879) =< aux(316) s(4879) =< aux(317) s(4885) =< aux(318) s(4886) =< aux(318) s(4888) =< aux(318) s(4887) =< aux(319) s(4888) =< aux(319) s(4884) =< aux(321) s(4886) =< aux(321) s(4890) =< aux(322) s(4891) =< aux(323) s(4892) =< aux(316)+1 s(4893) =< aux(316)+2 s(4894) =< aux(316) s(4895) =< aux(316)-1 s(4896) =< aux(316) s(4885) =< aux(317)*(1/2)+aux(318) s(4886) =< aux(317)*(1/2)+aux(318) s(4887) =< aux(317)*(1/2)+aux(318) s(4888) =< aux(317)*(1/2)+aux(318) s(4889) =< aux(317)*(1/2)+aux(318) s(4887) =< aux(317)*(1/3)+aux(319) s(4888) =< aux(317)*(1/3)+aux(319) s(4889) =< aux(317)*(1/3)+aux(319) s(4884) =< aux(317)*(3/5)+s(4879)*(1/5)+aux(321) s(4885) =< aux(317)*(3/5)+s(4879)*(1/5)+aux(321) s(4886) =< aux(317)*(3/5)+s(4879)*(1/5)+aux(321) s(4887) =< aux(317)*(3/5)+s(4879)*(1/5)+aux(321) s(4888) =< aux(317)*(3/5)+s(4879)*(1/5)+aux(321) s(4889) =< aux(317)*(3/5)+s(4879)*(1/5)+aux(321) s(4890) =< aux(317)*(2/7)+aux(322) s(4883) =< aux(317)*(2/7)+aux(322) s(4891) =< aux(317)*(4/11)+s(4879)*(1/11)+aux(323) s(4890) =< aux(317)*(4/11)+s(4879)*(1/11)+aux(323) s(4883) =< aux(317)*(4/11)+s(4879)*(1/11)+aux(323) s(4897) =< s(4889)*s(4892) s(4898) =< s(4889)*s(4892) s(4899) =< s(4889)*s(4893) s(4900) =< s(4889)*s(4893) s(4901) =< s(4888)*s(4894) s(4902) =< s(4886)*s(4894) s(4903) =< s(4885)*s(4893) s(4904) =< s(4884)*s(4892) s(4905) =< s(4890)*s(4894) s(4906) =< s(4890)*s(4895) s(4907) =< s(4891)*s(4894) s(4908) =< s(4898) s(4909) =< s(4900) s(4910) =< s(4903) s(4911) =< s(4910)*s(4893) s(4912) =< s(4904) s(4913) =< s(4912)*s(4892) s(4914) =< s(4906) s(4915) =< s(4907) s(4916) =< s(4915)*aux(316) with precondition: [V10=2,Out=1,V1>=2,V>=0] * Chain [66]: 1*s(5063)+3*s(5064)+6*s(5065)+1*s(5066)+1*s(5067)+1*s(5068)+9*s(5069)+4*s(5070)+4*s(5071)+1*s(5076)+1*s(5077)+1*s(5079)+1*s(5081)+1*s(5082)+1*s(5085)+3*s(5088)+3*s(5089)+7*s(5090)+1*s(5091)+7*s(5092)+1*s(5093)+3*s(5094)+7*s(5095)+1*s(5096)+2*s(5105)+6*s(5106)+12*s(5107)+2*s(5108)+2*s(5109)+2*s(5110)+18*s(5111)+8*s(5112)+8*s(5113)+16*s(5118)+2*s(5119)+2*s(5121)+2*s(5123)+2*s(5124)+2*s(5127)+6*s(5130)+6*s(5131)+14*s(5132)+2*s(5133)+14*s(5134)+2*s(5135)+6*s(5136)+14*s(5137)+2*s(5138)+2*s(5143)+4 Such that:s(5055) =< V1 s(5056) =< 2*V1+1 s(5057) =< V1/2 s(5058) =< 2/3*V1 s(5059) =< 2/3*V1+1/3 s(5060) =< 2/5*V1 s(5061) =< 3/7*V1 s(5062) =< 3/11*V1 aux(334) =< V aux(335) =< 2*V+1 aux(336) =< V/2 aux(337) =< 2/3*V aux(338) =< 2/3*V+1/3 aux(339) =< 2/5*V aux(340) =< 3/7*V aux(341) =< 3/11*V s(5101) =< aux(338) s(5118) =< aux(334) s(5143) =< s(5118)*aux(334) s(5105) =< aux(334) s(5106) =< aux(334) s(5107) =< aux(334) s(5108) =< aux(334) s(5109) =< aux(334) s(5110) =< aux(334) s(5111) =< aux(334) s(5101) =< aux(334) s(5101) =< aux(335) s(5107) =< aux(336) s(5108) =< aux(336) s(5110) =< aux(336) s(5109) =< aux(337) s(5110) =< aux(337) s(5106) =< aux(339) s(5108) =< aux(339) s(5112) =< aux(340) s(5113) =< aux(341) s(5114) =< aux(334)+1 s(5115) =< aux(334)+2 s(5116) =< aux(334) s(5117) =< aux(334)-1 s(5107) =< aux(335)*(1/2)+aux(336) s(5108) =< aux(335)*(1/2)+aux(336) s(5109) =< aux(335)*(1/2)+aux(336) s(5110) =< aux(335)*(1/2)+aux(336) s(5111) =< aux(335)*(1/2)+aux(336) s(5109) =< aux(335)*(1/3)+aux(337) s(5110) =< aux(335)*(1/3)+aux(337) s(5111) =< aux(335)*(1/3)+aux(337) s(5106) =< aux(335)*(3/5)+s(5101)*(1/5)+aux(339) s(5107) =< aux(335)*(3/5)+s(5101)*(1/5)+aux(339) s(5108) =< aux(335)*(3/5)+s(5101)*(1/5)+aux(339) s(5109) =< aux(335)*(3/5)+s(5101)*(1/5)+aux(339) s(5110) =< aux(335)*(3/5)+s(5101)*(1/5)+aux(339) s(5111) =< aux(335)*(3/5)+s(5101)*(1/5)+aux(339) s(5112) =< aux(335)*(2/7)+aux(340) s(5105) =< aux(335)*(2/7)+aux(340) s(5113) =< aux(335)*(4/11)+s(5101)*(1/11)+aux(341) s(5112) =< aux(335)*(4/11)+s(5101)*(1/11)+aux(341) s(5105) =< aux(335)*(4/11)+s(5101)*(1/11)+aux(341) s(5119) =< s(5111)*s(5114) s(5120) =< s(5111)*s(5114) s(5121) =< s(5111)*s(5115) s(5122) =< s(5111)*s(5115) s(5123) =< s(5110)*s(5116) s(5124) =< s(5108)*s(5116) s(5125) =< s(5107)*s(5115) s(5126) =< s(5106)*s(5114) s(5127) =< s(5112)*s(5116) s(5128) =< s(5112)*s(5117) s(5129) =< s(5113)*s(5116) s(5130) =< s(5120) s(5131) =< s(5122) s(5132) =< s(5125) s(5133) =< s(5132)*s(5115) s(5134) =< s(5126) s(5135) =< s(5134)*s(5114) s(5136) =< s(5128) s(5137) =< s(5129) s(5138) =< s(5137)*aux(334) s(5063) =< s(5055) s(5064) =< s(5055) s(5065) =< s(5055) s(5066) =< s(5055) s(5067) =< s(5055) s(5068) =< s(5055) s(5069) =< s(5055) s(5059) =< s(5055) s(5059) =< s(5056) s(5065) =< s(5057) s(5066) =< s(5057) s(5068) =< s(5057) s(5067) =< s(5058) s(5068) =< s(5058) s(5064) =< s(5060) s(5066) =< s(5060) s(5070) =< s(5061) s(5071) =< s(5062) s(5072) =< s(5055)+1 s(5073) =< s(5055)+2 s(5074) =< s(5055) s(5075) =< s(5055)-1 s(5076) =< s(5055) s(5065) =< s(5056)*(1/2)+s(5057) s(5066) =< s(5056)*(1/2)+s(5057) s(5067) =< s(5056)*(1/2)+s(5057) s(5068) =< s(5056)*(1/2)+s(5057) s(5069) =< s(5056)*(1/2)+s(5057) s(5067) =< s(5056)*(1/3)+s(5058) s(5068) =< s(5056)*(1/3)+s(5058) s(5069) =< s(5056)*(1/3)+s(5058) s(5064) =< s(5056)*(3/5)+s(5059)*(1/5)+s(5060) s(5065) =< s(5056)*(3/5)+s(5059)*(1/5)+s(5060) s(5066) =< s(5056)*(3/5)+s(5059)*(1/5)+s(5060) s(5067) =< s(5056)*(3/5)+s(5059)*(1/5)+s(5060) s(5068) =< s(5056)*(3/5)+s(5059)*(1/5)+s(5060) s(5069) =< s(5056)*(3/5)+s(5059)*(1/5)+s(5060) s(5070) =< s(5056)*(2/7)+s(5061) s(5063) =< s(5056)*(2/7)+s(5061) s(5071) =< s(5056)*(4/11)+s(5059)*(1/11)+s(5062) s(5070) =< s(5056)*(4/11)+s(5059)*(1/11)+s(5062) s(5063) =< s(5056)*(4/11)+s(5059)*(1/11)+s(5062) s(5077) =< s(5069)*s(5072) s(5078) =< s(5069)*s(5072) s(5079) =< s(5069)*s(5073) s(5080) =< s(5069)*s(5073) s(5081) =< s(5068)*s(5074) s(5082) =< s(5066)*s(5074) s(5083) =< s(5065)*s(5073) s(5084) =< s(5064)*s(5072) s(5085) =< s(5070)*s(5074) s(5086) =< s(5070)*s(5075) s(5087) =< s(5071)*s(5074) s(5088) =< s(5078) s(5089) =< s(5080) s(5090) =< s(5083) s(5091) =< s(5090)*s(5073) s(5092) =< s(5084) s(5093) =< s(5092)*s(5072) s(5094) =< s(5086) s(5095) =< s(5087) s(5096) =< s(5095)*s(5055) with precondition: [V10=2,V1>=2,Out>=2,V>=Out+2] * Chain [65]: 6*s(5199)+18*s(5200)+36*s(5201)+6*s(5202)+6*s(5203)+6*s(5204)+54*s(5205)+24*s(5206)+24*s(5207)+6*s(5212)+6*s(5213)+6*s(5215)+6*s(5217)+6*s(5218)+6*s(5221)+18*s(5224)+18*s(5225)+42*s(5226)+6*s(5227)+42*s(5228)+6*s(5229)+18*s(5230)+42*s(5231)+6*s(5232)+3*s(5241)+9*s(5242)+18*s(5243)+3*s(5244)+3*s(5245)+3*s(5246)+27*s(5247)+12*s(5248)+12*s(5249)+3*s(5254)+3*s(5255)+3*s(5257)+3*s(5259)+3*s(5260)+3*s(5263)+9*s(5266)+9*s(5267)+21*s(5268)+3*s(5269)+21*s(5270)+3*s(5271)+9*s(5272)+21*s(5273)+3*s(5274)+1 Such that:aux(342) =< V1 aux(343) =< 2*V1+1 aux(344) =< V1/2 aux(345) =< 2/3*V1 aux(346) =< 2/3*V1+1/3 aux(347) =< 2/5*V1 aux(348) =< 3/7*V1 aux(349) =< 3/11*V1 aux(350) =< V10 aux(351) =< 2*V10+1 aux(352) =< V10/2 aux(353) =< 2/3*V10 aux(354) =< 2/3*V10+1/3 aux(355) =< 2/5*V10 aux(356) =< 3/7*V10 aux(357) =< 3/11*V10 s(5195) =< aux(346) s(5237) =< aux(354) s(5241) =< aux(350) s(5242) =< aux(350) s(5243) =< aux(350) s(5244) =< aux(350) s(5245) =< aux(350) s(5246) =< aux(350) s(5247) =< aux(350) s(5237) =< aux(350) s(5237) =< aux(351) s(5243) =< aux(352) s(5244) =< aux(352) s(5246) =< aux(352) s(5245) =< aux(353) s(5246) =< aux(353) s(5242) =< aux(355) s(5244) =< aux(355) s(5248) =< aux(356) s(5249) =< aux(357) s(5250) =< aux(350)+1 s(5251) =< aux(350)+2 s(5252) =< aux(350) s(5253) =< aux(350)-1 s(5254) =< aux(350) s(5243) =< aux(351)*(1/2)+aux(352) s(5244) =< aux(351)*(1/2)+aux(352) s(5245) =< aux(351)*(1/2)+aux(352) s(5246) =< aux(351)*(1/2)+aux(352) s(5247) =< aux(351)*(1/2)+aux(352) s(5245) =< aux(351)*(1/3)+aux(353) s(5246) =< aux(351)*(1/3)+aux(353) s(5247) =< aux(351)*(1/3)+aux(353) s(5242) =< aux(351)*(3/5)+s(5237)*(1/5)+aux(355) s(5243) =< aux(351)*(3/5)+s(5237)*(1/5)+aux(355) s(5244) =< aux(351)*(3/5)+s(5237)*(1/5)+aux(355) s(5245) =< aux(351)*(3/5)+s(5237)*(1/5)+aux(355) s(5246) =< aux(351)*(3/5)+s(5237)*(1/5)+aux(355) s(5247) =< aux(351)*(3/5)+s(5237)*(1/5)+aux(355) s(5248) =< aux(351)*(2/7)+aux(356) s(5241) =< aux(351)*(2/7)+aux(356) s(5249) =< aux(351)*(4/11)+s(5237)*(1/11)+aux(357) s(5248) =< aux(351)*(4/11)+s(5237)*(1/11)+aux(357) s(5241) =< aux(351)*(4/11)+s(5237)*(1/11)+aux(357) s(5255) =< s(5247)*s(5250) s(5256) =< s(5247)*s(5250) s(5257) =< s(5247)*s(5251) s(5258) =< s(5247)*s(5251) s(5259) =< s(5246)*s(5252) s(5260) =< s(5244)*s(5252) s(5261) =< s(5243)*s(5251) s(5262) =< s(5242)*s(5250) s(5263) =< s(5248)*s(5252) s(5264) =< s(5248)*s(5253) s(5265) =< s(5249)*s(5252) s(5266) =< s(5256) s(5267) =< s(5258) s(5268) =< s(5261) s(5269) =< s(5268)*s(5251) s(5270) =< s(5262) s(5271) =< s(5270)*s(5250) s(5272) =< s(5264) s(5273) =< s(5265) s(5274) =< s(5273)*aux(350) s(5199) =< aux(342) s(5200) =< aux(342) s(5201) =< aux(342) s(5202) =< aux(342) s(5203) =< aux(342) s(5204) =< aux(342) s(5205) =< aux(342) s(5195) =< aux(342) s(5195) =< aux(343) s(5201) =< aux(344) s(5202) =< aux(344) s(5204) =< aux(344) s(5203) =< aux(345) s(5204) =< aux(345) s(5200) =< aux(347) s(5202) =< aux(347) s(5206) =< aux(348) s(5207) =< aux(349) s(5208) =< aux(342)+1 s(5209) =< aux(342)+2 s(5210) =< aux(342) s(5211) =< aux(342)-1 s(5212) =< aux(342) s(5201) =< aux(343)*(1/2)+aux(344) s(5202) =< aux(343)*(1/2)+aux(344) s(5203) =< aux(343)*(1/2)+aux(344) s(5204) =< aux(343)*(1/2)+aux(344) s(5205) =< aux(343)*(1/2)+aux(344) s(5203) =< aux(343)*(1/3)+aux(345) s(5204) =< aux(343)*(1/3)+aux(345) s(5205) =< aux(343)*(1/3)+aux(345) s(5200) =< aux(343)*(3/5)+s(5195)*(1/5)+aux(347) s(5201) =< aux(343)*(3/5)+s(5195)*(1/5)+aux(347) s(5202) =< aux(343)*(3/5)+s(5195)*(1/5)+aux(347) s(5203) =< aux(343)*(3/5)+s(5195)*(1/5)+aux(347) s(5204) =< aux(343)*(3/5)+s(5195)*(1/5)+aux(347) s(5205) =< aux(343)*(3/5)+s(5195)*(1/5)+aux(347) s(5206) =< aux(343)*(2/7)+aux(348) s(5199) =< aux(343)*(2/7)+aux(348) s(5207) =< aux(343)*(4/11)+s(5195)*(1/11)+aux(349) s(5206) =< aux(343)*(4/11)+s(5195)*(1/11)+aux(349) s(5199) =< aux(343)*(4/11)+s(5195)*(1/11)+aux(349) s(5213) =< s(5205)*s(5208) s(5214) =< s(5205)*s(5208) s(5215) =< s(5205)*s(5209) s(5216) =< s(5205)*s(5209) s(5217) =< s(5204)*s(5210) s(5218) =< s(5202)*s(5210) s(5219) =< s(5201)*s(5209) s(5220) =< s(5200)*s(5208) s(5221) =< s(5206)*s(5210) s(5222) =< s(5206)*s(5211) s(5223) =< s(5207)*s(5210) s(5224) =< s(5214) s(5225) =< s(5216) s(5226) =< s(5219) s(5227) =< s(5226)*s(5209) s(5228) =< s(5220) s(5229) =< s(5228)*s(5208) s(5230) =< s(5222) s(5231) =< s(5223) s(5232) =< s(5231)*aux(342) with precondition: [V=2,Out=0,V1>=0,V10>=0] * Chain [64]: 3*s(5577)+9*s(5578)+18*s(5579)+3*s(5580)+3*s(5581)+3*s(5582)+27*s(5583)+12*s(5584)+12*s(5585)+3*s(5590)+3*s(5591)+3*s(5593)+3*s(5595)+3*s(5596)+3*s(5599)+9*s(5602)+9*s(5603)+21*s(5604)+3*s(5605)+21*s(5606)+3*s(5607)+9*s(5608)+21*s(5609)+3*s(5610)+1*s(5619)+3*s(5620)+6*s(5621)+1*s(5622)+1*s(5623)+1*s(5624)+9*s(5625)+4*s(5626)+4*s(5627)+1*s(5632)+1*s(5633)+1*s(5635)+1*s(5637)+1*s(5638)+1*s(5641)+3*s(5644)+3*s(5645)+7*s(5646)+1*s(5647)+7*s(5648)+1*s(5649)+3*s(5650)+7*s(5651)+1*s(5652)+1*s(5654)+9*s(5655)+1*s(5699)+1*s(5744)+4 Such that:s(5744) =< 1 s(5699) =< 3 s(5611) =< V10 s(5654) =< V10+1 s(5612) =< 2*V10+1 s(5613) =< V10/2 s(5614) =< 2/3*V10 s(5615) =< 2/3*V10+1/3 s(5616) =< 2/5*V10 s(5617) =< 3/7*V10 s(5618) =< 3/11*V10 aux(358) =< 2 aux(359) =< V1 aux(360) =< 2*V1+1 aux(361) =< V1/2 aux(362) =< 2/3*V1 aux(363) =< 2/3*V1+1/3 aux(364) =< 2/5*V1 aux(365) =< 3/7*V1 aux(366) =< 3/11*V1 s(5573) =< aux(363) s(5655) =< aux(358) s(5577) =< aux(359) s(5578) =< aux(359) s(5579) =< aux(359) s(5580) =< aux(359) s(5581) =< aux(359) s(5582) =< aux(359) s(5583) =< aux(359) s(5573) =< aux(359) s(5573) =< aux(360) s(5579) =< aux(361) s(5580) =< aux(361) s(5582) =< aux(361) s(5581) =< aux(362) s(5582) =< aux(362) s(5578) =< aux(364) s(5580) =< aux(364) s(5584) =< aux(365) s(5585) =< aux(366) s(5586) =< aux(359)+1 s(5587) =< aux(359)+2 s(5588) =< aux(359) s(5589) =< aux(359)-1 s(5590) =< aux(359) s(5579) =< aux(360)*(1/2)+aux(361) s(5580) =< aux(360)*(1/2)+aux(361) s(5581) =< aux(360)*(1/2)+aux(361) s(5582) =< aux(360)*(1/2)+aux(361) s(5583) =< aux(360)*(1/2)+aux(361) s(5581) =< aux(360)*(1/3)+aux(362) s(5582) =< aux(360)*(1/3)+aux(362) s(5583) =< aux(360)*(1/3)+aux(362) s(5578) =< aux(360)*(3/5)+s(5573)*(1/5)+aux(364) s(5579) =< aux(360)*(3/5)+s(5573)*(1/5)+aux(364) s(5580) =< aux(360)*(3/5)+s(5573)*(1/5)+aux(364) s(5581) =< aux(360)*(3/5)+s(5573)*(1/5)+aux(364) s(5582) =< aux(360)*(3/5)+s(5573)*(1/5)+aux(364) s(5583) =< aux(360)*(3/5)+s(5573)*(1/5)+aux(364) s(5584) =< aux(360)*(2/7)+aux(365) s(5577) =< aux(360)*(2/7)+aux(365) s(5585) =< aux(360)*(4/11)+s(5573)*(1/11)+aux(366) s(5584) =< aux(360)*(4/11)+s(5573)*(1/11)+aux(366) s(5577) =< aux(360)*(4/11)+s(5573)*(1/11)+aux(366) s(5591) =< s(5583)*s(5586) s(5592) =< s(5583)*s(5586) s(5593) =< s(5583)*s(5587) s(5594) =< s(5583)*s(5587) s(5595) =< s(5582)*s(5588) s(5596) =< s(5580)*s(5588) s(5597) =< s(5579)*s(5587) s(5598) =< s(5578)*s(5586) s(5599) =< s(5584)*s(5588) s(5600) =< s(5584)*s(5589) s(5601) =< s(5585)*s(5588) s(5602) =< s(5592) s(5603) =< s(5594) s(5604) =< s(5597) s(5605) =< s(5604)*s(5587) s(5606) =< s(5598) s(5607) =< s(5606)*s(5586) s(5608) =< s(5600) s(5609) =< s(5601) s(5610) =< s(5609)*aux(359) s(5619) =< s(5611) s(5620) =< s(5611) s(5621) =< s(5611) s(5622) =< s(5611) s(5623) =< s(5611) s(5624) =< s(5611) s(5625) =< s(5611) s(5615) =< s(5611) s(5615) =< s(5612) s(5621) =< s(5613) s(5622) =< s(5613) s(5624) =< s(5613) s(5623) =< s(5614) s(5624) =< s(5614) s(5620) =< s(5616) s(5622) =< s(5616) s(5626) =< s(5617) s(5627) =< s(5618) s(5628) =< s(5611)+1 s(5629) =< s(5611)+2 s(5630) =< s(5611) s(5631) =< s(5611)-1 s(5632) =< s(5611) s(5621) =< s(5612)*(1/2)+s(5613) s(5622) =< s(5612)*(1/2)+s(5613) s(5623) =< s(5612)*(1/2)+s(5613) s(5624) =< s(5612)*(1/2)+s(5613) s(5625) =< s(5612)*(1/2)+s(5613) s(5623) =< s(5612)*(1/3)+s(5614) s(5624) =< s(5612)*(1/3)+s(5614) s(5625) =< s(5612)*(1/3)+s(5614) s(5620) =< s(5612)*(3/5)+s(5615)*(1/5)+s(5616) s(5621) =< s(5612)*(3/5)+s(5615)*(1/5)+s(5616) s(5622) =< s(5612)*(3/5)+s(5615)*(1/5)+s(5616) s(5623) =< s(5612)*(3/5)+s(5615)*(1/5)+s(5616) s(5624) =< s(5612)*(3/5)+s(5615)*(1/5)+s(5616) s(5625) =< s(5612)*(3/5)+s(5615)*(1/5)+s(5616) s(5626) =< s(5612)*(2/7)+s(5617) s(5619) =< s(5612)*(2/7)+s(5617) s(5627) =< s(5612)*(4/11)+s(5615)*(1/11)+s(5618) s(5626) =< s(5612)*(4/11)+s(5615)*(1/11)+s(5618) s(5619) =< s(5612)*(4/11)+s(5615)*(1/11)+s(5618) s(5633) =< s(5625)*s(5628) s(5634) =< s(5625)*s(5628) s(5635) =< s(5625)*s(5629) s(5636) =< s(5625)*s(5629) s(5637) =< s(5624)*s(5630) s(5638) =< s(5622)*s(5630) s(5639) =< s(5621)*s(5629) s(5640) =< s(5620)*s(5628) s(5641) =< s(5626)*s(5630) s(5642) =< s(5626)*s(5631) s(5643) =< s(5627)*s(5630) s(5644) =< s(5634) s(5645) =< s(5636) s(5646) =< s(5639) s(5647) =< s(5646)*s(5629) s(5648) =< s(5640) s(5649) =< s(5648)*s(5628) s(5650) =< s(5642) s(5651) =< s(5643) s(5652) =< s(5651)*s(5611) with precondition: [V=2,Out=1,V1>=2,V10>=0] * Chain [63]: 2*s(5754)+6*s(5755)+12*s(5756)+2*s(5757)+2*s(5758)+2*s(5759)+18*s(5760)+8*s(5761)+8*s(5762)+2*s(5767)+2*s(5768)+2*s(5770)+2*s(5772)+2*s(5773)+2*s(5776)+6*s(5779)+6*s(5780)+14*s(5781)+2*s(5782)+14*s(5783)+2*s(5784)+6*s(5785)+14*s(5786)+2*s(5787)+1*s(5796)+3*s(5797)+6*s(5798)+1*s(5799)+1*s(5800)+1*s(5801)+9*s(5802)+4*s(5803)+4*s(5804)+1*s(5809)+1*s(5810)+1*s(5812)+1*s(5814)+1*s(5815)+1*s(5818)+3*s(5821)+3*s(5822)+7*s(5823)+1*s(5824)+7*s(5825)+1*s(5826)+3*s(5827)+7*s(5828)+1*s(5829)+8*s(5830)+6*s(5831)+2*s(5834)+4 Such that:s(5788) =< V10 s(5789) =< 2*V10+1 s(5790) =< V10/2 s(5791) =< 2/3*V10 s(5792) =< 2/3*V10+1/3 s(5793) =< 2/5*V10 s(5794) =< 3/7*V10 s(5795) =< 3/11*V10 aux(369) =< 1 aux(370) =< 2 aux(371) =< V1 aux(372) =< 2*V1+1 aux(373) =< V1/2 aux(374) =< 2/3*V1 aux(375) =< 2/3*V1+1/3 aux(376) =< 2/5*V1 aux(377) =< 3/7*V1 aux(378) =< 3/11*V1 s(5831) =< aux(369) s(5750) =< aux(375) s(5830) =< aux(370) s(5834) =< s(5831)*aux(370) s(5796) =< s(5788) s(5797) =< s(5788) s(5798) =< s(5788) s(5799) =< s(5788) s(5800) =< s(5788) s(5801) =< s(5788) s(5802) =< s(5788) s(5792) =< s(5788) s(5792) =< s(5789) s(5798) =< s(5790) s(5799) =< s(5790) s(5801) =< s(5790) s(5800) =< s(5791) s(5801) =< s(5791) s(5797) =< s(5793) s(5799) =< s(5793) s(5803) =< s(5794) s(5804) =< s(5795) s(5805) =< s(5788)+1 s(5806) =< s(5788)+2 s(5807) =< s(5788) s(5808) =< s(5788)-1 s(5809) =< s(5788) s(5798) =< s(5789)*(1/2)+s(5790) s(5799) =< s(5789)*(1/2)+s(5790) s(5800) =< s(5789)*(1/2)+s(5790) s(5801) =< s(5789)*(1/2)+s(5790) s(5802) =< s(5789)*(1/2)+s(5790) s(5800) =< s(5789)*(1/3)+s(5791) s(5801) =< s(5789)*(1/3)+s(5791) s(5802) =< s(5789)*(1/3)+s(5791) s(5797) =< s(5789)*(3/5)+s(5792)*(1/5)+s(5793) s(5798) =< s(5789)*(3/5)+s(5792)*(1/5)+s(5793) s(5799) =< s(5789)*(3/5)+s(5792)*(1/5)+s(5793) s(5800) =< s(5789)*(3/5)+s(5792)*(1/5)+s(5793) s(5801) =< s(5789)*(3/5)+s(5792)*(1/5)+s(5793) s(5802) =< s(5789)*(3/5)+s(5792)*(1/5)+s(5793) s(5803) =< s(5789)*(2/7)+s(5794) s(5796) =< s(5789)*(2/7)+s(5794) s(5804) =< s(5789)*(4/11)+s(5792)*(1/11)+s(5795) s(5803) =< s(5789)*(4/11)+s(5792)*(1/11)+s(5795) s(5796) =< s(5789)*(4/11)+s(5792)*(1/11)+s(5795) s(5810) =< s(5802)*s(5805) s(5811) =< s(5802)*s(5805) s(5812) =< s(5802)*s(5806) s(5813) =< s(5802)*s(5806) s(5814) =< s(5801)*s(5807) s(5815) =< s(5799)*s(5807) s(5816) =< s(5798)*s(5806) s(5817) =< s(5797)*s(5805) s(5818) =< s(5803)*s(5807) s(5819) =< s(5803)*s(5808) s(5820) =< s(5804)*s(5807) s(5821) =< s(5811) s(5822) =< s(5813) s(5823) =< s(5816) s(5824) =< s(5823)*s(5806) s(5825) =< s(5817) s(5826) =< s(5825)*s(5805) s(5827) =< s(5819) s(5828) =< s(5820) s(5829) =< s(5828)*s(5788) s(5754) =< aux(371) s(5755) =< aux(371) s(5756) =< aux(371) s(5757) =< aux(371) s(5758) =< aux(371) s(5759) =< aux(371) s(5760) =< aux(371) s(5750) =< aux(371) s(5750) =< aux(372) s(5756) =< aux(373) s(5757) =< aux(373) s(5759) =< aux(373) s(5758) =< aux(374) s(5759) =< aux(374) s(5755) =< aux(376) s(5757) =< aux(376) s(5761) =< aux(377) s(5762) =< aux(378) s(5763) =< aux(371)+1 s(5764) =< aux(371)+2 s(5765) =< aux(371) s(5766) =< aux(371)-1 s(5767) =< aux(371) s(5756) =< aux(372)*(1/2)+aux(373) s(5757) =< aux(372)*(1/2)+aux(373) s(5758) =< aux(372)*(1/2)+aux(373) s(5759) =< aux(372)*(1/2)+aux(373) s(5760) =< aux(372)*(1/2)+aux(373) s(5758) =< aux(372)*(1/3)+aux(374) s(5759) =< aux(372)*(1/3)+aux(374) s(5760) =< aux(372)*(1/3)+aux(374) s(5755) =< aux(372)*(3/5)+s(5750)*(1/5)+aux(376) s(5756) =< aux(372)*(3/5)+s(5750)*(1/5)+aux(376) s(5757) =< aux(372)*(3/5)+s(5750)*(1/5)+aux(376) s(5758) =< aux(372)*(3/5)+s(5750)*(1/5)+aux(376) s(5759) =< aux(372)*(3/5)+s(5750)*(1/5)+aux(376) s(5760) =< aux(372)*(3/5)+s(5750)*(1/5)+aux(376) s(5761) =< aux(372)*(2/7)+aux(377) s(5754) =< aux(372)*(2/7)+aux(377) s(5762) =< aux(372)*(4/11)+s(5750)*(1/11)+aux(378) s(5761) =< aux(372)*(4/11)+s(5750)*(1/11)+aux(378) s(5754) =< aux(372)*(4/11)+s(5750)*(1/11)+aux(378) s(5768) =< s(5760)*s(5763) s(5769) =< s(5760)*s(5763) s(5770) =< s(5760)*s(5764) s(5771) =< s(5760)*s(5764) s(5772) =< s(5759)*s(5765) s(5773) =< s(5757)*s(5765) s(5774) =< s(5756)*s(5764) s(5775) =< s(5755)*s(5763) s(5776) =< s(5761)*s(5765) s(5777) =< s(5761)*s(5766) s(5778) =< s(5762)*s(5765) s(5779) =< s(5769) s(5780) =< s(5771) s(5781) =< s(5774) s(5782) =< s(5781)*s(5764) s(5783) =< s(5775) s(5784) =< s(5783)*s(5763) s(5785) =< s(5777) s(5786) =< s(5778) s(5787) =< s(5786)*aux(371) with precondition: [V=2,Out=2,V1>=2,V10>=0] #### Cost of chains of start(V1,V,V10): * Chain [72]: 7*s(6549)+124*s(6550)+3*s(6552)+1*s(6555)+115*s(6558)+27*s(6562)+5*s(6569)+3*s(6571)+1*s(6574)+54*s(6583)+162*s(6584)+324*s(6585)+54*s(6586)+54*s(6587)+54*s(6588)+486*s(6589)+216*s(6590)+216*s(6591)+54*s(6597)+54*s(6599)+54*s(6601)+54*s(6602)+54*s(6605)+162*s(6608)+162*s(6609)+378*s(6610)+54*s(6611)+378*s(6612)+54*s(6613)+162*s(6614)+378*s(6615)+54*s(6616)+76*s(6634)+45*s(6638)+135*s(6639)+270*s(6640)+45*s(6641)+45*s(6642)+45*s(6643)+405*s(6644)+180*s(6645)+180*s(6646)+45*s(6651)+45*s(6653)+45*s(6655)+45*s(6656)+45*s(6659)+135*s(6662)+135*s(6663)+315*s(6664)+45*s(6665)+315*s(6666)+45*s(6667)+135*s(6668)+315*s(6669)+45*s(6670)+5*s(7101)+2*s(7122)+22*s(7304)+66*s(7305)+132*s(7306)+22*s(7307)+22*s(7308)+22*s(7309)+198*s(7310)+88*s(7311)+88*s(7312)+22*s(7317)+22*s(7318)+22*s(7320)+22*s(7322)+22*s(7323)+22*s(7326)+66*s(7329)+66*s(7330)+154*s(7331)+22*s(7332)+154*s(7333)+22*s(7334)+66*s(7335)+154*s(7336)+22*s(7337)+6*s(7436)+6*s(7611)+6 Such that:s(6571) =< V1-V s(6552) =< V-V10 aux(436) =< 1 aux(437) =< 2 aux(438) =< 3 aux(439) =< V1 aux(440) =< 2*V1+1 aux(441) =< V1/2 aux(442) =< 2/3*V1 aux(443) =< 2/3*V1+1/3 aux(444) =< 2/5*V1 aux(445) =< 3/7*V1 aux(446) =< 3/11*V1 aux(447) =< V aux(448) =< 2*V+1 aux(449) =< V/2 aux(450) =< 2/3*V aux(451) =< 2/3*V+1/3 aux(452) =< 2/5*V aux(453) =< 3/7*V aux(454) =< 3/11*V aux(455) =< V10 aux(456) =< V10+1 aux(457) =< 2*V10+1 aux(458) =< V10/2 aux(459) =< 2/3*V10 aux(460) =< 2/3*V10+1/3 aux(461) =< 2/5*V10 aux(462) =< 3/7*V10 aux(463) =< 3/11*V10 s(6562) =< aux(436) s(6634) =< aux(437) s(6558) =< aux(439) s(6579) =< aux(443) s(6550) =< aux(447) s(6636) =< aux(451) s(6549) =< aux(456) s(6583) =< aux(439) s(6584) =< aux(439) s(6585) =< aux(439) s(6586) =< aux(439) s(6587) =< aux(439) s(6588) =< aux(439) s(6589) =< aux(439) s(6579) =< aux(439) s(6579) =< aux(440) s(6585) =< aux(441) s(6586) =< aux(441) s(6588) =< aux(441) s(6587) =< aux(442) s(6588) =< aux(442) s(6584) =< aux(444) s(6586) =< aux(444) s(6590) =< aux(445) s(6591) =< aux(446) s(6592) =< aux(439)+1 s(6593) =< aux(439)+2 s(6594) =< aux(439) s(6595) =< aux(439)-1 s(6585) =< aux(440)*(1/2)+aux(441) s(6586) =< aux(440)*(1/2)+aux(441) s(6587) =< aux(440)*(1/2)+aux(441) s(6588) =< aux(440)*(1/2)+aux(441) s(6589) =< aux(440)*(1/2)+aux(441) s(6587) =< aux(440)*(1/3)+aux(442) s(6588) =< aux(440)*(1/3)+aux(442) s(6589) =< aux(440)*(1/3)+aux(442) s(6584) =< aux(440)*(3/5)+s(6579)*(1/5)+aux(444) s(6585) =< aux(440)*(3/5)+s(6579)*(1/5)+aux(444) s(6586) =< aux(440)*(3/5)+s(6579)*(1/5)+aux(444) s(6587) =< aux(440)*(3/5)+s(6579)*(1/5)+aux(444) s(6588) =< aux(440)*(3/5)+s(6579)*(1/5)+aux(444) s(6589) =< aux(440)*(3/5)+s(6579)*(1/5)+aux(444) s(6590) =< aux(440)*(2/7)+aux(445) s(6583) =< aux(440)*(2/7)+aux(445) s(6591) =< aux(440)*(4/11)+s(6579)*(1/11)+aux(446) s(6590) =< aux(440)*(4/11)+s(6579)*(1/11)+aux(446) s(6583) =< aux(440)*(4/11)+s(6579)*(1/11)+aux(446) s(6597) =< s(6589)*s(6592) s(6598) =< s(6589)*s(6592) s(6599) =< s(6589)*s(6593) s(6600) =< s(6589)*s(6593) s(6601) =< s(6588)*s(6594) s(6602) =< s(6586)*s(6594) s(6603) =< s(6585)*s(6593) s(6604) =< s(6584)*s(6592) s(6605) =< s(6590)*s(6594) s(6606) =< s(6590)*s(6595) s(6607) =< s(6591)*s(6594) s(6608) =< s(6598) s(6609) =< s(6600) s(6610) =< s(6603) s(6611) =< s(6610)*s(6593) s(6612) =< s(6604) s(6613) =< s(6612)*s(6592) s(6614) =< s(6606) s(6615) =< s(6607) s(6616) =< s(6615)*aux(439) s(6638) =< aux(447) s(6639) =< aux(447) s(6640) =< aux(447) s(6641) =< aux(447) s(6642) =< aux(447) s(6643) =< aux(447) s(6644) =< aux(447) s(6636) =< aux(447) s(6636) =< aux(448) s(6640) =< aux(449) s(6641) =< aux(449) s(6643) =< aux(449) s(6642) =< aux(450) s(6643) =< aux(450) s(6639) =< aux(452) s(6641) =< aux(452) s(6645) =< aux(453) s(6646) =< aux(454) s(6647) =< aux(447)+1 s(6648) =< aux(447)+2 s(6649) =< aux(447) s(6650) =< aux(447)-1 s(6640) =< aux(448)*(1/2)+aux(449) s(6641) =< aux(448)*(1/2)+aux(449) s(6642) =< aux(448)*(1/2)+aux(449) s(6643) =< aux(448)*(1/2)+aux(449) s(6644) =< aux(448)*(1/2)+aux(449) s(6642) =< aux(448)*(1/3)+aux(450) s(6643) =< aux(448)*(1/3)+aux(450) s(6644) =< aux(448)*(1/3)+aux(450) s(6639) =< aux(448)*(3/5)+s(6636)*(1/5)+aux(452) s(6640) =< aux(448)*(3/5)+s(6636)*(1/5)+aux(452) s(6641) =< aux(448)*(3/5)+s(6636)*(1/5)+aux(452) s(6642) =< aux(448)*(3/5)+s(6636)*(1/5)+aux(452) s(6643) =< aux(448)*(3/5)+s(6636)*(1/5)+aux(452) s(6644) =< aux(448)*(3/5)+s(6636)*(1/5)+aux(452) s(6645) =< aux(448)*(2/7)+aux(453) s(6638) =< aux(448)*(2/7)+aux(453) s(6646) =< aux(448)*(4/11)+s(6636)*(1/11)+aux(454) s(6645) =< aux(448)*(4/11)+s(6636)*(1/11)+aux(454) s(6638) =< aux(448)*(4/11)+s(6636)*(1/11)+aux(454) s(6651) =< s(6644)*s(6647) s(6652) =< s(6644)*s(6647) s(6653) =< s(6644)*s(6648) s(6654) =< s(6644)*s(6648) s(6655) =< s(6643)*s(6649) s(6656) =< s(6641)*s(6649) s(6657) =< s(6640)*s(6648) s(6658) =< s(6639)*s(6647) s(6659) =< s(6645)*s(6649) s(6660) =< s(6645)*s(6650) s(6661) =< s(6646)*s(6649) s(6662) =< s(6652) s(6663) =< s(6654) s(6664) =< s(6657) s(6665) =< s(6664)*s(6648) s(6666) =< s(6658) s(6667) =< s(6666)*s(6647) s(6668) =< s(6660) s(6669) =< s(6661) s(6670) =< s(6669)*aux(447) s(7101) =< s(6562)*aux(437) s(7436) =< aux(438) s(7303) =< aux(460) s(7304) =< aux(455) s(7305) =< aux(455) s(7306) =< aux(455) s(7307) =< aux(455) s(7308) =< aux(455) s(7309) =< aux(455) s(7310) =< aux(455) s(7303) =< aux(455) s(7303) =< aux(457) s(7306) =< aux(458) s(7307) =< aux(458) s(7309) =< aux(458) s(7308) =< aux(459) s(7309) =< aux(459) s(7305) =< aux(461) s(7307) =< aux(461) s(7311) =< aux(462) s(7312) =< aux(463) s(7313) =< aux(455)+1 s(7314) =< aux(455)+2 s(7315) =< aux(455) s(7316) =< aux(455)-1 s(7317) =< aux(455) s(7306) =< aux(457)*(1/2)+aux(458) s(7307) =< aux(457)*(1/2)+aux(458) s(7308) =< aux(457)*(1/2)+aux(458) s(7309) =< aux(457)*(1/2)+aux(458) s(7310) =< aux(457)*(1/2)+aux(458) s(7308) =< aux(457)*(1/3)+aux(459) s(7309) =< aux(457)*(1/3)+aux(459) s(7310) =< aux(457)*(1/3)+aux(459) s(7305) =< aux(457)*(3/5)+s(7303)*(1/5)+aux(461) s(7306) =< aux(457)*(3/5)+s(7303)*(1/5)+aux(461) s(7307) =< aux(457)*(3/5)+s(7303)*(1/5)+aux(461) s(7308) =< aux(457)*(3/5)+s(7303)*(1/5)+aux(461) s(7309) =< aux(457)*(3/5)+s(7303)*(1/5)+aux(461) s(7310) =< aux(457)*(3/5)+s(7303)*(1/5)+aux(461) s(7311) =< aux(457)*(2/7)+aux(462) s(7304) =< aux(457)*(2/7)+aux(462) s(7312) =< aux(457)*(4/11)+s(7303)*(1/11)+aux(463) s(7311) =< aux(457)*(4/11)+s(7303)*(1/11)+aux(463) s(7304) =< aux(457)*(4/11)+s(7303)*(1/11)+aux(463) s(7318) =< s(7310)*s(7313) s(7319) =< s(7310)*s(7313) s(7320) =< s(7310)*s(7314) s(7321) =< s(7310)*s(7314) s(7322) =< s(7309)*s(7315) s(7323) =< s(7307)*s(7315) s(7324) =< s(7306)*s(7314) s(7325) =< s(7305)*s(7313) s(7326) =< s(7311)*s(7315) s(7327) =< s(7311)*s(7316) s(7328) =< s(7312)*s(7315) s(7329) =< s(7319) s(7330) =< s(7321) s(7331) =< s(7324) s(7332) =< s(7331)*s(7314) s(7333) =< s(7325) s(7334) =< s(7333)*s(7313) s(7335) =< s(7327) s(7336) =< s(7328) s(7337) =< s(7336)*aux(455) s(7611) =< s(6550)*aux(447) s(7122) =< s(6634)*aux(437) s(6569) =< s(6558)*aux(439) s(6574) =< s(6571)*aux(439) s(6555) =< s(6552)*aux(447) with precondition: [] Closed-form bounds of start(V1,V,V10): ------------------------------------- * Chain [72] with precondition: [] - Upper bound: nat(V1)*3355+221+nat(V1)*1625*nat(V1)+nat(V1)*108*nat(V1)*nat(V1)+nat(V1)*54*nat(V1)*nat(3/11*V1)+nat(V1)*54*nat(3/7*V1)+nat(V1)*378*nat(3/11*V1)+nat(V1-V)*nat(V1)+nat(V)*2824+nat(V)*1356*nat(V)+nat(V)*90*nat(V)*nat(V)+nat(V)*45*nat(V)*nat(3/11*V)+nat(V)*45*nat(3/7*V)+nat(V)*315*nat(3/11*V)+nat(V-V10)*nat(V)+nat(V10)*1342+nat(V10)*660*nat(V10)+nat(V10)*44*nat(V10)*nat(V10)+nat(V10)*22*nat(V10)*nat(3/11*V10)+nat(V10)*22*nat(3/7*V10)+nat(V10)*154*nat(3/11*V10)+nat(nat(V1)+ -1)*162*nat(3/7*V1)+nat(nat(V)+ -1)*135*nat(3/7*V)+nat(nat(V10)+ -1)*66*nat(3/7*V10)+nat(3/7*V1)*216+nat(3/7*V)*180+nat(3/7*V10)*88+nat(3/11*V1)*216+nat(3/11*V)*180+nat(3/11*V10)*88+nat(V10+1)*7+nat(V1-V)*3+nat(V-V10)*3 - Complexity: n^3 ### Maximum cost of start(V1,V,V10): nat(V1)*3355+221+nat(V1)*1625*nat(V1)+nat(V1)*108*nat(V1)*nat(V1)+nat(V1)*54*nat(V1)*nat(3/11*V1)+nat(V1)*54*nat(3/7*V1)+nat(V1)*378*nat(3/11*V1)+nat(V1-V)*nat(V1)+nat(V)*2824+nat(V)*1356*nat(V)+nat(V)*90*nat(V)*nat(V)+nat(V)*45*nat(V)*nat(3/11*V)+nat(V)*45*nat(3/7*V)+nat(V)*315*nat(3/11*V)+nat(V-V10)*nat(V)+nat(V10)*1342+nat(V10)*660*nat(V10)+nat(V10)*44*nat(V10)*nat(V10)+nat(V10)*22*nat(V10)*nat(3/11*V10)+nat(V10)*22*nat(3/7*V10)+nat(V10)*154*nat(3/11*V10)+nat(nat(V1)+ -1)*162*nat(3/7*V1)+nat(nat(V)+ -1)*135*nat(3/7*V)+nat(nat(V10)+ -1)*66*nat(3/7*V10)+nat(3/7*V1)*216+nat(3/7*V)*180+nat(3/7*V10)*88+nat(3/11*V1)*216+nat(3/11*V)*180+nat(3/11*V10)*88+nat(V10+1)*7+nat(V1-V)*3+nat(V-V10)*3 Asymptotic class: n^3 * Total analysis performed in 33389 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: lt(0', s(x)) -> true lt(x, 0') -> false lt(s(x), s(y)) -> lt(x, y) minus(x, y) -> help(lt(y, x), x, y) help(true, x, y) -> s(minus(x, s(y))) help(false, x, y) -> 0' The (relative) TRS S consists of the following rules: encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_lt(x_1, x_2)) -> lt(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_help(x_1, x_2, x_3)) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) encode_lt(x_1, x_2) -> lt(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_help(x_1, x_2, x_3) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) Rewrite Strategy: INNERMOST ---------------------------------------- (17) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (18) Obligation: Innermost TRS: Rules: lt(0', s(x)) -> true lt(x, 0') -> false lt(s(x), s(y)) -> lt(x, y) minus(x, y) -> help(lt(y, x), x, y) help(true, x, y) -> s(minus(x, s(y))) help(false, x, y) -> 0' encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_lt(x_1, x_2)) -> lt(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_help(x_1, x_2, x_3)) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) encode_lt(x_1, x_2) -> lt(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_help(x_1, x_2, x_3) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) Types: lt :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help 0' :: 0':s:true:false:cons_lt:cons_minus:cons_help s :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help true :: 0':s:true:false:cons_lt:cons_minus:cons_help false :: 0':s:true:false:cons_lt:cons_minus:cons_help minus :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help help :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encArg :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help cons_lt :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help cons_minus :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help cons_help :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_lt :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_0 :: 0':s:true:false:cons_lt:cons_minus:cons_help encode_s :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_true :: 0':s:true:false:cons_lt:cons_minus:cons_help encode_false :: 0':s:true:false:cons_lt:cons_minus:cons_help encode_minus :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_help :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help hole_0':s:true:false:cons_lt:cons_minus:cons_help1_4 :: 0':s:true:false:cons_lt:cons_minus:cons_help gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4 :: Nat -> 0':s:true:false:cons_lt:cons_minus:cons_help ---------------------------------------- (19) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: lt, minus, help, encArg They will be analysed ascendingly in the following order: lt < minus lt < encArg minus = help minus < encArg help < encArg ---------------------------------------- (20) Obligation: Innermost TRS: Rules: lt(0', s(x)) -> true lt(x, 0') -> false lt(s(x), s(y)) -> lt(x, y) minus(x, y) -> help(lt(y, x), x, y) help(true, x, y) -> s(minus(x, s(y))) help(false, x, y) -> 0' encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_lt(x_1, x_2)) -> lt(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_help(x_1, x_2, x_3)) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) encode_lt(x_1, x_2) -> lt(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_help(x_1, x_2, x_3) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) Types: lt :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help 0' :: 0':s:true:false:cons_lt:cons_minus:cons_help s :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help true :: 0':s:true:false:cons_lt:cons_minus:cons_help false :: 0':s:true:false:cons_lt:cons_minus:cons_help minus :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help help :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encArg :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help cons_lt :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help cons_minus :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help cons_help :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_lt :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_0 :: 0':s:true:false:cons_lt:cons_minus:cons_help encode_s :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_true :: 0':s:true:false:cons_lt:cons_minus:cons_help encode_false :: 0':s:true:false:cons_lt:cons_minus:cons_help encode_minus :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_help :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help hole_0':s:true:false:cons_lt:cons_minus:cons_help1_4 :: 0':s:true:false:cons_lt:cons_minus:cons_help gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4 :: Nat -> 0':s:true:false:cons_lt:cons_minus:cons_help Generator Equations: gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(0) <=> 0' gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(+(x, 1)) <=> s(gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(x)) The following defined symbols remain to be analysed: lt, minus, help, encArg They will be analysed ascendingly in the following order: lt < minus lt < encArg minus = help minus < encArg help < encArg ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: lt(gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(n4_4), gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(+(1, n4_4))) -> true, rt in Omega(1 + n4_4) Induction Base: lt(gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(0), gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(+(1, 0))) ->_R^Omega(1) true Induction Step: lt(gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(+(n4_4, 1)), gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(+(1, +(n4_4, 1)))) ->_R^Omega(1) lt(gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(n4_4), gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(+(1, n4_4))) ->_IH true 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: lt(0', s(x)) -> true lt(x, 0') -> false lt(s(x), s(y)) -> lt(x, y) minus(x, y) -> help(lt(y, x), x, y) help(true, x, y) -> s(minus(x, s(y))) help(false, x, y) -> 0' encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_lt(x_1, x_2)) -> lt(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_help(x_1, x_2, x_3)) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) encode_lt(x_1, x_2) -> lt(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_help(x_1, x_2, x_3) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) Types: lt :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help 0' :: 0':s:true:false:cons_lt:cons_minus:cons_help s :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help true :: 0':s:true:false:cons_lt:cons_minus:cons_help false :: 0':s:true:false:cons_lt:cons_minus:cons_help minus :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help help :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encArg :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help cons_lt :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help cons_minus :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help cons_help :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_lt :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_0 :: 0':s:true:false:cons_lt:cons_minus:cons_help encode_s :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_true :: 0':s:true:false:cons_lt:cons_minus:cons_help encode_false :: 0':s:true:false:cons_lt:cons_minus:cons_help encode_minus :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_help :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help hole_0':s:true:false:cons_lt:cons_minus:cons_help1_4 :: 0':s:true:false:cons_lt:cons_minus:cons_help gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4 :: Nat -> 0':s:true:false:cons_lt:cons_minus:cons_help Generator Equations: gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(0) <=> 0' gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(+(x, 1)) <=> s(gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(x)) The following defined symbols remain to be analysed: lt, minus, help, encArg They will be analysed ascendingly in the following order: lt < minus lt < encArg minus = help minus < encArg help < encArg ---------------------------------------- (24) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (25) BOUNDS(n^1, INF) ---------------------------------------- (26) Obligation: Innermost TRS: Rules: lt(0', s(x)) -> true lt(x, 0') -> false lt(s(x), s(y)) -> lt(x, y) minus(x, y) -> help(lt(y, x), x, y) help(true, x, y) -> s(minus(x, s(y))) help(false, x, y) -> 0' encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_lt(x_1, x_2)) -> lt(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_help(x_1, x_2, x_3)) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) encode_lt(x_1, x_2) -> lt(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_help(x_1, x_2, x_3) -> help(encArg(x_1), encArg(x_2), encArg(x_3)) Types: lt :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help 0' :: 0':s:true:false:cons_lt:cons_minus:cons_help s :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help true :: 0':s:true:false:cons_lt:cons_minus:cons_help false :: 0':s:true:false:cons_lt:cons_minus:cons_help minus :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help help :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encArg :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help cons_lt :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help cons_minus :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help cons_help :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_lt :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_0 :: 0':s:true:false:cons_lt:cons_minus:cons_help encode_s :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_true :: 0':s:true:false:cons_lt:cons_minus:cons_help encode_false :: 0':s:true:false:cons_lt:cons_minus:cons_help encode_minus :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help encode_help :: 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help -> 0':s:true:false:cons_lt:cons_minus:cons_help hole_0':s:true:false:cons_lt:cons_minus:cons_help1_4 :: 0':s:true:false:cons_lt:cons_minus:cons_help gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4 :: Nat -> 0':s:true:false:cons_lt:cons_minus:cons_help Lemmas: lt(gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(n4_4), gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(+(1, n4_4))) -> true, rt in Omega(1 + n4_4) Generator Equations: gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(0) <=> 0' gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(+(x, 1)) <=> s(gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(x)) The following defined symbols remain to be analysed: help, minus, encArg They will be analysed ascendingly in the following order: minus = help minus < encArg help < encArg ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(n1546_4)) -> gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(n1546_4), rt in Omega(0) Induction Base: encArg(gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(0)) ->_R^Omega(0) 0' Induction Step: encArg(gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(+(n1546_4, 1))) ->_R^Omega(0) s(encArg(gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(n1546_4))) ->_IH s(gen_0':s:true:false:cons_lt:cons_minus:cons_help2_4(c1547_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)