/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 298 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), 12 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 57.1 s] (14) BOUNDS(1, n^3) (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (16) TRS for Loop Detection (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) TRS for Loop Detection ---------------------------------------- (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: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(neq(x, 0), y, y) cond2(false, x, y) -> cond1(neq(x, 0), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) neq(0, 0) -> false neq(0, s(x)) -> true neq(s(x), 0) -> true neq(s(x), s(y)) -> neq(x, y) p(0) -> 0 p(s(x)) -> x 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(true) -> true encArg(0) -> 0 encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(neq(x, 0), y, y) cond2(false, x, y) -> cond1(neq(x, 0), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) neq(0, 0) -> false neq(0, s(x)) -> true neq(s(x), 0) -> true neq(s(x), s(y)) -> neq(x, y) p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(0) -> 0 encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(neq(x, 0), y, y) cond2(false, x, y) -> cond1(neq(x, 0), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) neq(0, 0) -> false neq(0, s(x)) -> true neq(s(x), 0) -> true neq(s(x), s(y)) -> neq(x, y) p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(0) -> 0 encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) [1] cond2(true, x, y) -> cond1(neq(x, 0), y, y) [1] cond2(false, x, y) -> cond1(neq(x, 0), p(x), y) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] neq(0, 0) -> false [1] neq(0, s(x)) -> true [1] neq(s(x), 0) -> true [1] neq(s(x), s(y)) -> neq(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(true) -> true [0] encArg(0) -> 0 [0] encArg(false) -> false [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0] encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_true -> true [0] encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0] encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_false -> false [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) [1] cond2(true, x, y) -> cond1(neq(x, 0), y, y) [1] cond2(false, x, y) -> cond1(neq(x, 0), p(x), y) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] neq(0, 0) -> false [1] neq(0, s(x)) -> true [1] neq(s(x), 0) -> true [1] neq(s(x), s(y)) -> neq(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(true) -> true [0] encArg(0) -> 0 [0] encArg(false) -> false [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0] encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_true -> true [0] encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0] encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_false -> false [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] The TRS has the following type information: cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p neq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p 0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encArg :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_neq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p cons_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_neq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p encode_s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p 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_cond1(v0, v1, v2) -> null_encode_cond1 [0] encode_true -> null_encode_true [0] encode_cond2(v0, v1, v2) -> null_encode_cond2 [0] encode_gr(v0, v1) -> null_encode_gr [0] encode_neq(v0, v1) -> null_encode_neq [0] encode_0 -> null_encode_0 [0] encode_false -> null_encode_false [0] encode_p(v0) -> null_encode_p [0] encode_s(v0) -> null_encode_s [0] cond1(v0, v1, v2) -> null_cond1 [0] cond2(v0, v1, v2) -> null_cond2 [0] gr(v0, v1) -> null_gr [0] neq(v0, v1) -> null_neq [0] p(v0) -> null_p [0] And the following fresh constants: null_encArg, null_encode_cond1, null_encode_true, null_encode_cond2, null_encode_gr, null_encode_neq, null_encode_0, null_encode_false, null_encode_p, null_encode_s, null_cond1, null_cond2, null_gr, null_neq, null_p ---------------------------------------- (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: cond1(true, x, y) -> cond2(gr(x, y), x, y) [1] cond2(true, x, y) -> cond1(neq(x, 0), y, y) [1] cond2(false, x, y) -> cond1(neq(x, 0), p(x), y) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] neq(0, 0) -> false [1] neq(0, s(x)) -> true [1] neq(s(x), 0) -> true [1] neq(s(x), s(y)) -> neq(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(true) -> true [0] encArg(0) -> 0 [0] encArg(false) -> false [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0] encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_true -> true [0] encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0] encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_false -> false [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encArg(v0) -> null_encArg [0] encode_cond1(v0, v1, v2) -> null_encode_cond1 [0] encode_true -> null_encode_true [0] encode_cond2(v0, v1, v2) -> null_encode_cond2 [0] encode_gr(v0, v1) -> null_encode_gr [0] encode_neq(v0, v1) -> null_encode_neq [0] encode_0 -> null_encode_0 [0] encode_false -> null_encode_false [0] encode_p(v0) -> null_encode_p [0] encode_s(v0) -> null_encode_s [0] cond1(v0, v1, v2) -> null_cond1 [0] cond2(v0, v1, v2) -> null_cond2 [0] gr(v0, v1) -> null_gr [0] neq(v0, v1) -> null_neq [0] p(v0) -> null_p [0] The TRS has the following type information: cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p neq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p 0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p encArg :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p cons_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p cons_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p cons_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p cons_neq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p cons_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p encode_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p encode_true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p encode_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p encode_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p encode_neq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p encode_0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p encode_false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p encode_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p encode_s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p null_encArg :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_neq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p null_encode_s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p null_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p null_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p null_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p null_neq :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p null_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_neq:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_neq:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_neq:null_p 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: true => 2 0 => 0 false => 1 null_encArg => 0 null_encode_cond1 => 0 null_encode_true => 0 null_encode_cond2 => 0 null_encode_gr => 0 null_encode_neq => 0 null_encode_0 => 0 null_encode_false => 0 null_encode_p => 0 null_encode_s => 0 null_cond1 => 0 null_cond2 => 0 null_gr => 0 null_neq => 0 null_p => 0 ---------------------------------------- (12) Obligation: Complexity RNTS consisting of the following rules: cond1(z, z', z'') -{ 1 }-> cond2(gr(x, y), x, y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0 cond1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 cond2(z, z', z'') -{ 1 }-> cond1(neq(x, 0), y, y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0 cond2(z, z', z'') -{ 1 }-> cond1(neq(x, 0), p(x), y) :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0 cond2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encArg(z) -{ 0 }-> p(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> neq(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> cond2(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 }-> cond1(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_cond1(z, z', z'') -{ 0 }-> cond1(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_cond1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_cond2(z, z', z'') -{ 0 }-> cond2(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_cond2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_false -{ 0 }-> 1 :|: encode_false -{ 0 }-> 0 :|: encode_gr(z, z') -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_neq(z, z') -{ 0 }-> neq(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_neq(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_p(z) -{ 0 }-> p(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 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 :|: gr(z, z') -{ 1 }-> gr(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x gr(z, z') -{ 1 }-> 2 :|: x >= 0, z = 1 + x, z' = 0 gr(z, z') -{ 1 }-> 1 :|: z' = x, x >= 0, z = 0 gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 neq(z, z') -{ 1 }-> neq(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x neq(z, z') -{ 1 }-> 2 :|: z' = 1 + x, x >= 0, z = 0 neq(z, z') -{ 1 }-> 2 :|: x >= 0, z = 1 + x, z' = 0 neq(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0 neq(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 p(z) -{ 1 }-> x :|: x >= 0, z = 1 + x p(z) -{ 1 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 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, V2),0,[cond1(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]). eq(start(V1, V, V2),0,[cond2(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]). eq(start(V1, V, V2),0,[gr(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V2),0,[neq(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V2),0,[p(V1, Out)],[V1 >= 0]). eq(start(V1, V, V2),0,[encArg(V1, Out)],[V1 >= 0]). eq(start(V1, V, V2),0,[fun(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]). eq(start(V1, V, V2),0,[fun1(Out)],[]). eq(start(V1, V, V2),0,[fun2(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]). eq(start(V1, V, V2),0,[fun3(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V2),0,[fun4(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V2),0,[fun5(Out)],[]). eq(start(V1, V, V2),0,[fun6(Out)],[]). eq(start(V1, V, V2),0,[fun7(V1, Out)],[V1 >= 0]). eq(start(V1, V, V2),0,[fun8(V1, Out)],[V1 >= 0]). eq(cond1(V1, V, V2, Out),1,[gr(V4, V3, Ret0),cond2(Ret0, V4, V3, Ret)],[Out = Ret,V1 = 2,V = V4,V2 = V3,V4 >= 0,V3 >= 0]). eq(cond2(V1, V, V2, Out),1,[neq(V5, 0, Ret01),cond1(Ret01, V6, V6, Ret1)],[Out = Ret1,V1 = 2,V = V5,V2 = V6,V5 >= 0,V6 >= 0]). eq(cond2(V1, V, V2, Out),1,[neq(V8, 0, Ret02),p(V8, Ret11),cond1(Ret02, Ret11, V7, Ret2)],[Out = Ret2,V = V8,V2 = V7,V1 = 1,V8 >= 0,V7 >= 0]). eq(gr(V1, V, Out),1,[],[Out = 1,V = V9,V9 >= 0,V1 = 0]). eq(gr(V1, V, Out),1,[],[Out = 2,V10 >= 0,V1 = 1 + V10,V = 0]). eq(gr(V1, V, Out),1,[gr(V12, V11, Ret3)],[Out = Ret3,V = 1 + V11,V12 >= 0,V11 >= 0,V1 = 1 + V12]). eq(neq(V1, V, Out),1,[],[Out = 1,V1 = 0,V = 0]). eq(neq(V1, V, Out),1,[],[Out = 2,V = 1 + V13,V13 >= 0,V1 = 0]). eq(neq(V1, V, Out),1,[],[Out = 2,V14 >= 0,V1 = 1 + V14,V = 0]). eq(neq(V1, V, Out),1,[neq(V16, V15, Ret4)],[Out = Ret4,V = 1 + V15,V16 >= 0,V15 >= 0,V1 = 1 + V16]). eq(p(V1, Out),1,[],[Out = 0,V1 = 0]). eq(p(V1, Out),1,[],[Out = V17,V17 >= 0,V1 = 1 + V17]). eq(encArg(V1, Out),0,[],[Out = 2,V1 = 2]). eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]). eq(encArg(V1, Out),0,[],[Out = 1,V1 = 1]). eq(encArg(V1, Out),0,[encArg(V18, Ret12)],[Out = 1 + Ret12,V1 = 1 + V18,V18 >= 0]). eq(encArg(V1, Out),0,[encArg(V20, Ret03),encArg(V21, Ret13),encArg(V19, Ret21),cond1(Ret03, Ret13, Ret21, Ret5)],[Out = Ret5,V20 >= 0,V1 = 1 + V19 + V20 + V21,V19 >= 0,V21 >= 0]). eq(encArg(V1, Out),0,[encArg(V22, Ret04),encArg(V24, Ret14),encArg(V23, Ret22),cond2(Ret04, Ret14, Ret22, Ret6)],[Out = Ret6,V22 >= 0,V1 = 1 + V22 + V23 + V24,V23 >= 0,V24 >= 0]). eq(encArg(V1, Out),0,[encArg(V26, Ret05),encArg(V25, Ret15),gr(Ret05, Ret15, Ret7)],[Out = Ret7,V26 >= 0,V1 = 1 + V25 + V26,V25 >= 0]). eq(encArg(V1, Out),0,[encArg(V28, Ret06),encArg(V27, Ret16),neq(Ret06, Ret16, Ret8)],[Out = Ret8,V28 >= 0,V1 = 1 + V27 + V28,V27 >= 0]). eq(encArg(V1, Out),0,[encArg(V29, Ret07),p(Ret07, Ret9)],[Out = Ret9,V1 = 1 + V29,V29 >= 0]). eq(fun(V1, V, V2, Out),0,[encArg(V31, Ret08),encArg(V32, Ret17),encArg(V30, Ret23),cond1(Ret08, Ret17, Ret23, Ret10)],[Out = Ret10,V31 >= 0,V30 >= 0,V32 >= 0,V1 = V31,V = V32,V2 = V30]). eq(fun1(Out),0,[],[Out = 2]). eq(fun2(V1, V, V2, Out),0,[encArg(V35, Ret09),encArg(V34, Ret18),encArg(V33, Ret24),cond2(Ret09, Ret18, Ret24, Ret19)],[Out = Ret19,V35 >= 0,V33 >= 0,V34 >= 0,V1 = V35,V = V34,V2 = V33]). eq(fun3(V1, V, Out),0,[encArg(V37, Ret010),encArg(V36, Ret110),gr(Ret010, Ret110, Ret20)],[Out = Ret20,V37 >= 0,V36 >= 0,V1 = V37,V = V36]). eq(fun4(V1, V, Out),0,[encArg(V38, Ret011),encArg(V39, Ret111),neq(Ret011, Ret111, Ret25)],[Out = Ret25,V38 >= 0,V39 >= 0,V1 = V38,V = V39]). eq(fun5(Out),0,[],[Out = 0]). eq(fun6(Out),0,[],[Out = 1]). eq(fun7(V1, Out),0,[encArg(V40, Ret012),p(Ret012, Ret26)],[Out = Ret26,V40 >= 0,V1 = V40]). eq(fun8(V1, Out),0,[encArg(V41, Ret112)],[Out = 1 + Ret112,V41 >= 0,V1 = V41]). eq(encArg(V1, Out),0,[],[Out = 0,V42 >= 0,V1 = V42]). eq(fun(V1, V, V2, Out),0,[],[Out = 0,V44 >= 0,V2 = V45,V43 >= 0,V1 = V44,V = V43,V45 >= 0]). eq(fun1(Out),0,[],[Out = 0]). eq(fun2(V1, V, V2, Out),0,[],[Out = 0,V48 >= 0,V2 = V46,V47 >= 0,V1 = V48,V = V47,V46 >= 0]). eq(fun3(V1, V, Out),0,[],[Out = 0,V49 >= 0,V50 >= 0,V1 = V49,V = V50]). eq(fun4(V1, V, Out),0,[],[Out = 0,V51 >= 0,V52 >= 0,V1 = V51,V = V52]). eq(fun6(Out),0,[],[Out = 0]). eq(fun7(V1, Out),0,[],[Out = 0,V53 >= 0,V1 = V53]). eq(fun8(V1, Out),0,[],[Out = 0,V54 >= 0,V1 = V54]). eq(cond1(V1, V, V2, Out),0,[],[Out = 0,V55 >= 0,V2 = V57,V56 >= 0,V1 = V55,V = V56,V57 >= 0]). eq(cond2(V1, V, V2, Out),0,[],[Out = 0,V58 >= 0,V2 = V60,V59 >= 0,V1 = V58,V = V59,V60 >= 0]). eq(gr(V1, V, Out),0,[],[Out = 0,V62 >= 0,V61 >= 0,V1 = V62,V = V61]). eq(neq(V1, V, Out),0,[],[Out = 0,V64 >= 0,V63 >= 0,V1 = V64,V = V63]). eq(p(V1, Out),0,[],[Out = 0,V65 >= 0,V1 = V65]). input_output_vars(cond1(V1,V,V2,Out),[V1,V,V2],[Out]). input_output_vars(cond2(V1,V,V2,Out),[V1,V,V2],[Out]). input_output_vars(gr(V1,V,Out),[V1,V],[Out]). input_output_vars(neq(V1,V,Out),[V1,V],[Out]). input_output_vars(p(V1,Out),[V1],[Out]). input_output_vars(encArg(V1,Out),[V1],[Out]). input_output_vars(fun(V1,V,V2,Out),[V1,V,V2],[Out]). input_output_vars(fun1(Out),[],[Out]). input_output_vars(fun2(V1,V,V2,Out),[V1,V,V2],[Out]). input_output_vars(fun3(V1,V,Out),[V1,V],[Out]). input_output_vars(fun4(V1,V,Out),[V1,V],[Out]). input_output_vars(fun5(Out),[],[Out]). input_output_vars(fun6(Out),[],[Out]). input_output_vars(fun7(V1,Out),[V1],[Out]). input_output_vars(fun8(V1,Out),[V1],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [neq/3] 1. non_recursive : [p/2] 2. recursive : [gr/3] 3. recursive : [cond1/4,cond2/4] 4. recursive [non_tail,multiple] : [encArg/2] 5. non_recursive : [fun/4] 6. non_recursive : [fun1/1] 7. non_recursive : [fun2/4] 8. non_recursive : [fun3/3] 9. non_recursive : [fun4/3] 10. non_recursive : [fun5/1] 11. non_recursive : [fun6/1] 12. non_recursive : [fun7/2] 13. non_recursive : [fun8/2] 14. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into neq/3 1. SCC is partially evaluated into p/2 2. SCC is partially evaluated into gr/3 3. SCC is partially evaluated into cond2/4 4. SCC is partially evaluated into encArg/2 5. SCC is partially evaluated into fun/4 6. SCC is partially evaluated into fun1/1 7. SCC is partially evaluated into fun2/4 8. SCC is partially evaluated into fun3/3 9. SCC is partially evaluated into fun4/3 10. SCC is completely evaluated into other SCCs 11. SCC is partially evaluated into fun6/1 12. SCC is partially evaluated into fun7/2 13. SCC is partially evaluated into fun8/2 14. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations neq/3 * CE 29 is refined into CE [60] * CE 27 is refined into CE [61] * CE 26 is refined into CE [62] * CE 25 is refined into CE [63] * CE 28 is refined into CE [64] ### Cost equations --> "Loop" of neq/3 * CEs [64] --> Loop 34 * CEs [60] --> Loop 35 * CEs [61] --> Loop 36 * CEs [62] --> Loop 37 * CEs [63] --> Loop 38 ### Ranking functions of CR neq(V1,V,Out) * RF of phase [34]: [V,V1] #### Partial ranking functions of CR neq(V1,V,Out) * Partial RF of phase [34]: - RF of loop [34:1]: V V1 ### Specialization of cost equations p/2 * CE 31 is refined into CE [65] * CE 30 is refined into CE [66] * CE 32 is refined into CE [67] ### Cost equations --> "Loop" of p/2 * CEs [65] --> Loop 39 * CEs [66,67] --> Loop 40 ### Ranking functions of CR p(V1,Out) #### Partial ranking functions of CR p(V1,Out) ### Specialization of cost equations gr/3 * CE 19 is refined into CE [68] * CE 17 is refined into CE [69] * CE 16 is refined into CE [70] * CE 18 is refined into CE [71] ### Cost equations --> "Loop" of gr/3 * CEs [71] --> Loop 41 * CEs [68] --> Loop 42 * CEs [69] --> Loop 43 * CEs [70] --> Loop 44 ### Ranking functions of CR gr(V1,V,Out) * RF of phase [41]: [V,V1] #### Partial ranking functions of CR gr(V1,V,Out) * Partial RF of phase [41]: - RF of loop [41:1]: V V1 ### Specialization of cost equations cond2/4 * CE 21 is refined into CE [72,73,74] * CE 20 is refined into CE [75,76,77,78,79] * CE 24 is refined into CE [80] * CE 23 is refined into CE [81,82,83] * CE 22 is refined into CE [84,85,86,87,88,89,90] ### Cost equations --> "Loop" of cond2/4 * CEs [83] --> Loop 45 * CEs [82] --> Loop 46 * CEs [81] --> Loop 47 * CEs [90] --> Loop 48 * CEs [89] --> Loop 49 * CEs [88] --> Loop 50 * CEs [85] --> Loop 51 * CEs [87] --> Loop 52 * CEs [84,86] --> Loop 53 * CEs [72,73,74] --> Loop 54 * CEs [75,76,77,78,79,80] --> Loop 55 ### Ranking functions of CR cond2(V1,V,V2,Out) * RF of phase [49]: [V-1] #### Partial ranking functions of CR cond2(V1,V,V2,Out) * Partial RF of phase [49]: - RF of loop [49:1]: V-1 ### Specialization of cost equations encArg/2 * CE 36 is refined into CE [91] * CE 35 is refined into CE [92] * CE 37 is refined into CE [93] * CE 38 is refined into CE [94] * CE 42 is refined into CE [95,96] * CE 40 is refined into CE [97,98,99,100,101] * CE 41 is refined into CE [102,103,104,105,106,107,108] * CE 34 is refined into CE [109,110,111,112,113,114,115] * CE 33 is refined into CE [116] * CE 39 is refined into CE [117,118] ### Cost equations --> "Loop" of encArg/2 * CEs [110,111] --> Loop 56 * CEs [109,112,113,114,115,116,117,118] --> Loop 57 * CEs [101,108] --> Loop 58 * CEs [107] --> Loop 59 * CEs [98,104] --> Loop 60 * CEs [103] --> Loop 61 * CEs [100,106] --> Loop 62 * CEs [97,102] --> Loop 63 * CEs [99,105] --> Loop 64 * CEs [94] --> Loop 65 * CEs [96] --> Loop 66 * CEs [95] --> Loop 67 * CEs [91] --> Loop 68 * CEs [92] --> Loop 69 * CEs [93] --> Loop 70 ### Ranking functions of CR encArg(V1,Out) * RF of phase [56,57,58,59,60,61,62,63,64,65,66,67]: [V1] #### Partial ranking functions of CR encArg(V1,Out) * Partial RF of phase [56,57,58,59,60,61,62,63,64,65,66,67]: - RF of loop [56:1,56:2,56:3,57:1,57:2,57:3,58:1,58:2,59:1,59:2,60:1,60:2,61:1,61:2,62:1,62:2,63:1,63:2,64:1,64:2,65:1,66:1,67:1]: V1 ### Specialization of cost equations fun/4 * CE 43 is refined into CE [119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145] * CE 44 is refined into CE [146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211] * CE 45 is refined into CE [212] ### Cost equations --> "Loop" of fun/4 * CEs [122,123,124,140,141,142,162,163,164,165,166,167,168,169,170,171,172] --> Loop 71 * CEs [120,126,129,135,138,144,153,154,155,156,157,175,176,186,187,188,189,190,208,209] --> Loop 72 * CEs [119,121,125,127,128,130,131,132,133,134,136,137,139,143,145,146,147,148,149,150,151,152,158,159,160,161,173,174,177,178,179,180,181,182,183,184,185,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,210,211,212] --> Loop 73 ### Ranking functions of CR fun(V1,V,V2,Out) #### Partial ranking functions of CR fun(V1,V,V2,Out) ### Specialization of cost equations fun1/1 * CE 46 is refined into CE [213] * CE 47 is refined into CE [214] ### Cost equations --> "Loop" of fun1/1 * CEs [213] --> Loop 74 * CEs [214] --> Loop 75 ### Ranking functions of CR fun1(Out) #### Partial ranking functions of CR fun1(Out) ### Specialization of cost equations fun2/4 * CE 48 is refined into CE [215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259] * CE 49 is refined into CE [260] ### Cost equations --> "Loop" of fun2/4 * CEs [221,222,223,224,225,226,254,255,256] --> Loop 76 * CEs [217,218,229,230,235,236,247,248,252,258] --> Loop 77 * CEs [215,216,219,220,227,228,231,232,233,234,237,238,239,240,241,242,243,244,245,246,249,250,251,253,257,259,260] --> Loop 78 ### Ranking functions of CR fun2(V1,V,V2,Out) #### Partial ranking functions of CR fun2(V1,V,V2,Out) ### Specialization of cost equations fun3/3 * CE 50 is refined into CE [261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286] * CE 51 is refined into CE [287] ### Cost equations --> "Loop" of fun3/3 * CEs [269] --> Loop 79 * CEs [266,268,283] --> Loop 80 * CEs [267,284] --> Loop 81 * CEs [262,265,271,273,276,279] --> Loop 82 * CEs [261,264,270,275,278,281,285] --> Loop 83 * CEs [263,272,274,277,280,282,286,287] --> Loop 84 ### Ranking functions of CR fun3(V1,V,Out) #### Partial ranking functions of CR fun3(V1,V,Out) ### Specialization of cost equations fun4/3 * CE 52 is refined into CE [288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318] * CE 53 is refined into CE [319] ### Cost equations --> "Loop" of fun4/3 * CEs [295,298,299,313,315] --> Loop 85 * CEs [297] --> Loop 86 * CEs [296,316] --> Loop 87 * CEs [289,290,293,294,301,303,306,307,310] --> Loop 88 * CEs [288,292,300,305,309,312,317] --> Loop 89 * CEs [291,302,304,308,311,314,318,319] --> Loop 90 ### Ranking functions of CR fun4(V1,V,Out) #### Partial ranking functions of CR fun4(V1,V,Out) ### Specialization of cost equations fun6/1 * CE 54 is refined into CE [320] * CE 55 is refined into CE [321] ### Cost equations --> "Loop" of fun6/1 * CEs [320] --> Loop 91 * CEs [321] --> Loop 92 ### Ranking functions of CR fun6(Out) #### Partial ranking functions of CR fun6(Out) ### Specialization of cost equations fun7/2 * CE 56 is refined into CE [322,323,324,325,326] * CE 57 is refined into CE [327] ### Cost equations --> "Loop" of fun7/2 * CEs [323,325] --> Loop 93 * CEs [322,324,326,327] --> Loop 94 ### Ranking functions of CR fun7(V1,Out) #### Partial ranking functions of CR fun7(V1,Out) ### Specialization of cost equations fun8/2 * CE 58 is refined into CE [328,329,330] * CE 59 is refined into CE [331] ### Cost equations --> "Loop" of fun8/2 * CEs [330] --> Loop 95 * CEs [331] --> Loop 96 * CEs [328,329] --> Loop 97 ### Ranking functions of CR fun8(V1,Out) #### Partial ranking functions of CR fun8(V1,Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [332] * CE 2 is refined into CE [333,334,335,336,337,338,339] * CE 3 is refined into CE [340,341] * CE 4 is refined into CE [342,343,344,345,346] * CE 5 is refined into CE [347,348,349,350,351,352,353] * CE 6 is refined into CE [354,355] * CE 7 is refined into CE [356,357,358] * CE 8 is refined into CE [359,360] * CE 9 is refined into CE [361,362] * CE 10 is refined into CE [363,364] * CE 11 is refined into CE [365,366,367] * CE 12 is refined into CE [368,369,370,371] * CE 13 is refined into CE [372,373] * CE 14 is refined into CE [374,375] * CE 15 is refined into CE [376,377,378] ### Cost equations --> "Loop" of start/3 * CEs [332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378] --> Loop 98 ### Ranking functions of CR start(V1,V,V2) #### Partial ranking functions of CR start(V1,V,V2) Computing Bounds ===================================== #### Cost of chains of neq(V1,V,Out): * Chain [[34],38]: 1*it(34)+1 Such that:it(34) =< V1 with precondition: [Out=1,V1=V,V1>=1] * Chain [[34],37]: 1*it(34)+1 Such that:it(34) =< V1 with precondition: [Out=2,V1>=1,V>=V1+1] * Chain [[34],36]: 1*it(34)+1 Such that:it(34) =< V with precondition: [Out=2,V>=1,V1>=V+1] * Chain [[34],35]: 1*it(34)+0 Such that:it(34) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [38]: 1 with precondition: [V1=0,V=0,Out=1] * Chain [37]: 1 with precondition: [V1=0,Out=2,V>=1] * Chain [36]: 1 with precondition: [V=0,Out=2,V1>=1] * Chain [35]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of p(V1,Out): * Chain [40]: 1 with precondition: [Out=0,V1>=0] * Chain [39]: 1 with precondition: [V1=Out+1,V1>=1] #### Cost of chains of gr(V1,V,Out): * Chain [[41],44]: 1*it(41)+1 Such that:it(41) =< V1 with precondition: [Out=1,V1>=1,V>=V1] * Chain [[41],43]: 1*it(41)+1 Such that:it(41) =< V with precondition: [Out=2,V>=1,V1>=V+1] * Chain [[41],42]: 1*it(41)+0 Such that:it(41) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [44]: 1 with precondition: [V1=0,Out=1,V>=0] * Chain [43]: 1 with precondition: [V=0,Out=2,V1>=1] * Chain [42]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of cond2(V1,V,V2,Out): * Chain [[49],55]: 5*it(49)+1*s(7)+3 Such that:aux(3) =< V it(49) =< aux(3) s(7) =< it(49)*aux(3) with precondition: [V1=1,Out=0,V>=2,V2+1>=V] * Chain [[49],53,55]: 5*it(49)+1*s(7)+8 Such that:aux(4) =< V it(49) =< aux(4) s(7) =< it(49)*aux(4) with precondition: [V1=1,Out=0,V>=2,V2+1>=V] * Chain [[49],51,55]: 5*it(49)+1*s(7)+1*s(8)+7 Such that:s(8) =< V2 aux(5) =< V it(49) =< aux(5) s(7) =< it(49)*aux(5) with precondition: [V1=1,Out=0,V>=2,V2+1>=V] * Chain [[49],50,55]: 5*it(49)+1*s(7)+1*s(9)+7 Such that:s(9) =< V2 aux(6) =< V it(49) =< aux(6) s(7) =< it(49)*aux(6) with precondition: [V1=1,Out=0,V>=2,V2+1>=V] * Chain [55]: 3 with precondition: [Out=0,V1>=0,V>=0,V2>=0] * Chain [54]: 2 with precondition: [V1=2,Out=0,V>=0,V2>=0] * Chain [53,55]: 8 with precondition: [V1=1,Out=0,V>=1,V2>=0] * Chain [52,55]: 8 with precondition: [V1=1,V2=0,Out=0,V>=2] * Chain [52,54]: 7 with precondition: [V1=1,V2=0,Out=0,V>=2] * Chain [52,47,55]: 12 with precondition: [V1=1,V2=0,Out=0,V>=2] * Chain [52,46,55]: 11 with precondition: [V1=1,V2=0,Out=0,V>=2] * Chain [51,55]: 1*s(8)+7 Such that:s(8) =< V2 with precondition: [V1=1,Out=0,V>=1,V2>=0] * Chain [50,55]: 1*s(9)+7 Such that:s(9) =< V2 with precondition: [V1=1,Out=0,V>=1,V2>=0] * Chain [48,55]: 1*s(12)+8 Such that:s(12) =< V2 with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [48,54]: 1*s(12)+7 Such that:s(12) =< V2 with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [48,46,55]: 2*s(11)+11 Such that:aux(7) =< V2 s(11) =< aux(7) with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [48,45,[49],55]: 7*it(49)+1*s(7)+12 Such that:aux(9) =< V2 it(49) =< aux(9) s(7) =< it(49)*aux(9) with precondition: [V1=1,Out=0,V2>=2,V>=V2+2] * Chain [48,45,[49],53,55]: 7*it(49)+1*s(7)+17 Such that:aux(11) =< V2 it(49) =< aux(11) s(7) =< it(49)*aux(11) with precondition: [V1=1,Out=0,V2>=2,V>=V2+2] * Chain [48,45,[49],51,55]: 8*it(49)+1*s(7)+16 Such that:aux(13) =< V2 it(49) =< aux(13) s(7) =< it(49)*aux(13) with precondition: [V1=1,Out=0,V2>=2,V>=V2+2] * Chain [48,45,[49],50,55]: 8*it(49)+1*s(7)+16 Such that:aux(15) =< V2 it(49) =< aux(15) s(7) =< it(49)*aux(15) with precondition: [V1=1,Out=0,V2>=2,V>=V2+2] * Chain [48,45,55]: 2*s(12)+12 Such that:aux(16) =< V2 s(12) =< aux(16) with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [48,45,53,55]: 2*s(12)+17 Such that:aux(17) =< V2 s(12) =< aux(17) with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [48,45,51,55]: 3*s(8)+16 Such that:aux(19) =< V2 s(8) =< aux(19) with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [48,45,50,55]: 3*s(9)+16 Such that:aux(21) =< V2 s(9) =< aux(21) with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [47,55]: 7 with precondition: [V1=2,V2=0,Out=0,V>=1] * Chain [46,55]: 1*s(11)+6 Such that:s(11) =< V2 with precondition: [V1=2,Out=0,V>=1,V2>=0] * Chain [45,[49],55]: 6*it(49)+1*s(7)+7 Such that:aux(8) =< V2 it(49) =< aux(8) s(7) =< it(49)*aux(8) with precondition: [V1=2,Out=0,V>=1,V2>=2] * Chain [45,[49],53,55]: 6*it(49)+1*s(7)+12 Such that:aux(10) =< V2 it(49) =< aux(10) s(7) =< it(49)*aux(10) with precondition: [V1=2,Out=0,V>=1,V2>=2] * Chain [45,[49],51,55]: 7*it(49)+1*s(7)+11 Such that:aux(12) =< V2 it(49) =< aux(12) s(7) =< it(49)*aux(12) with precondition: [V1=2,Out=0,V>=1,V2>=2] * Chain [45,[49],50,55]: 7*it(49)+1*s(7)+11 Such that:aux(14) =< V2 it(49) =< aux(14) s(7) =< it(49)*aux(14) with precondition: [V1=2,Out=0,V>=1,V2>=2] * Chain [45,55]: 1*s(13)+7 Such that:s(13) =< V2 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [45,53,55]: 1*s(13)+12 Such that:s(13) =< V2 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [45,51,55]: 2*s(8)+11 Such that:aux(18) =< V2 s(8) =< aux(18) with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [45,50,55]: 2*s(9)+11 Such that:aux(20) =< V2 s(9) =< aux(20) with precondition: [V1=2,Out=0,V>=1,V2>=1] #### Cost of chains of encArg(V1,Out): * Chain [70]: 0 with precondition: [V1=1,Out=1] * Chain [69]: 0 with precondition: [V1=2,Out=2] * Chain [68]: 0 with precondition: [Out=0,V1>=0] * Chain [multiple([56,57,58,59,60,61,62,63,64,65,66,67],[[70],[69],[68]])]: 19*it(56)+19*it(57)+2*it(58)+2*it(60)+1*it(62)+1*it(63)+2*it(66)+20*s(145)+4*s(146)+260*s(148)+24*s(149)+130*s(150)+20*s(151)+2*s(154)+1*s(156)+2*s(157)+2*s(159)+0 Such that:it([70]) =< 2/3*V1+1/3 aux(47) =< V1 aux(48) =< 2*V1+1 aux(49) =< V1/2 aux(50) =< V1/3 aux(51) =< 2/3*V1 aux(52) =< 2/5*V1 it(57) =< aux(47) it(58) =< aux(47) it(60) =< aux(47) it(62) =< aux(47) it(63) =< aux(47) it(64) =< aux(47) it(66) =< aux(47) it([70]) =< aux(47) it([68]) =< aux(48) it([70]) =< aux(48) it(62) =< aux(49) it(56) =< aux(50) it(60) =< aux(51) it(62) =< aux(51) it(58) =< aux(52) aux(37) =< aux(47)+2 aux(41) =< aux(47)+1 aux(35) =< aux(47) aux(36) =< aux(47)+3 it(62) =< it([68])*(1/2)+aux(49) it(63) =< it([68])*(1/2)+aux(49) it(64) =< it([68])*(1/2)+aux(49) it(60) =< it([68])*(1/3)+aux(51) it(62) =< it([68])*(1/3)+aux(51) it(63) =< it([68])*(1/3)+aux(51) it(64) =< it([68])*(1/3)+aux(51) it(58) =< it([68])*(3/5)+it([70])*(1/5)+aux(52) it(60) =< it([68])*(3/5)+it([70])*(1/5)+aux(52) it(62) =< it([68])*(3/5)+it([70])*(1/5)+aux(52) it(63) =< it([68])*(3/5)+it([70])*(1/5)+aux(52) it(64) =< it([68])*(3/5)+it([70])*(1/5)+aux(52) it(56) =< it([68])*(1/3)+aux(50) it(57) =< it([68])*(1/3)+aux(50) s(160) =< it(64)*aux(37) s(158) =< it(62)*aux(41) s(156) =< it(58)*aux(41) s(155) =< it(58)*aux(35) s(152) =< it(57)*aux(37) s(153) =< it(57)*aux(36) s(147) =< it(56)*aux(35) s(159) =< s(160) s(157) =< s(158) s(154) =< s(155) s(150) =< s(153) s(151) =< s(150)*aux(36) s(148) =< s(152) s(149) =< s(148)*aux(37) s(145) =< s(147) s(146) =< s(145)*aux(47) with precondition: [V1>=1,Out>=0,V1>=Out] #### Cost of chains of fun(V1,V,V2,Out): * Chain [73]: 361*s(204)+38*s(205)+38*s(206)+19*s(207)+19*s(208)+38*s(210)+361*s(211)+19*s(218)+38*s(223)+38*s(224)+38*s(225)+2470*s(226)+380*s(227)+4940*s(228)+456*s(229)+380*s(230)+76*s(231)+532*s(239)+56*s(240)+56*s(241)+28*s(242)+28*s(243)+360*s(245)+532*s(246)+28*s(253)+56*s(258)+56*s(259)+56*s(260)+3640*s(261)+560*s(262)+7280*s(263)+672*s(264)+560*s(265)+112*s(266)+589*s(274)+62*s(275)+62*s(276)+31*s(277)+31*s(278)+747*s(280)+589*s(281)+31*s(288)+62*s(293)+62*s(294)+62*s(295)+4030*s(296)+620*s(297)+8060*s(298)+744*s(299)+620*s(300)+124*s(301)+60*s(902)+52*s(1012)+259*s(2835)+40*s(2836)+83*s(2995)+8*s(3001)+19 Such that:aux(93) =< 1 aux(94) =< 2 aux(95) =< V1 aux(96) =< 2*V1+1 aux(97) =< V1/2 aux(98) =< V1/3 aux(99) =< 2/3*V1 aux(100) =< 2/3*V1+1/3 aux(101) =< 2/5*V1 aux(102) =< V aux(103) =< 2*V+1 aux(104) =< V/2 aux(105) =< V/3 aux(106) =< 2/3*V aux(107) =< 2/3*V+1/3 aux(108) =< 2/5*V aux(109) =< V2 aux(110) =< 2*V2+1 aux(111) =< V2/2 aux(112) =< V2/3 aux(113) =< 2/3*V2 aux(114) =< 2/3*V2+1/3 aux(115) =< 2/5*V2 s(202) =< aux(100) s(237) =< aux(107) s(272) =< aux(114) s(2835) =< aux(94) s(2836) =< s(2835)*aux(94) s(274) =< aux(109) s(275) =< aux(109) s(276) =< aux(109) s(277) =< aux(109) s(278) =< aux(109) s(279) =< aux(109) s(280) =< aux(109) s(272) =< aux(109) s(272) =< aux(110) s(277) =< aux(111) s(281) =< aux(112) s(276) =< aux(113) s(277) =< aux(113) s(275) =< aux(115) s(282) =< aux(109)+2 s(283) =< aux(109)+1 s(284) =< aux(109) s(285) =< aux(109)+3 s(277) =< aux(110)*(1/2)+aux(111) s(278) =< aux(110)*(1/2)+aux(111) s(279) =< aux(110)*(1/2)+aux(111) s(276) =< aux(110)*(1/3)+aux(113) s(277) =< aux(110)*(1/3)+aux(113) s(278) =< aux(110)*(1/3)+aux(113) s(279) =< aux(110)*(1/3)+aux(113) s(275) =< aux(110)*(3/5)+s(272)*(1/5)+aux(115) s(276) =< aux(110)*(3/5)+s(272)*(1/5)+aux(115) s(277) =< aux(110)*(3/5)+s(272)*(1/5)+aux(115) s(278) =< aux(110)*(3/5)+s(272)*(1/5)+aux(115) s(279) =< aux(110)*(3/5)+s(272)*(1/5)+aux(115) s(281) =< aux(110)*(1/3)+aux(112) s(274) =< aux(110)*(1/3)+aux(112) s(286) =< s(279)*s(282) s(287) =< s(277)*s(283) s(288) =< s(275)*s(283) s(289) =< s(275)*s(284) s(290) =< s(274)*s(282) s(291) =< s(274)*s(285) s(292) =< s(281)*s(284) s(293) =< s(286) s(294) =< s(287) s(295) =< s(289) s(296) =< s(291) s(297) =< s(296)*s(285) s(298) =< s(290) s(299) =< s(298)*s(282) s(300) =< s(292) s(301) =< s(300)*aux(109) s(902) =< s(280)*aux(109) s(2995) =< aux(93) s(3001) =< s(2995)*aux(93) s(239) =< aux(102) s(240) =< aux(102) s(241) =< aux(102) s(242) =< aux(102) s(243) =< aux(102) s(244) =< aux(102) s(245) =< aux(102) s(237) =< aux(102) s(237) =< aux(103) s(242) =< aux(104) s(246) =< aux(105) s(241) =< aux(106) s(242) =< aux(106) s(240) =< aux(108) s(247) =< aux(102)+2 s(248) =< aux(102)+1 s(249) =< aux(102) s(250) =< aux(102)+3 s(242) =< aux(103)*(1/2)+aux(104) s(243) =< aux(103)*(1/2)+aux(104) s(244) =< aux(103)*(1/2)+aux(104) s(241) =< aux(103)*(1/3)+aux(106) s(242) =< aux(103)*(1/3)+aux(106) s(243) =< aux(103)*(1/3)+aux(106) s(244) =< aux(103)*(1/3)+aux(106) s(240) =< aux(103)*(3/5)+s(237)*(1/5)+aux(108) s(241) =< aux(103)*(3/5)+s(237)*(1/5)+aux(108) s(242) =< aux(103)*(3/5)+s(237)*(1/5)+aux(108) s(243) =< aux(103)*(3/5)+s(237)*(1/5)+aux(108) s(244) =< aux(103)*(3/5)+s(237)*(1/5)+aux(108) s(246) =< aux(103)*(1/3)+aux(105) s(239) =< aux(103)*(1/3)+aux(105) s(251) =< s(244)*s(247) s(252) =< s(242)*s(248) s(253) =< s(240)*s(248) s(254) =< s(240)*s(249) s(255) =< s(239)*s(247) s(256) =< s(239)*s(250) s(257) =< s(246)*s(249) s(258) =< s(251) s(259) =< s(252) s(260) =< s(254) s(261) =< s(256) s(262) =< s(261)*s(250) s(263) =< s(255) s(264) =< s(263)*s(247) s(265) =< s(257) s(266) =< s(265)*aux(102) s(204) =< aux(95) s(205) =< aux(95) s(206) =< aux(95) s(207) =< aux(95) s(208) =< aux(95) s(209) =< aux(95) s(210) =< aux(95) s(202) =< aux(95) s(202) =< aux(96) s(207) =< aux(97) s(211) =< aux(98) s(206) =< aux(99) s(207) =< aux(99) s(205) =< aux(101) s(212) =< aux(95)+2 s(213) =< aux(95)+1 s(214) =< aux(95) s(215) =< aux(95)+3 s(207) =< aux(96)*(1/2)+aux(97) s(208) =< aux(96)*(1/2)+aux(97) s(209) =< aux(96)*(1/2)+aux(97) s(206) =< aux(96)*(1/3)+aux(99) s(207) =< aux(96)*(1/3)+aux(99) s(208) =< aux(96)*(1/3)+aux(99) s(209) =< aux(96)*(1/3)+aux(99) s(205) =< aux(96)*(3/5)+s(202)*(1/5)+aux(101) s(206) =< aux(96)*(3/5)+s(202)*(1/5)+aux(101) s(207) =< aux(96)*(3/5)+s(202)*(1/5)+aux(101) s(208) =< aux(96)*(3/5)+s(202)*(1/5)+aux(101) s(209) =< aux(96)*(3/5)+s(202)*(1/5)+aux(101) s(211) =< aux(96)*(1/3)+aux(98) s(204) =< aux(96)*(1/3)+aux(98) s(216) =< s(209)*s(212) s(217) =< s(207)*s(213) s(218) =< s(205)*s(213) s(219) =< s(205)*s(214) s(220) =< s(204)*s(212) s(221) =< s(204)*s(215) s(222) =< s(211)*s(214) s(223) =< s(216) s(224) =< s(217) s(225) =< s(219) s(226) =< s(221) s(227) =< s(226)*s(215) s(228) =< s(220) s(229) =< s(228)*s(212) s(230) =< s(222) s(231) =< s(230)*aux(95) s(1012) =< s(245)*aux(102) with precondition: [Out=0,V1>=0,V>=0,V2>=0] * Chain [72]: 171*s(3174)+18*s(3175)+18*s(3176)+9*s(3177)+9*s(3178)+18*s(3180)+171*s(3181)+9*s(3188)+18*s(3193)+18*s(3194)+18*s(3195)+1170*s(3196)+180*s(3197)+2340*s(3198)+216*s(3199)+180*s(3200)+36*s(3201)+247*s(3209)+26*s(3210)+26*s(3211)+13*s(3212)+13*s(3213)+148*s(3215)+247*s(3216)+13*s(3223)+26*s(3228)+26*s(3229)+26*s(3230)+1690*s(3231)+260*s(3232)+3380*s(3233)+312*s(3234)+260*s(3235)+52*s(3236)+650*s(3414)+56*s(3417)+24*s(3493)+19 Such that:aux(130) =< 2 aux(131) =< V1 aux(132) =< 2*V1+1 aux(133) =< V1/2 aux(134) =< V1/3 aux(135) =< 2/3*V1 aux(136) =< 2/3*V1+1/3 aux(137) =< 2/5*V1 aux(138) =< V aux(139) =< 2*V+1 aux(140) =< V/2 aux(141) =< V/3 aux(142) =< 2/3*V aux(143) =< 2/3*V+1/3 aux(144) =< 2/5*V s(3172) =< aux(136) s(3207) =< aux(143) s(3414) =< aux(130) s(3417) =< s(3414)*aux(130) s(3209) =< aux(138) s(3210) =< aux(138) s(3211) =< aux(138) s(3212) =< aux(138) s(3213) =< aux(138) s(3214) =< aux(138) s(3215) =< aux(138) s(3207) =< aux(138) s(3207) =< aux(139) s(3212) =< aux(140) s(3216) =< aux(141) s(3211) =< aux(142) s(3212) =< aux(142) s(3210) =< aux(144) s(3217) =< aux(138)+2 s(3218) =< aux(138)+1 s(3219) =< aux(138) s(3220) =< aux(138)+3 s(3212) =< aux(139)*(1/2)+aux(140) s(3213) =< aux(139)*(1/2)+aux(140) s(3214) =< aux(139)*(1/2)+aux(140) s(3211) =< aux(139)*(1/3)+aux(142) s(3212) =< aux(139)*(1/3)+aux(142) s(3213) =< aux(139)*(1/3)+aux(142) s(3214) =< aux(139)*(1/3)+aux(142) s(3210) =< aux(139)*(3/5)+s(3207)*(1/5)+aux(144) s(3211) =< aux(139)*(3/5)+s(3207)*(1/5)+aux(144) s(3212) =< aux(139)*(3/5)+s(3207)*(1/5)+aux(144) s(3213) =< aux(139)*(3/5)+s(3207)*(1/5)+aux(144) s(3214) =< aux(139)*(3/5)+s(3207)*(1/5)+aux(144) s(3216) =< aux(139)*(1/3)+aux(141) s(3209) =< aux(139)*(1/3)+aux(141) s(3221) =< s(3214)*s(3217) s(3222) =< s(3212)*s(3218) s(3223) =< s(3210)*s(3218) s(3224) =< s(3210)*s(3219) s(3225) =< s(3209)*s(3217) s(3226) =< s(3209)*s(3220) s(3227) =< s(3216)*s(3219) s(3228) =< s(3221) s(3229) =< s(3222) s(3230) =< s(3224) s(3231) =< s(3226) s(3232) =< s(3231)*s(3220) s(3233) =< s(3225) s(3234) =< s(3233)*s(3217) s(3235) =< s(3227) s(3236) =< s(3235)*aux(138) s(3174) =< aux(131) s(3175) =< aux(131) s(3176) =< aux(131) s(3177) =< aux(131) s(3178) =< aux(131) s(3179) =< aux(131) s(3180) =< aux(131) s(3172) =< aux(131) s(3172) =< aux(132) s(3177) =< aux(133) s(3181) =< aux(134) s(3176) =< aux(135) s(3177) =< aux(135) s(3175) =< aux(137) s(3182) =< aux(131)+2 s(3183) =< aux(131)+1 s(3184) =< aux(131) s(3185) =< aux(131)+3 s(3177) =< aux(132)*(1/2)+aux(133) s(3178) =< aux(132)*(1/2)+aux(133) s(3179) =< aux(132)*(1/2)+aux(133) s(3176) =< aux(132)*(1/3)+aux(135) s(3177) =< aux(132)*(1/3)+aux(135) s(3178) =< aux(132)*(1/3)+aux(135) s(3179) =< aux(132)*(1/3)+aux(135) s(3175) =< aux(132)*(3/5)+s(3172)*(1/5)+aux(137) s(3176) =< aux(132)*(3/5)+s(3172)*(1/5)+aux(137) s(3177) =< aux(132)*(3/5)+s(3172)*(1/5)+aux(137) s(3178) =< aux(132)*(3/5)+s(3172)*(1/5)+aux(137) s(3179) =< aux(132)*(3/5)+s(3172)*(1/5)+aux(137) s(3181) =< aux(132)*(1/3)+aux(134) s(3174) =< aux(132)*(1/3)+aux(134) s(3186) =< s(3179)*s(3182) s(3187) =< s(3177)*s(3183) s(3188) =< s(3175)*s(3183) s(3189) =< s(3175)*s(3184) s(3190) =< s(3174)*s(3182) s(3191) =< s(3174)*s(3185) s(3192) =< s(3181)*s(3184) s(3193) =< s(3186) s(3194) =< s(3187) s(3195) =< s(3189) s(3196) =< s(3191) s(3197) =< s(3196)*s(3185) s(3198) =< s(3190) s(3199) =< s(3198)*s(3182) s(3200) =< s(3192) s(3201) =< s(3200)*aux(131) s(3493) =< s(3215)*aux(138) with precondition: [V2=2,Out=0,V1>=0,V>=0] * Chain [71]: 266*s(4032)+28*s(4033)+28*s(4034)+14*s(4035)+14*s(4036)+28*s(4038)+266*s(4039)+14*s(4046)+28*s(4051)+28*s(4052)+28*s(4053)+1820*s(4054)+280*s(4055)+3640*s(4056)+336*s(4057)+280*s(4058)+56*s(4059)+152*s(4067)+16*s(4068)+16*s(4069)+8*s(4070)+8*s(4071)+113*s(4073)+152*s(4074)+8*s(4081)+16*s(4086)+16*s(4087)+16*s(4088)+1040*s(4089)+160*s(4090)+2080*s(4091)+192*s(4092)+160*s(4093)+32*s(4094)+259*s(4273)+40*s(4274)+8*s(4425)+83*s(4573)+8*s(4579)+19 Such that:aux(153) =< 1 aux(154) =< 2 aux(155) =< V1 aux(156) =< 2*V1+1 aux(157) =< V1/2 aux(158) =< V1/3 aux(159) =< 2/3*V1 aux(160) =< 2/3*V1+1/3 aux(161) =< 2/5*V1 aux(162) =< V2 aux(163) =< 2*V2+1 aux(164) =< V2/2 aux(165) =< V2/3 aux(166) =< 2/3*V2 aux(167) =< 2/3*V2+1/3 aux(168) =< 2/5*V2 s(4030) =< aux(160) s(4065) =< aux(167) s(4273) =< aux(154) s(4274) =< s(4273)*aux(154) s(4067) =< aux(162) s(4068) =< aux(162) s(4069) =< aux(162) s(4070) =< aux(162) s(4071) =< aux(162) s(4072) =< aux(162) s(4073) =< aux(162) s(4065) =< aux(162) s(4065) =< aux(163) s(4070) =< aux(164) s(4074) =< aux(165) s(4069) =< aux(166) s(4070) =< aux(166) s(4068) =< aux(168) s(4075) =< aux(162)+2 s(4076) =< aux(162)+1 s(4077) =< aux(162) s(4078) =< aux(162)+3 s(4070) =< aux(163)*(1/2)+aux(164) s(4071) =< aux(163)*(1/2)+aux(164) s(4072) =< aux(163)*(1/2)+aux(164) s(4069) =< aux(163)*(1/3)+aux(166) s(4070) =< aux(163)*(1/3)+aux(166) s(4071) =< aux(163)*(1/3)+aux(166) s(4072) =< aux(163)*(1/3)+aux(166) s(4068) =< aux(163)*(3/5)+s(4065)*(1/5)+aux(168) s(4069) =< aux(163)*(3/5)+s(4065)*(1/5)+aux(168) s(4070) =< aux(163)*(3/5)+s(4065)*(1/5)+aux(168) s(4071) =< aux(163)*(3/5)+s(4065)*(1/5)+aux(168) s(4072) =< aux(163)*(3/5)+s(4065)*(1/5)+aux(168) s(4074) =< aux(163)*(1/3)+aux(165) s(4067) =< aux(163)*(1/3)+aux(165) s(4079) =< s(4072)*s(4075) s(4080) =< s(4070)*s(4076) s(4081) =< s(4068)*s(4076) s(4082) =< s(4068)*s(4077) s(4083) =< s(4067)*s(4075) s(4084) =< s(4067)*s(4078) s(4085) =< s(4074)*s(4077) s(4086) =< s(4079) s(4087) =< s(4080) s(4088) =< s(4082) s(4089) =< s(4084) s(4090) =< s(4089)*s(4078) s(4091) =< s(4083) s(4092) =< s(4091)*s(4075) s(4093) =< s(4085) s(4094) =< s(4093)*aux(162) s(4032) =< aux(155) s(4033) =< aux(155) s(4034) =< aux(155) s(4035) =< aux(155) s(4036) =< aux(155) s(4037) =< aux(155) s(4038) =< aux(155) s(4030) =< aux(155) s(4030) =< aux(156) s(4035) =< aux(157) s(4039) =< aux(158) s(4034) =< aux(159) s(4035) =< aux(159) s(4033) =< aux(161) s(4040) =< aux(155)+2 s(4041) =< aux(155)+1 s(4042) =< aux(155) s(4043) =< aux(155)+3 s(4035) =< aux(156)*(1/2)+aux(157) s(4036) =< aux(156)*(1/2)+aux(157) s(4037) =< aux(156)*(1/2)+aux(157) s(4034) =< aux(156)*(1/3)+aux(159) s(4035) =< aux(156)*(1/3)+aux(159) s(4036) =< aux(156)*(1/3)+aux(159) s(4037) =< aux(156)*(1/3)+aux(159) s(4033) =< aux(156)*(3/5)+s(4030)*(1/5)+aux(161) s(4034) =< aux(156)*(3/5)+s(4030)*(1/5)+aux(161) s(4035) =< aux(156)*(3/5)+s(4030)*(1/5)+aux(161) s(4036) =< aux(156)*(3/5)+s(4030)*(1/5)+aux(161) s(4037) =< aux(156)*(3/5)+s(4030)*(1/5)+aux(161) s(4039) =< aux(156)*(1/3)+aux(158) s(4032) =< aux(156)*(1/3)+aux(158) s(4044) =< s(4037)*s(4040) s(4045) =< s(4035)*s(4041) s(4046) =< s(4033)*s(4041) s(4047) =< s(4033)*s(4042) s(4048) =< s(4032)*s(4040) s(4049) =< s(4032)*s(4043) s(4050) =< s(4039)*s(4042) s(4051) =< s(4044) s(4052) =< s(4045) s(4053) =< s(4047) s(4054) =< s(4049) s(4055) =< s(4054)*s(4043) s(4056) =< s(4048) s(4057) =< s(4056)*s(4040) s(4058) =< s(4050) s(4059) =< s(4058)*aux(155) s(4425) =< s(4073)*aux(162) s(4573) =< aux(153) s(4579) =< s(4573)*aux(153) with precondition: [V=2,Out=0,V1>=0,V2>=0] #### Cost of chains of fun1(Out): * Chain [75]: 0 with precondition: [Out=0] * Chain [74]: 0 with precondition: [Out=2] #### Cost of chains of fun2(V1,V,V2,Out): * Chain [78]: 152*s(5061)+16*s(5062)+16*s(5063)+8*s(5064)+8*s(5065)+16*s(5067)+152*s(5068)+8*s(5075)+16*s(5080)+16*s(5081)+16*s(5082)+1040*s(5083)+160*s(5084)+2080*s(5085)+192*s(5086)+160*s(5087)+32*s(5088)+190*s(5096)+20*s(5097)+20*s(5098)+10*s(5099)+10*s(5100)+140*s(5102)+190*s(5103)+10*s(5110)+20*s(5115)+20*s(5116)+20*s(5117)+1300*s(5118)+200*s(5119)+2600*s(5120)+240*s(5121)+200*s(5122)+40*s(5123)+228*s(5131)+24*s(5132)+24*s(5133)+12*s(5134)+12*s(5135)+525*s(5137)+228*s(5138)+12*s(5145)+24*s(5150)+24*s(5151)+24*s(5152)+1560*s(5153)+240*s(5154)+3120*s(5155)+288*s(5156)+240*s(5157)+48*s(5158)+24*s(5163)+48*s(5164)+141*s(5916)+20*s(5917)+17 Such that:aux(207) =< 2 aux(208) =< V1 aux(209) =< 2*V1+1 aux(210) =< V1/2 aux(211) =< V1/3 aux(212) =< 2/3*V1 aux(213) =< 2/3*V1+1/3 aux(214) =< 2/5*V1 aux(215) =< V aux(216) =< 2*V+1 aux(217) =< V/2 aux(218) =< V/3 aux(219) =< 2/3*V aux(220) =< 2/3*V+1/3 aux(221) =< 2/5*V aux(222) =< V2 aux(223) =< 2*V2+1 aux(224) =< V2/2 aux(225) =< V2/3 aux(226) =< 2/3*V2 aux(227) =< 2/3*V2+1/3 aux(228) =< 2/5*V2 s(5059) =< aux(213) s(5094) =< aux(220) s(5129) =< aux(227) s(5916) =< aux(207) s(5917) =< s(5916)*aux(207) s(5137) =< aux(222) s(5164) =< s(5137)*aux(222) s(5131) =< aux(222) s(5132) =< aux(222) s(5133) =< aux(222) s(5134) =< aux(222) s(5135) =< aux(222) s(5136) =< aux(222) s(5129) =< aux(222) s(5129) =< aux(223) s(5134) =< aux(224) s(5138) =< aux(225) s(5133) =< aux(226) s(5134) =< aux(226) s(5132) =< aux(228) s(5139) =< aux(222)+2 s(5140) =< aux(222)+1 s(5141) =< aux(222) s(5142) =< aux(222)+3 s(5134) =< aux(223)*(1/2)+aux(224) s(5135) =< aux(223)*(1/2)+aux(224) s(5136) =< aux(223)*(1/2)+aux(224) s(5133) =< aux(223)*(1/3)+aux(226) s(5134) =< aux(223)*(1/3)+aux(226) s(5135) =< aux(223)*(1/3)+aux(226) s(5136) =< aux(223)*(1/3)+aux(226) s(5132) =< aux(223)*(3/5)+s(5129)*(1/5)+aux(228) s(5133) =< aux(223)*(3/5)+s(5129)*(1/5)+aux(228) s(5134) =< aux(223)*(3/5)+s(5129)*(1/5)+aux(228) s(5135) =< aux(223)*(3/5)+s(5129)*(1/5)+aux(228) s(5136) =< aux(223)*(3/5)+s(5129)*(1/5)+aux(228) s(5138) =< aux(223)*(1/3)+aux(225) s(5131) =< aux(223)*(1/3)+aux(225) s(5143) =< s(5136)*s(5139) s(5144) =< s(5134)*s(5140) s(5145) =< s(5132)*s(5140) s(5146) =< s(5132)*s(5141) s(5147) =< s(5131)*s(5139) s(5148) =< s(5131)*s(5142) s(5149) =< s(5138)*s(5141) s(5150) =< s(5143) s(5151) =< s(5144) s(5152) =< s(5146) s(5153) =< s(5148) s(5154) =< s(5153)*s(5142) s(5155) =< s(5147) s(5156) =< s(5155)*s(5139) s(5157) =< s(5149) s(5158) =< s(5157)*aux(222) s(5102) =< aux(215) s(5163) =< s(5102)*aux(215) s(5096) =< aux(215) s(5097) =< aux(215) s(5098) =< aux(215) s(5099) =< aux(215) s(5100) =< aux(215) s(5101) =< aux(215) s(5094) =< aux(215) s(5094) =< aux(216) s(5099) =< aux(217) s(5103) =< aux(218) s(5098) =< aux(219) s(5099) =< aux(219) s(5097) =< aux(221) s(5104) =< aux(215)+2 s(5105) =< aux(215)+1 s(5106) =< aux(215) s(5107) =< aux(215)+3 s(5099) =< aux(216)*(1/2)+aux(217) s(5100) =< aux(216)*(1/2)+aux(217) s(5101) =< aux(216)*(1/2)+aux(217) s(5098) =< aux(216)*(1/3)+aux(219) s(5099) =< aux(216)*(1/3)+aux(219) s(5100) =< aux(216)*(1/3)+aux(219) s(5101) =< aux(216)*(1/3)+aux(219) s(5097) =< aux(216)*(3/5)+s(5094)*(1/5)+aux(221) s(5098) =< aux(216)*(3/5)+s(5094)*(1/5)+aux(221) s(5099) =< aux(216)*(3/5)+s(5094)*(1/5)+aux(221) s(5100) =< aux(216)*(3/5)+s(5094)*(1/5)+aux(221) s(5101) =< aux(216)*(3/5)+s(5094)*(1/5)+aux(221) s(5103) =< aux(216)*(1/3)+aux(218) s(5096) =< aux(216)*(1/3)+aux(218) s(5108) =< s(5101)*s(5104) s(5109) =< s(5099)*s(5105) s(5110) =< s(5097)*s(5105) s(5111) =< s(5097)*s(5106) s(5112) =< s(5096)*s(5104) s(5113) =< s(5096)*s(5107) s(5114) =< s(5103)*s(5106) s(5115) =< s(5108) s(5116) =< s(5109) s(5117) =< s(5111) s(5118) =< s(5113) s(5119) =< s(5118)*s(5107) s(5120) =< s(5112) s(5121) =< s(5120)*s(5104) s(5122) =< s(5114) s(5123) =< s(5122)*aux(215) s(5061) =< aux(208) s(5062) =< aux(208) s(5063) =< aux(208) s(5064) =< aux(208) s(5065) =< aux(208) s(5066) =< aux(208) s(5067) =< aux(208) s(5059) =< aux(208) s(5059) =< aux(209) s(5064) =< aux(210) s(5068) =< aux(211) s(5063) =< aux(212) s(5064) =< aux(212) s(5062) =< aux(214) s(5069) =< aux(208)+2 s(5070) =< aux(208)+1 s(5071) =< aux(208) s(5072) =< aux(208)+3 s(5064) =< aux(209)*(1/2)+aux(210) s(5065) =< aux(209)*(1/2)+aux(210) s(5066) =< aux(209)*(1/2)+aux(210) s(5063) =< aux(209)*(1/3)+aux(212) s(5064) =< aux(209)*(1/3)+aux(212) s(5065) =< aux(209)*(1/3)+aux(212) s(5066) =< aux(209)*(1/3)+aux(212) s(5062) =< aux(209)*(3/5)+s(5059)*(1/5)+aux(214) s(5063) =< aux(209)*(3/5)+s(5059)*(1/5)+aux(214) s(5064) =< aux(209)*(3/5)+s(5059)*(1/5)+aux(214) s(5065) =< aux(209)*(3/5)+s(5059)*(1/5)+aux(214) s(5066) =< aux(209)*(3/5)+s(5059)*(1/5)+aux(214) s(5068) =< aux(209)*(1/3)+aux(211) s(5061) =< aux(209)*(1/3)+aux(211) s(5073) =< s(5066)*s(5069) s(5074) =< s(5064)*s(5070) s(5075) =< s(5062)*s(5070) s(5076) =< s(5062)*s(5071) s(5077) =< s(5061)*s(5069) s(5078) =< s(5061)*s(5072) s(5079) =< s(5068)*s(5071) s(5080) =< s(5073) s(5081) =< s(5074) s(5082) =< s(5076) s(5083) =< s(5078) s(5084) =< s(5083)*s(5072) s(5085) =< s(5077) s(5086) =< s(5085)*s(5069) s(5087) =< s(5079) s(5088) =< s(5087)*aux(208) with precondition: [Out=0,V1>=0,V>=0,V2>=0] * Chain [77]: 76*s(6234)+8*s(6235)+8*s(6236)+4*s(6237)+4*s(6238)+8*s(6240)+76*s(6241)+4*s(6248)+8*s(6253)+8*s(6254)+8*s(6255)+520*s(6256)+80*s(6257)+1040*s(6258)+96*s(6259)+80*s(6260)+16*s(6261)+95*s(6269)+10*s(6270)+10*s(6271)+5*s(6272)+5*s(6273)+70*s(6275)+95*s(6276)+5*s(6283)+10*s(6288)+10*s(6289)+10*s(6290)+650*s(6291)+100*s(6292)+1300*s(6293)+120*s(6294)+100*s(6295)+20*s(6296)+420*s(6299)+12*s(6301)+40*s(6302)+17 Such that:aux(232) =< 2 aux(233) =< V1 aux(234) =< 2*V1+1 aux(235) =< V1/2 aux(236) =< V1/3 aux(237) =< 2/3*V1 aux(238) =< 2/3*V1+1/3 aux(239) =< 2/5*V1 aux(240) =< V aux(241) =< 2*V+1 aux(242) =< V/2 aux(243) =< V/3 aux(244) =< 2/3*V aux(245) =< 2/3*V+1/3 aux(246) =< 2/5*V s(6232) =< aux(238) s(6267) =< aux(245) s(6299) =< aux(232) s(6275) =< aux(240) s(6301) =< s(6275)*aux(240) s(6302) =< s(6299)*aux(232) s(6269) =< aux(240) s(6270) =< aux(240) s(6271) =< aux(240) s(6272) =< aux(240) s(6273) =< aux(240) s(6274) =< aux(240) s(6267) =< aux(240) s(6267) =< aux(241) s(6272) =< aux(242) s(6276) =< aux(243) s(6271) =< aux(244) s(6272) =< aux(244) s(6270) =< aux(246) s(6277) =< aux(240)+2 s(6278) =< aux(240)+1 s(6279) =< aux(240) s(6280) =< aux(240)+3 s(6272) =< aux(241)*(1/2)+aux(242) s(6273) =< aux(241)*(1/2)+aux(242) s(6274) =< aux(241)*(1/2)+aux(242) s(6271) =< aux(241)*(1/3)+aux(244) s(6272) =< aux(241)*(1/3)+aux(244) s(6273) =< aux(241)*(1/3)+aux(244) s(6274) =< aux(241)*(1/3)+aux(244) s(6270) =< aux(241)*(3/5)+s(6267)*(1/5)+aux(246) s(6271) =< aux(241)*(3/5)+s(6267)*(1/5)+aux(246) s(6272) =< aux(241)*(3/5)+s(6267)*(1/5)+aux(246) s(6273) =< aux(241)*(3/5)+s(6267)*(1/5)+aux(246) s(6274) =< aux(241)*(3/5)+s(6267)*(1/5)+aux(246) s(6276) =< aux(241)*(1/3)+aux(243) s(6269) =< aux(241)*(1/3)+aux(243) s(6281) =< s(6274)*s(6277) s(6282) =< s(6272)*s(6278) s(6283) =< s(6270)*s(6278) s(6284) =< s(6270)*s(6279) s(6285) =< s(6269)*s(6277) s(6286) =< s(6269)*s(6280) s(6287) =< s(6276)*s(6279) s(6288) =< s(6281) s(6289) =< s(6282) s(6290) =< s(6284) s(6291) =< s(6286) s(6292) =< s(6291)*s(6280) s(6293) =< s(6285) s(6294) =< s(6293)*s(6277) s(6295) =< s(6287) s(6296) =< s(6295)*aux(240) s(6234) =< aux(233) s(6235) =< aux(233) s(6236) =< aux(233) s(6237) =< aux(233) s(6238) =< aux(233) s(6239) =< aux(233) s(6240) =< aux(233) s(6232) =< aux(233) s(6232) =< aux(234) s(6237) =< aux(235) s(6241) =< aux(236) s(6236) =< aux(237) s(6237) =< aux(237) s(6235) =< aux(239) s(6242) =< aux(233)+2 s(6243) =< aux(233)+1 s(6244) =< aux(233) s(6245) =< aux(233)+3 s(6237) =< aux(234)*(1/2)+aux(235) s(6238) =< aux(234)*(1/2)+aux(235) s(6239) =< aux(234)*(1/2)+aux(235) s(6236) =< aux(234)*(1/3)+aux(237) s(6237) =< aux(234)*(1/3)+aux(237) s(6238) =< aux(234)*(1/3)+aux(237) s(6239) =< aux(234)*(1/3)+aux(237) s(6235) =< aux(234)*(3/5)+s(6232)*(1/5)+aux(239) s(6236) =< aux(234)*(3/5)+s(6232)*(1/5)+aux(239) s(6237) =< aux(234)*(3/5)+s(6232)*(1/5)+aux(239) s(6238) =< aux(234)*(3/5)+s(6232)*(1/5)+aux(239) s(6239) =< aux(234)*(3/5)+s(6232)*(1/5)+aux(239) s(6241) =< aux(234)*(1/3)+aux(236) s(6234) =< aux(234)*(1/3)+aux(236) s(6246) =< s(6239)*s(6242) s(6247) =< s(6237)*s(6243) s(6248) =< s(6235)*s(6243) s(6249) =< s(6235)*s(6244) s(6250) =< s(6234)*s(6242) s(6251) =< s(6234)*s(6245) s(6252) =< s(6241)*s(6244) s(6253) =< s(6246) s(6254) =< s(6247) s(6255) =< s(6249) s(6256) =< s(6251) s(6257) =< s(6256)*s(6245) s(6258) =< s(6250) s(6259) =< s(6258)*s(6242) s(6260) =< s(6252) s(6261) =< s(6260)*aux(233) with precondition: [V2=2,Out=0,V1>=0,V>=0] * Chain [76]: 114*s(6597)+12*s(6598)+12*s(6599)+6*s(6600)+6*s(6601)+12*s(6603)+114*s(6604)+6*s(6611)+12*s(6616)+12*s(6617)+12*s(6618)+780*s(6619)+120*s(6620)+1560*s(6621)+144*s(6622)+120*s(6623)+24*s(6624)+57*s(6632)+6*s(6633)+6*s(6634)+3*s(6635)+3*s(6636)+135*s(6638)+57*s(6639)+3*s(6646)+6*s(6651)+6*s(6652)+6*s(6653)+390*s(6654)+60*s(6655)+780*s(6656)+72*s(6657)+60*s(6658)+12*s(6659)+249*s(6663)+36*s(6664)+12*s(6665)+17 Such that:aux(252) =< 2 aux(253) =< V1 aux(254) =< 2*V1+1 aux(255) =< V1/2 aux(256) =< V1/3 aux(257) =< 2/3*V1 aux(258) =< 2/3*V1+1/3 aux(259) =< 2/5*V1 aux(260) =< V2 aux(261) =< 2*V2+1 aux(262) =< V2/2 aux(263) =< V2/3 aux(264) =< 2/3*V2 aux(265) =< 2/3*V2+1/3 aux(266) =< 2/5*V2 s(6595) =< aux(258) s(6630) =< aux(265) s(6663) =< aux(252) s(6664) =< s(6663)*aux(252) s(6638) =< aux(260) s(6665) =< s(6638)*aux(260) s(6632) =< aux(260) s(6633) =< aux(260) s(6634) =< aux(260) s(6635) =< aux(260) s(6636) =< aux(260) s(6637) =< aux(260) s(6630) =< aux(260) s(6630) =< aux(261) s(6635) =< aux(262) s(6639) =< aux(263) s(6634) =< aux(264) s(6635) =< aux(264) s(6633) =< aux(266) s(6640) =< aux(260)+2 s(6641) =< aux(260)+1 s(6642) =< aux(260) s(6643) =< aux(260)+3 s(6635) =< aux(261)*(1/2)+aux(262) s(6636) =< aux(261)*(1/2)+aux(262) s(6637) =< aux(261)*(1/2)+aux(262) s(6634) =< aux(261)*(1/3)+aux(264) s(6635) =< aux(261)*(1/3)+aux(264) s(6636) =< aux(261)*(1/3)+aux(264) s(6637) =< aux(261)*(1/3)+aux(264) s(6633) =< aux(261)*(3/5)+s(6630)*(1/5)+aux(266) s(6634) =< aux(261)*(3/5)+s(6630)*(1/5)+aux(266) s(6635) =< aux(261)*(3/5)+s(6630)*(1/5)+aux(266) s(6636) =< aux(261)*(3/5)+s(6630)*(1/5)+aux(266) s(6637) =< aux(261)*(3/5)+s(6630)*(1/5)+aux(266) s(6639) =< aux(261)*(1/3)+aux(263) s(6632) =< aux(261)*(1/3)+aux(263) s(6644) =< s(6637)*s(6640) s(6645) =< s(6635)*s(6641) s(6646) =< s(6633)*s(6641) s(6647) =< s(6633)*s(6642) s(6648) =< s(6632)*s(6640) s(6649) =< s(6632)*s(6643) s(6650) =< s(6639)*s(6642) s(6651) =< s(6644) s(6652) =< s(6645) s(6653) =< s(6647) s(6654) =< s(6649) s(6655) =< s(6654)*s(6643) s(6656) =< s(6648) s(6657) =< s(6656)*s(6640) s(6658) =< s(6650) s(6659) =< s(6658)*aux(260) s(6597) =< aux(253) s(6598) =< aux(253) s(6599) =< aux(253) s(6600) =< aux(253) s(6601) =< aux(253) s(6602) =< aux(253) s(6603) =< aux(253) s(6595) =< aux(253) s(6595) =< aux(254) s(6600) =< aux(255) s(6604) =< aux(256) s(6599) =< aux(257) s(6600) =< aux(257) s(6598) =< aux(259) s(6605) =< aux(253)+2 s(6606) =< aux(253)+1 s(6607) =< aux(253) s(6608) =< aux(253)+3 s(6600) =< aux(254)*(1/2)+aux(255) s(6601) =< aux(254)*(1/2)+aux(255) s(6602) =< aux(254)*(1/2)+aux(255) s(6599) =< aux(254)*(1/3)+aux(257) s(6600) =< aux(254)*(1/3)+aux(257) s(6601) =< aux(254)*(1/3)+aux(257) s(6602) =< aux(254)*(1/3)+aux(257) s(6598) =< aux(254)*(3/5)+s(6595)*(1/5)+aux(259) s(6599) =< aux(254)*(3/5)+s(6595)*(1/5)+aux(259) s(6600) =< aux(254)*(3/5)+s(6595)*(1/5)+aux(259) s(6601) =< aux(254)*(3/5)+s(6595)*(1/5)+aux(259) s(6602) =< aux(254)*(3/5)+s(6595)*(1/5)+aux(259) s(6604) =< aux(254)*(1/3)+aux(256) s(6597) =< aux(254)*(1/3)+aux(256) s(6609) =< s(6602)*s(6605) s(6610) =< s(6600)*s(6606) s(6611) =< s(6598)*s(6606) s(6612) =< s(6598)*s(6607) s(6613) =< s(6597)*s(6605) s(6614) =< s(6597)*s(6608) s(6615) =< s(6604)*s(6607) s(6616) =< s(6609) s(6617) =< s(6610) s(6618) =< s(6612) s(6619) =< s(6614) s(6620) =< s(6619)*s(6608) s(6621) =< s(6613) s(6622) =< s(6621)*s(6605) s(6623) =< s(6615) s(6624) =< s(6623)*aux(253) with precondition: [V=2,Out=0,V1>=0,V2>=0] #### Cost of chains of fun3(V1,V,Out): * Chain [84]: 38*s(7146)+4*s(7147)+4*s(7148)+2*s(7149)+2*s(7150)+4*s(7152)+38*s(7153)+2*s(7160)+4*s(7165)+4*s(7166)+4*s(7167)+260*s(7168)+40*s(7169)+520*s(7170)+48*s(7171)+40*s(7172)+8*s(7173)+57*s(7181)+6*s(7182)+6*s(7183)+3*s(7184)+3*s(7185)+9*s(7187)+57*s(7188)+3*s(7195)+6*s(7200)+6*s(7201)+6*s(7202)+390*s(7203)+60*s(7204)+780*s(7205)+72*s(7206)+60*s(7207)+12*s(7208)+1*s(7282)+0 Such that:s(7282) =< 2 aux(285) =< V1 aux(286) =< 2*V1+1 aux(287) =< V1/2 aux(288) =< V1/3 aux(289) =< 2/3*V1 aux(290) =< 2/3*V1+1/3 aux(291) =< 2/5*V1 aux(292) =< V aux(293) =< 2*V+1 aux(294) =< V/2 aux(295) =< V/3 aux(296) =< 2/3*V aux(297) =< 2/3*V+1/3 aux(298) =< 2/5*V s(7144) =< aux(290) s(7179) =< aux(297) s(7187) =< aux(292) s(7181) =< aux(292) s(7182) =< aux(292) s(7183) =< aux(292) s(7184) =< aux(292) s(7185) =< aux(292) s(7186) =< aux(292) s(7179) =< aux(292) s(7179) =< aux(293) s(7184) =< aux(294) s(7188) =< aux(295) s(7183) =< aux(296) s(7184) =< aux(296) s(7182) =< aux(298) s(7189) =< aux(292)+2 s(7190) =< aux(292)+1 s(7191) =< aux(292) s(7192) =< aux(292)+3 s(7184) =< aux(293)*(1/2)+aux(294) s(7185) =< aux(293)*(1/2)+aux(294) s(7186) =< aux(293)*(1/2)+aux(294) s(7183) =< aux(293)*(1/3)+aux(296) s(7184) =< aux(293)*(1/3)+aux(296) s(7185) =< aux(293)*(1/3)+aux(296) s(7186) =< aux(293)*(1/3)+aux(296) s(7182) =< aux(293)*(3/5)+s(7179)*(1/5)+aux(298) s(7183) =< aux(293)*(3/5)+s(7179)*(1/5)+aux(298) s(7184) =< aux(293)*(3/5)+s(7179)*(1/5)+aux(298) s(7185) =< aux(293)*(3/5)+s(7179)*(1/5)+aux(298) s(7186) =< aux(293)*(3/5)+s(7179)*(1/5)+aux(298) s(7188) =< aux(293)*(1/3)+aux(295) s(7181) =< aux(293)*(1/3)+aux(295) s(7193) =< s(7186)*s(7189) s(7194) =< s(7184)*s(7190) s(7195) =< s(7182)*s(7190) s(7196) =< s(7182)*s(7191) s(7197) =< s(7181)*s(7189) s(7198) =< s(7181)*s(7192) s(7199) =< s(7188)*s(7191) s(7200) =< s(7193) s(7201) =< s(7194) s(7202) =< s(7196) s(7203) =< s(7198) s(7204) =< s(7203)*s(7192) s(7205) =< s(7197) s(7206) =< s(7205)*s(7189) s(7207) =< s(7199) s(7208) =< s(7207)*aux(292) s(7146) =< aux(285) s(7147) =< aux(285) s(7148) =< aux(285) s(7149) =< aux(285) s(7150) =< aux(285) s(7151) =< aux(285) s(7152) =< aux(285) s(7144) =< aux(285) s(7144) =< aux(286) s(7149) =< aux(287) s(7153) =< aux(288) s(7148) =< aux(289) s(7149) =< aux(289) s(7147) =< aux(291) s(7154) =< aux(285)+2 s(7155) =< aux(285)+1 s(7156) =< aux(285) s(7157) =< aux(285)+3 s(7149) =< aux(286)*(1/2)+aux(287) s(7150) =< aux(286)*(1/2)+aux(287) s(7151) =< aux(286)*(1/2)+aux(287) s(7148) =< aux(286)*(1/3)+aux(289) s(7149) =< aux(286)*(1/3)+aux(289) s(7150) =< aux(286)*(1/3)+aux(289) s(7151) =< aux(286)*(1/3)+aux(289) s(7147) =< aux(286)*(3/5)+s(7144)*(1/5)+aux(291) s(7148) =< aux(286)*(3/5)+s(7144)*(1/5)+aux(291) s(7149) =< aux(286)*(3/5)+s(7144)*(1/5)+aux(291) s(7150) =< aux(286)*(3/5)+s(7144)*(1/5)+aux(291) s(7151) =< aux(286)*(3/5)+s(7144)*(1/5)+aux(291) s(7153) =< aux(286)*(1/3)+aux(288) s(7146) =< aux(286)*(1/3)+aux(288) s(7158) =< s(7151)*s(7154) s(7159) =< s(7149)*s(7155) s(7160) =< s(7147)*s(7155) s(7161) =< s(7147)*s(7156) s(7162) =< s(7146)*s(7154) s(7163) =< s(7146)*s(7157) s(7164) =< s(7153)*s(7156) s(7165) =< s(7158) s(7166) =< s(7159) s(7167) =< s(7161) s(7168) =< s(7163) s(7169) =< s(7168)*s(7157) s(7170) =< s(7162) s(7171) =< s(7170)*s(7154) s(7172) =< s(7164) s(7173) =< s(7172)*aux(285) with precondition: [Out=0,V1>=0,V>=0] * Chain [83]: 57*s(7328)+6*s(7329)+6*s(7330)+3*s(7331)+3*s(7332)+6*s(7334)+57*s(7335)+3*s(7342)+6*s(7347)+6*s(7348)+6*s(7349)+390*s(7350)+60*s(7351)+780*s(7352)+72*s(7353)+60*s(7354)+12*s(7355)+76*s(7363)+8*s(7364)+8*s(7365)+4*s(7366)+4*s(7367)+9*s(7369)+76*s(7370)+4*s(7377)+8*s(7382)+8*s(7383)+8*s(7384)+520*s(7385)+80*s(7386)+1040*s(7387)+96*s(7388)+80*s(7389)+16*s(7390)+2*s(7532)+1 Such that:aux(300) =< 2 aux(301) =< V1 aux(302) =< 2*V1+1 aux(303) =< V1/2 aux(304) =< V1/3 aux(305) =< 2/3*V1 aux(306) =< 2/3*V1+1/3 aux(307) =< 2/5*V1 aux(308) =< V aux(309) =< 2*V+1 aux(310) =< V/2 aux(311) =< V/3 aux(312) =< 2/3*V aux(313) =< 2/3*V+1/3 aux(314) =< 2/5*V s(7532) =< aux(300) s(7326) =< aux(306) s(7361) =< aux(313) s(7363) =< aux(308) s(7364) =< aux(308) s(7365) =< aux(308) s(7366) =< aux(308) s(7367) =< aux(308) s(7368) =< aux(308) s(7369) =< aux(308) s(7361) =< aux(308) s(7361) =< aux(309) s(7366) =< aux(310) s(7370) =< aux(311) s(7365) =< aux(312) s(7366) =< aux(312) s(7364) =< aux(314) s(7371) =< aux(308)+2 s(7372) =< aux(308)+1 s(7373) =< aux(308) s(7374) =< aux(308)+3 s(7366) =< aux(309)*(1/2)+aux(310) s(7367) =< aux(309)*(1/2)+aux(310) s(7368) =< aux(309)*(1/2)+aux(310) s(7365) =< aux(309)*(1/3)+aux(312) s(7366) =< aux(309)*(1/3)+aux(312) s(7367) =< aux(309)*(1/3)+aux(312) s(7368) =< aux(309)*(1/3)+aux(312) s(7364) =< aux(309)*(3/5)+s(7361)*(1/5)+aux(314) s(7365) =< aux(309)*(3/5)+s(7361)*(1/5)+aux(314) s(7366) =< aux(309)*(3/5)+s(7361)*(1/5)+aux(314) s(7367) =< aux(309)*(3/5)+s(7361)*(1/5)+aux(314) s(7368) =< aux(309)*(3/5)+s(7361)*(1/5)+aux(314) s(7370) =< aux(309)*(1/3)+aux(311) s(7363) =< aux(309)*(1/3)+aux(311) s(7375) =< s(7368)*s(7371) s(7376) =< s(7366)*s(7372) s(7377) =< s(7364)*s(7372) s(7378) =< s(7364)*s(7373) s(7379) =< s(7363)*s(7371) s(7380) =< s(7363)*s(7374) s(7381) =< s(7370)*s(7373) s(7382) =< s(7375) s(7383) =< s(7376) s(7384) =< s(7378) s(7385) =< s(7380) s(7386) =< s(7385)*s(7374) s(7387) =< s(7379) s(7388) =< s(7387)*s(7371) s(7389) =< s(7381) s(7390) =< s(7389)*aux(308) s(7328) =< aux(301) s(7329) =< aux(301) s(7330) =< aux(301) s(7331) =< aux(301) s(7332) =< aux(301) s(7333) =< aux(301) s(7334) =< aux(301) s(7326) =< aux(301) s(7326) =< aux(302) s(7331) =< aux(303) s(7335) =< aux(304) s(7330) =< aux(305) s(7331) =< aux(305) s(7329) =< aux(307) s(7336) =< aux(301)+2 s(7337) =< aux(301)+1 s(7338) =< aux(301) s(7339) =< aux(301)+3 s(7331) =< aux(302)*(1/2)+aux(303) s(7332) =< aux(302)*(1/2)+aux(303) s(7333) =< aux(302)*(1/2)+aux(303) s(7330) =< aux(302)*(1/3)+aux(305) s(7331) =< aux(302)*(1/3)+aux(305) s(7332) =< aux(302)*(1/3)+aux(305) s(7333) =< aux(302)*(1/3)+aux(305) s(7329) =< aux(302)*(3/5)+s(7326)*(1/5)+aux(307) s(7330) =< aux(302)*(3/5)+s(7326)*(1/5)+aux(307) s(7331) =< aux(302)*(3/5)+s(7326)*(1/5)+aux(307) s(7332) =< aux(302)*(3/5)+s(7326)*(1/5)+aux(307) s(7333) =< aux(302)*(3/5)+s(7326)*(1/5)+aux(307) s(7335) =< aux(302)*(1/3)+aux(304) s(7328) =< aux(302)*(1/3)+aux(304) s(7340) =< s(7333)*s(7336) s(7341) =< s(7331)*s(7337) s(7342) =< s(7329)*s(7337) s(7343) =< s(7329)*s(7338) s(7344) =< s(7328)*s(7336) s(7345) =< s(7328)*s(7339) s(7346) =< s(7335)*s(7338) s(7347) =< s(7340) s(7348) =< s(7341) s(7349) =< s(7343) s(7350) =< s(7345) s(7351) =< s(7350)*s(7339) s(7352) =< s(7344) s(7353) =< s(7352)*s(7336) s(7354) =< s(7346) s(7355) =< s(7354)*aux(301) with precondition: [Out=1,V1>=0,V>=0] * Chain [82]: 57*s(7576)+6*s(7577)+6*s(7578)+3*s(7579)+3*s(7580)+6*s(7582)+57*s(7583)+3*s(7590)+6*s(7595)+6*s(7596)+6*s(7597)+390*s(7598)+60*s(7599)+780*s(7600)+72*s(7601)+60*s(7602)+12*s(7603)+76*s(7611)+8*s(7612)+8*s(7613)+4*s(7614)+4*s(7615)+9*s(7617)+76*s(7618)+4*s(7625)+8*s(7630)+8*s(7631)+8*s(7632)+520*s(7633)+80*s(7634)+1040*s(7635)+96*s(7636)+80*s(7637)+16*s(7638)+1*s(7815)+1 Such that:s(7815) =< 1 aux(316) =< V1 aux(317) =< 2*V1+1 aux(318) =< V1/2 aux(319) =< V1/3 aux(320) =< 2/3*V1 aux(321) =< 2/3*V1+1/3 aux(322) =< 2/5*V1 aux(323) =< V aux(324) =< 2*V+1 aux(325) =< V/2 aux(326) =< V/3 aux(327) =< 2/3*V aux(328) =< 2/3*V+1/3 aux(329) =< 2/5*V s(7574) =< aux(321) s(7609) =< aux(328) s(7611) =< aux(323) s(7612) =< aux(323) s(7613) =< aux(323) s(7614) =< aux(323) s(7615) =< aux(323) s(7616) =< aux(323) s(7617) =< aux(323) s(7609) =< aux(323) s(7609) =< aux(324) s(7614) =< aux(325) s(7618) =< aux(326) s(7613) =< aux(327) s(7614) =< aux(327) s(7612) =< aux(329) s(7619) =< aux(323)+2 s(7620) =< aux(323)+1 s(7621) =< aux(323) s(7622) =< aux(323)+3 s(7614) =< aux(324)*(1/2)+aux(325) s(7615) =< aux(324)*(1/2)+aux(325) s(7616) =< aux(324)*(1/2)+aux(325) s(7613) =< aux(324)*(1/3)+aux(327) s(7614) =< aux(324)*(1/3)+aux(327) s(7615) =< aux(324)*(1/3)+aux(327) s(7616) =< aux(324)*(1/3)+aux(327) s(7612) =< aux(324)*(3/5)+s(7609)*(1/5)+aux(329) s(7613) =< aux(324)*(3/5)+s(7609)*(1/5)+aux(329) s(7614) =< aux(324)*(3/5)+s(7609)*(1/5)+aux(329) s(7615) =< aux(324)*(3/5)+s(7609)*(1/5)+aux(329) s(7616) =< aux(324)*(3/5)+s(7609)*(1/5)+aux(329) s(7618) =< aux(324)*(1/3)+aux(326) s(7611) =< aux(324)*(1/3)+aux(326) s(7623) =< s(7616)*s(7619) s(7624) =< s(7614)*s(7620) s(7625) =< s(7612)*s(7620) s(7626) =< s(7612)*s(7621) s(7627) =< s(7611)*s(7619) s(7628) =< s(7611)*s(7622) s(7629) =< s(7618)*s(7621) s(7630) =< s(7623) s(7631) =< s(7624) s(7632) =< s(7626) s(7633) =< s(7628) s(7634) =< s(7633)*s(7622) s(7635) =< s(7627) s(7636) =< s(7635)*s(7619) s(7637) =< s(7629) s(7638) =< s(7637)*aux(323) s(7576) =< aux(316) s(7577) =< aux(316) s(7578) =< aux(316) s(7579) =< aux(316) s(7580) =< aux(316) s(7581) =< aux(316) s(7582) =< aux(316) s(7574) =< aux(316) s(7574) =< aux(317) s(7579) =< aux(318) s(7583) =< aux(319) s(7578) =< aux(320) s(7579) =< aux(320) s(7577) =< aux(322) s(7584) =< aux(316)+2 s(7585) =< aux(316)+1 s(7586) =< aux(316) s(7587) =< aux(316)+3 s(7579) =< aux(317)*(1/2)+aux(318) s(7580) =< aux(317)*(1/2)+aux(318) s(7581) =< aux(317)*(1/2)+aux(318) s(7578) =< aux(317)*(1/3)+aux(320) s(7579) =< aux(317)*(1/3)+aux(320) s(7580) =< aux(317)*(1/3)+aux(320) s(7581) =< aux(317)*(1/3)+aux(320) s(7577) =< aux(317)*(3/5)+s(7574)*(1/5)+aux(322) s(7578) =< aux(317)*(3/5)+s(7574)*(1/5)+aux(322) s(7579) =< aux(317)*(3/5)+s(7574)*(1/5)+aux(322) s(7580) =< aux(317)*(3/5)+s(7574)*(1/5)+aux(322) s(7581) =< aux(317)*(3/5)+s(7574)*(1/5)+aux(322) s(7583) =< aux(317)*(1/3)+aux(319) s(7576) =< aux(317)*(1/3)+aux(319) s(7588) =< s(7581)*s(7584) s(7589) =< s(7579)*s(7585) s(7590) =< s(7577)*s(7585) s(7591) =< s(7577)*s(7586) s(7592) =< s(7576)*s(7584) s(7593) =< s(7576)*s(7587) s(7594) =< s(7583)*s(7586) s(7595) =< s(7588) s(7596) =< s(7589) s(7597) =< s(7591) s(7598) =< s(7593) s(7599) =< s(7598)*s(7587) s(7600) =< s(7592) s(7601) =< s(7600)*s(7584) s(7602) =< s(7594) s(7603) =< s(7602)*aux(316) with precondition: [Out=2,V1>=1,V>=0] * Chain [81]: 19*s(7823)+2*s(7824)+2*s(7825)+1*s(7826)+1*s(7827)+2*s(7829)+19*s(7830)+1*s(7837)+2*s(7842)+2*s(7843)+2*s(7844)+130*s(7845)+20*s(7846)+260*s(7847)+24*s(7848)+20*s(7849)+4*s(7850)+2*s(7851)+0 Such that:s(7816) =< V1 s(7817) =< 2*V1+1 s(7818) =< V1/2 s(7819) =< V1/3 s(7820) =< 2/3*V1 s(7821) =< 2/3*V1+1/3 s(7822) =< 2/5*V1 aux(330) =< 2 s(7851) =< aux(330) s(7823) =< s(7816) s(7824) =< s(7816) s(7825) =< s(7816) s(7826) =< s(7816) s(7827) =< s(7816) s(7828) =< s(7816) s(7829) =< s(7816) s(7821) =< s(7816) s(7821) =< s(7817) s(7826) =< s(7818) s(7830) =< s(7819) s(7825) =< s(7820) s(7826) =< s(7820) s(7824) =< s(7822) s(7831) =< s(7816)+2 s(7832) =< s(7816)+1 s(7833) =< s(7816) s(7834) =< s(7816)+3 s(7826) =< s(7817)*(1/2)+s(7818) s(7827) =< s(7817)*(1/2)+s(7818) s(7828) =< s(7817)*(1/2)+s(7818) s(7825) =< s(7817)*(1/3)+s(7820) s(7826) =< s(7817)*(1/3)+s(7820) s(7827) =< s(7817)*(1/3)+s(7820) s(7828) =< s(7817)*(1/3)+s(7820) s(7824) =< s(7817)*(3/5)+s(7821)*(1/5)+s(7822) s(7825) =< s(7817)*(3/5)+s(7821)*(1/5)+s(7822) s(7826) =< s(7817)*(3/5)+s(7821)*(1/5)+s(7822) s(7827) =< s(7817)*(3/5)+s(7821)*(1/5)+s(7822) s(7828) =< s(7817)*(3/5)+s(7821)*(1/5)+s(7822) s(7830) =< s(7817)*(1/3)+s(7819) s(7823) =< s(7817)*(1/3)+s(7819) s(7835) =< s(7828)*s(7831) s(7836) =< s(7826)*s(7832) s(7837) =< s(7824)*s(7832) s(7838) =< s(7824)*s(7833) s(7839) =< s(7823)*s(7831) s(7840) =< s(7823)*s(7834) s(7841) =< s(7830)*s(7833) s(7842) =< s(7835) s(7843) =< s(7836) s(7844) =< s(7838) s(7845) =< s(7840) s(7846) =< s(7845)*s(7834) s(7847) =< s(7839) s(7848) =< s(7847)*s(7831) s(7849) =< s(7841) s(7850) =< s(7849)*s(7816) with precondition: [V=2,Out=0,V1>=0] * Chain [80]: 38*s(7860)+4*s(7861)+4*s(7862)+2*s(7863)+2*s(7864)+5*s(7866)+38*s(7867)+2*s(7874)+4*s(7879)+4*s(7880)+4*s(7881)+260*s(7882)+40*s(7883)+520*s(7884)+48*s(7885)+40*s(7886)+8*s(7887)+1 Such that:aux(332) =< V1 aux(333) =< 2*V1+1 aux(334) =< V1/2 aux(335) =< V1/3 aux(336) =< 2/3*V1 aux(337) =< 2/3*V1+1/3 aux(338) =< 2/5*V1 s(7858) =< aux(337) s(7860) =< aux(332) s(7861) =< aux(332) s(7862) =< aux(332) s(7863) =< aux(332) s(7864) =< aux(332) s(7865) =< aux(332) s(7866) =< aux(332) s(7858) =< aux(332) s(7858) =< aux(333) s(7863) =< aux(334) s(7867) =< aux(335) s(7862) =< aux(336) s(7863) =< aux(336) s(7861) =< aux(338) s(7868) =< aux(332)+2 s(7869) =< aux(332)+1 s(7870) =< aux(332) s(7871) =< aux(332)+3 s(7863) =< aux(333)*(1/2)+aux(334) s(7864) =< aux(333)*(1/2)+aux(334) s(7865) =< aux(333)*(1/2)+aux(334) s(7862) =< aux(333)*(1/3)+aux(336) s(7863) =< aux(333)*(1/3)+aux(336) s(7864) =< aux(333)*(1/3)+aux(336) s(7865) =< aux(333)*(1/3)+aux(336) s(7861) =< aux(333)*(3/5)+s(7858)*(1/5)+aux(338) s(7862) =< aux(333)*(3/5)+s(7858)*(1/5)+aux(338) s(7863) =< aux(333)*(3/5)+s(7858)*(1/5)+aux(338) s(7864) =< aux(333)*(3/5)+s(7858)*(1/5)+aux(338) s(7865) =< aux(333)*(3/5)+s(7858)*(1/5)+aux(338) s(7867) =< aux(333)*(1/3)+aux(335) s(7860) =< aux(333)*(1/3)+aux(335) s(7872) =< s(7865)*s(7868) s(7873) =< s(7863)*s(7869) s(7874) =< s(7861)*s(7869) s(7875) =< s(7861)*s(7870) s(7876) =< s(7860)*s(7868) s(7877) =< s(7860)*s(7871) s(7878) =< s(7867)*s(7870) s(7879) =< s(7872) s(7880) =< s(7873) s(7881) =< s(7875) s(7882) =< s(7877) s(7883) =< s(7882)*s(7871) s(7884) =< s(7876) s(7885) =< s(7884)*s(7868) s(7886) =< s(7878) s(7887) =< s(7886)*aux(332) with precondition: [V=2,Out=1,V1>=0] * Chain [79]: 19*s(7931)+2*s(7932)+2*s(7933)+1*s(7934)+1*s(7935)+2*s(7937)+19*s(7938)+1*s(7945)+2*s(7950)+2*s(7951)+2*s(7952)+130*s(7953)+20*s(7954)+260*s(7955)+24*s(7956)+20*s(7957)+4*s(7958)+1*s(7959)+1 Such that:s(7959) =< 2 s(7924) =< V1 s(7925) =< 2*V1+1 s(7926) =< V1/2 s(7927) =< V1/3 s(7928) =< 2/3*V1 s(7929) =< 2/3*V1+1/3 s(7930) =< 2/5*V1 s(7931) =< s(7924) s(7932) =< s(7924) s(7933) =< s(7924) s(7934) =< s(7924) s(7935) =< s(7924) s(7936) =< s(7924) s(7937) =< s(7924) s(7929) =< s(7924) s(7929) =< s(7925) s(7934) =< s(7926) s(7938) =< s(7927) s(7933) =< s(7928) s(7934) =< s(7928) s(7932) =< s(7930) s(7939) =< s(7924)+2 s(7940) =< s(7924)+1 s(7941) =< s(7924) s(7942) =< s(7924)+3 s(7934) =< s(7925)*(1/2)+s(7926) s(7935) =< s(7925)*(1/2)+s(7926) s(7936) =< s(7925)*(1/2)+s(7926) s(7933) =< s(7925)*(1/3)+s(7928) s(7934) =< s(7925)*(1/3)+s(7928) s(7935) =< s(7925)*(1/3)+s(7928) s(7936) =< s(7925)*(1/3)+s(7928) s(7932) =< s(7925)*(3/5)+s(7929)*(1/5)+s(7930) s(7933) =< s(7925)*(3/5)+s(7929)*(1/5)+s(7930) s(7934) =< s(7925)*(3/5)+s(7929)*(1/5)+s(7930) s(7935) =< s(7925)*(3/5)+s(7929)*(1/5)+s(7930) s(7936) =< s(7925)*(3/5)+s(7929)*(1/5)+s(7930) s(7938) =< s(7925)*(1/3)+s(7927) s(7931) =< s(7925)*(1/3)+s(7927) s(7943) =< s(7936)*s(7939) s(7944) =< s(7934)*s(7940) s(7945) =< s(7932)*s(7940) s(7946) =< s(7932)*s(7941) s(7947) =< s(7931)*s(7939) s(7948) =< s(7931)*s(7942) s(7949) =< s(7938)*s(7941) s(7950) =< s(7943) s(7951) =< s(7944) s(7952) =< s(7946) s(7953) =< s(7948) s(7954) =< s(7953)*s(7942) s(7955) =< s(7947) s(7956) =< s(7955)*s(7939) s(7957) =< s(7949) s(7958) =< s(7957)*s(7924) with precondition: [V=2,Out=2,V1>=3] #### Cost of chains of fun4(V1,V,Out): * Chain [90]: 38*s(8296)+4*s(8297)+4*s(8298)+2*s(8299)+2*s(8300)+4*s(8302)+38*s(8303)+2*s(8310)+4*s(8315)+4*s(8316)+4*s(8317)+260*s(8318)+40*s(8319)+520*s(8320)+48*s(8321)+40*s(8322)+8*s(8323)+57*s(8331)+6*s(8332)+6*s(8333)+3*s(8334)+3*s(8335)+9*s(8337)+57*s(8338)+3*s(8345)+6*s(8350)+6*s(8351)+6*s(8352)+390*s(8353)+60*s(8354)+780*s(8355)+72*s(8356)+60*s(8357)+12*s(8358)+1*s(8432)+0 Such that:s(8432) =< 2 aux(364) =< V1 aux(365) =< 2*V1+1 aux(366) =< V1/2 aux(367) =< V1/3 aux(368) =< 2/3*V1 aux(369) =< 2/3*V1+1/3 aux(370) =< 2/5*V1 aux(371) =< V aux(372) =< 2*V+1 aux(373) =< V/2 aux(374) =< V/3 aux(375) =< 2/3*V aux(376) =< 2/3*V+1/3 aux(377) =< 2/5*V s(8294) =< aux(369) s(8329) =< aux(376) s(8337) =< aux(371) s(8331) =< aux(371) s(8332) =< aux(371) s(8333) =< aux(371) s(8334) =< aux(371) s(8335) =< aux(371) s(8336) =< aux(371) s(8329) =< aux(371) s(8329) =< aux(372) s(8334) =< aux(373) s(8338) =< aux(374) s(8333) =< aux(375) s(8334) =< aux(375) s(8332) =< aux(377) s(8339) =< aux(371)+2 s(8340) =< aux(371)+1 s(8341) =< aux(371) s(8342) =< aux(371)+3 s(8334) =< aux(372)*(1/2)+aux(373) s(8335) =< aux(372)*(1/2)+aux(373) s(8336) =< aux(372)*(1/2)+aux(373) s(8333) =< aux(372)*(1/3)+aux(375) s(8334) =< aux(372)*(1/3)+aux(375) s(8335) =< aux(372)*(1/3)+aux(375) s(8336) =< aux(372)*(1/3)+aux(375) s(8332) =< aux(372)*(3/5)+s(8329)*(1/5)+aux(377) s(8333) =< aux(372)*(3/5)+s(8329)*(1/5)+aux(377) s(8334) =< aux(372)*(3/5)+s(8329)*(1/5)+aux(377) s(8335) =< aux(372)*(3/5)+s(8329)*(1/5)+aux(377) s(8336) =< aux(372)*(3/5)+s(8329)*(1/5)+aux(377) s(8338) =< aux(372)*(1/3)+aux(374) s(8331) =< aux(372)*(1/3)+aux(374) s(8343) =< s(8336)*s(8339) s(8344) =< s(8334)*s(8340) s(8345) =< s(8332)*s(8340) s(8346) =< s(8332)*s(8341) s(8347) =< s(8331)*s(8339) s(8348) =< s(8331)*s(8342) s(8349) =< s(8338)*s(8341) s(8350) =< s(8343) s(8351) =< s(8344) s(8352) =< s(8346) s(8353) =< s(8348) s(8354) =< s(8353)*s(8342) s(8355) =< s(8347) s(8356) =< s(8355)*s(8339) s(8357) =< s(8349) s(8358) =< s(8357)*aux(371) s(8296) =< aux(364) s(8297) =< aux(364) s(8298) =< aux(364) s(8299) =< aux(364) s(8300) =< aux(364) s(8301) =< aux(364) s(8302) =< aux(364) s(8294) =< aux(364) s(8294) =< aux(365) s(8299) =< aux(366) s(8303) =< aux(367) s(8298) =< aux(368) s(8299) =< aux(368) s(8297) =< aux(370) s(8304) =< aux(364)+2 s(8305) =< aux(364)+1 s(8306) =< aux(364) s(8307) =< aux(364)+3 s(8299) =< aux(365)*(1/2)+aux(366) s(8300) =< aux(365)*(1/2)+aux(366) s(8301) =< aux(365)*(1/2)+aux(366) s(8298) =< aux(365)*(1/3)+aux(368) s(8299) =< aux(365)*(1/3)+aux(368) s(8300) =< aux(365)*(1/3)+aux(368) s(8301) =< aux(365)*(1/3)+aux(368) s(8297) =< aux(365)*(3/5)+s(8294)*(1/5)+aux(370) s(8298) =< aux(365)*(3/5)+s(8294)*(1/5)+aux(370) s(8299) =< aux(365)*(3/5)+s(8294)*(1/5)+aux(370) s(8300) =< aux(365)*(3/5)+s(8294)*(1/5)+aux(370) s(8301) =< aux(365)*(3/5)+s(8294)*(1/5)+aux(370) s(8303) =< aux(365)*(1/3)+aux(367) s(8296) =< aux(365)*(1/3)+aux(367) s(8308) =< s(8301)*s(8304) s(8309) =< s(8299)*s(8305) s(8310) =< s(8297)*s(8305) s(8311) =< s(8297)*s(8306) s(8312) =< s(8296)*s(8304) s(8313) =< s(8296)*s(8307) s(8314) =< s(8303)*s(8306) s(8315) =< s(8308) s(8316) =< s(8309) s(8317) =< s(8311) s(8318) =< s(8313) s(8319) =< s(8318)*s(8307) s(8320) =< s(8312) s(8321) =< s(8320)*s(8304) s(8322) =< s(8314) s(8323) =< s(8322)*aux(364) with precondition: [Out=0,V1>=0,V>=0] * Chain [89]: 57*s(8478)+6*s(8479)+6*s(8480)+3*s(8481)+3*s(8482)+6*s(8484)+57*s(8485)+3*s(8492)+6*s(8497)+6*s(8498)+6*s(8499)+390*s(8500)+60*s(8501)+780*s(8502)+72*s(8503)+60*s(8504)+12*s(8505)+76*s(8513)+8*s(8514)+8*s(8515)+4*s(8516)+4*s(8517)+9*s(8519)+76*s(8520)+4*s(8527)+8*s(8532)+8*s(8533)+8*s(8534)+520*s(8535)+80*s(8536)+1040*s(8537)+96*s(8538)+80*s(8539)+16*s(8540)+2*s(8682)+1 Such that:aux(379) =< 2 aux(380) =< V1 aux(381) =< 2*V1+1 aux(382) =< V1/2 aux(383) =< V1/3 aux(384) =< 2/3*V1 aux(385) =< 2/3*V1+1/3 aux(386) =< 2/5*V1 aux(387) =< V aux(388) =< 2*V+1 aux(389) =< V/2 aux(390) =< V/3 aux(391) =< 2/3*V aux(392) =< 2/3*V+1/3 aux(393) =< 2/5*V s(8682) =< aux(379) s(8476) =< aux(385) s(8511) =< aux(392) s(8513) =< aux(387) s(8514) =< aux(387) s(8515) =< aux(387) s(8516) =< aux(387) s(8517) =< aux(387) s(8518) =< aux(387) s(8519) =< aux(387) s(8511) =< aux(387) s(8511) =< aux(388) s(8516) =< aux(389) s(8520) =< aux(390) s(8515) =< aux(391) s(8516) =< aux(391) s(8514) =< aux(393) s(8521) =< aux(387)+2 s(8522) =< aux(387)+1 s(8523) =< aux(387) s(8524) =< aux(387)+3 s(8516) =< aux(388)*(1/2)+aux(389) s(8517) =< aux(388)*(1/2)+aux(389) s(8518) =< aux(388)*(1/2)+aux(389) s(8515) =< aux(388)*(1/3)+aux(391) s(8516) =< aux(388)*(1/3)+aux(391) s(8517) =< aux(388)*(1/3)+aux(391) s(8518) =< aux(388)*(1/3)+aux(391) s(8514) =< aux(388)*(3/5)+s(8511)*(1/5)+aux(393) s(8515) =< aux(388)*(3/5)+s(8511)*(1/5)+aux(393) s(8516) =< aux(388)*(3/5)+s(8511)*(1/5)+aux(393) s(8517) =< aux(388)*(3/5)+s(8511)*(1/5)+aux(393) s(8518) =< aux(388)*(3/5)+s(8511)*(1/5)+aux(393) s(8520) =< aux(388)*(1/3)+aux(390) s(8513) =< aux(388)*(1/3)+aux(390) s(8525) =< s(8518)*s(8521) s(8526) =< s(8516)*s(8522) s(8527) =< s(8514)*s(8522) s(8528) =< s(8514)*s(8523) s(8529) =< s(8513)*s(8521) s(8530) =< s(8513)*s(8524) s(8531) =< s(8520)*s(8523) s(8532) =< s(8525) s(8533) =< s(8526) s(8534) =< s(8528) s(8535) =< s(8530) s(8536) =< s(8535)*s(8524) s(8537) =< s(8529) s(8538) =< s(8537)*s(8521) s(8539) =< s(8531) s(8540) =< s(8539)*aux(387) s(8478) =< aux(380) s(8479) =< aux(380) s(8480) =< aux(380) s(8481) =< aux(380) s(8482) =< aux(380) s(8483) =< aux(380) s(8484) =< aux(380) s(8476) =< aux(380) s(8476) =< aux(381) s(8481) =< aux(382) s(8485) =< aux(383) s(8480) =< aux(384) s(8481) =< aux(384) s(8479) =< aux(386) s(8486) =< aux(380)+2 s(8487) =< aux(380)+1 s(8488) =< aux(380) s(8489) =< aux(380)+3 s(8481) =< aux(381)*(1/2)+aux(382) s(8482) =< aux(381)*(1/2)+aux(382) s(8483) =< aux(381)*(1/2)+aux(382) s(8480) =< aux(381)*(1/3)+aux(384) s(8481) =< aux(381)*(1/3)+aux(384) s(8482) =< aux(381)*(1/3)+aux(384) s(8483) =< aux(381)*(1/3)+aux(384) s(8479) =< aux(381)*(3/5)+s(8476)*(1/5)+aux(386) s(8480) =< aux(381)*(3/5)+s(8476)*(1/5)+aux(386) s(8481) =< aux(381)*(3/5)+s(8476)*(1/5)+aux(386) s(8482) =< aux(381)*(3/5)+s(8476)*(1/5)+aux(386) s(8483) =< aux(381)*(3/5)+s(8476)*(1/5)+aux(386) s(8485) =< aux(381)*(1/3)+aux(383) s(8478) =< aux(381)*(1/3)+aux(383) s(8490) =< s(8483)*s(8486) s(8491) =< s(8481)*s(8487) s(8492) =< s(8479)*s(8487) s(8493) =< s(8479)*s(8488) s(8494) =< s(8478)*s(8486) s(8495) =< s(8478)*s(8489) s(8496) =< s(8485)*s(8488) s(8497) =< s(8490) s(8498) =< s(8491) s(8499) =< s(8493) s(8500) =< s(8495) s(8501) =< s(8500)*s(8489) s(8502) =< s(8494) s(8503) =< s(8502)*s(8486) s(8504) =< s(8496) s(8505) =< s(8504)*aux(380) with precondition: [Out=1,V1>=0,V>=0] * Chain [88]: 95*s(8726)+10*s(8727)+10*s(8728)+5*s(8729)+5*s(8730)+10*s(8732)+95*s(8733)+5*s(8740)+10*s(8745)+10*s(8746)+10*s(8747)+650*s(8748)+100*s(8749)+1300*s(8750)+120*s(8751)+100*s(8752)+20*s(8753)+133*s(8761)+14*s(8762)+14*s(8763)+7*s(8764)+7*s(8765)+16*s(8767)+133*s(8768)+7*s(8775)+14*s(8780)+14*s(8781)+14*s(8782)+910*s(8783)+140*s(8784)+1820*s(8785)+168*s(8786)+140*s(8787)+28*s(8788)+1*s(9106)+1*s(9142)+1 Such that:s(9142) =< 1 s(9106) =< 2 aux(396) =< V1 aux(397) =< 2*V1+1 aux(398) =< V1/2 aux(399) =< V1/3 aux(400) =< 2/3*V1 aux(401) =< 2/3*V1+1/3 aux(402) =< 2/5*V1 aux(403) =< V aux(404) =< 2*V+1 aux(405) =< V/2 aux(406) =< V/3 aux(407) =< 2/3*V aux(408) =< 2/3*V+1/3 aux(409) =< 2/5*V s(8724) =< aux(401) s(8759) =< aux(408) s(8761) =< aux(403) s(8762) =< aux(403) s(8763) =< aux(403) s(8764) =< aux(403) s(8765) =< aux(403) s(8766) =< aux(403) s(8767) =< aux(403) s(8759) =< aux(403) s(8759) =< aux(404) s(8764) =< aux(405) s(8768) =< aux(406) s(8763) =< aux(407) s(8764) =< aux(407) s(8762) =< aux(409) s(8769) =< aux(403)+2 s(8770) =< aux(403)+1 s(8771) =< aux(403) s(8772) =< aux(403)+3 s(8764) =< aux(404)*(1/2)+aux(405) s(8765) =< aux(404)*(1/2)+aux(405) s(8766) =< aux(404)*(1/2)+aux(405) s(8763) =< aux(404)*(1/3)+aux(407) s(8764) =< aux(404)*(1/3)+aux(407) s(8765) =< aux(404)*(1/3)+aux(407) s(8766) =< aux(404)*(1/3)+aux(407) s(8762) =< aux(404)*(3/5)+s(8759)*(1/5)+aux(409) s(8763) =< aux(404)*(3/5)+s(8759)*(1/5)+aux(409) s(8764) =< aux(404)*(3/5)+s(8759)*(1/5)+aux(409) s(8765) =< aux(404)*(3/5)+s(8759)*(1/5)+aux(409) s(8766) =< aux(404)*(3/5)+s(8759)*(1/5)+aux(409) s(8768) =< aux(404)*(1/3)+aux(406) s(8761) =< aux(404)*(1/3)+aux(406) s(8773) =< s(8766)*s(8769) s(8774) =< s(8764)*s(8770) s(8775) =< s(8762)*s(8770) s(8776) =< s(8762)*s(8771) s(8777) =< s(8761)*s(8769) s(8778) =< s(8761)*s(8772) s(8779) =< s(8768)*s(8771) s(8780) =< s(8773) s(8781) =< s(8774) s(8782) =< s(8776) s(8783) =< s(8778) s(8784) =< s(8783)*s(8772) s(8785) =< s(8777) s(8786) =< s(8785)*s(8769) s(8787) =< s(8779) s(8788) =< s(8787)*aux(403) s(8726) =< aux(396) s(8727) =< aux(396) s(8728) =< aux(396) s(8729) =< aux(396) s(8730) =< aux(396) s(8731) =< aux(396) s(8732) =< aux(396) s(8724) =< aux(396) s(8724) =< aux(397) s(8729) =< aux(398) s(8733) =< aux(399) s(8728) =< aux(400) s(8729) =< aux(400) s(8727) =< aux(402) s(8734) =< aux(396)+2 s(8735) =< aux(396)+1 s(8736) =< aux(396) s(8737) =< aux(396)+3 s(8729) =< aux(397)*(1/2)+aux(398) s(8730) =< aux(397)*(1/2)+aux(398) s(8731) =< aux(397)*(1/2)+aux(398) s(8728) =< aux(397)*(1/3)+aux(400) s(8729) =< aux(397)*(1/3)+aux(400) s(8730) =< aux(397)*(1/3)+aux(400) s(8731) =< aux(397)*(1/3)+aux(400) s(8727) =< aux(397)*(3/5)+s(8724)*(1/5)+aux(402) s(8728) =< aux(397)*(3/5)+s(8724)*(1/5)+aux(402) s(8729) =< aux(397)*(3/5)+s(8724)*(1/5)+aux(402) s(8730) =< aux(397)*(3/5)+s(8724)*(1/5)+aux(402) s(8731) =< aux(397)*(3/5)+s(8724)*(1/5)+aux(402) s(8733) =< aux(397)*(1/3)+aux(399) s(8726) =< aux(397)*(1/3)+aux(399) s(8738) =< s(8731)*s(8734) s(8739) =< s(8729)*s(8735) s(8740) =< s(8727)*s(8735) s(8741) =< s(8727)*s(8736) s(8742) =< s(8726)*s(8734) s(8743) =< s(8726)*s(8737) s(8744) =< s(8733)*s(8736) s(8745) =< s(8738) s(8746) =< s(8739) s(8747) =< s(8741) s(8748) =< s(8743) s(8749) =< s(8748)*s(8737) s(8750) =< s(8742) s(8751) =< s(8750)*s(8734) s(8752) =< s(8744) s(8753) =< s(8752)*aux(396) with precondition: [Out=2,V1>=1,V>=0] * Chain [87]: 19*s(9150)+2*s(9151)+2*s(9152)+1*s(9153)+1*s(9154)+2*s(9156)+19*s(9157)+1*s(9164)+2*s(9169)+2*s(9170)+2*s(9171)+130*s(9172)+20*s(9173)+260*s(9174)+24*s(9175)+20*s(9176)+4*s(9177)+2*s(9178)+0 Such that:s(9143) =< V1 s(9144) =< 2*V1+1 s(9145) =< V1/2 s(9146) =< V1/3 s(9147) =< 2/3*V1 s(9148) =< 2/3*V1+1/3 s(9149) =< 2/5*V1 aux(410) =< 2 s(9178) =< aux(410) s(9150) =< s(9143) s(9151) =< s(9143) s(9152) =< s(9143) s(9153) =< s(9143) s(9154) =< s(9143) s(9155) =< s(9143) s(9156) =< s(9143) s(9148) =< s(9143) s(9148) =< s(9144) s(9153) =< s(9145) s(9157) =< s(9146) s(9152) =< s(9147) s(9153) =< s(9147) s(9151) =< s(9149) s(9158) =< s(9143)+2 s(9159) =< s(9143)+1 s(9160) =< s(9143) s(9161) =< s(9143)+3 s(9153) =< s(9144)*(1/2)+s(9145) s(9154) =< s(9144)*(1/2)+s(9145) s(9155) =< s(9144)*(1/2)+s(9145) s(9152) =< s(9144)*(1/3)+s(9147) s(9153) =< s(9144)*(1/3)+s(9147) s(9154) =< s(9144)*(1/3)+s(9147) s(9155) =< s(9144)*(1/3)+s(9147) s(9151) =< s(9144)*(3/5)+s(9148)*(1/5)+s(9149) s(9152) =< s(9144)*(3/5)+s(9148)*(1/5)+s(9149) s(9153) =< s(9144)*(3/5)+s(9148)*(1/5)+s(9149) s(9154) =< s(9144)*(3/5)+s(9148)*(1/5)+s(9149) s(9155) =< s(9144)*(3/5)+s(9148)*(1/5)+s(9149) s(9157) =< s(9144)*(1/3)+s(9146) s(9150) =< s(9144)*(1/3)+s(9146) s(9162) =< s(9155)*s(9158) s(9163) =< s(9153)*s(9159) s(9164) =< s(9151)*s(9159) s(9165) =< s(9151)*s(9160) s(9166) =< s(9150)*s(9158) s(9167) =< s(9150)*s(9161) s(9168) =< s(9157)*s(9160) s(9169) =< s(9162) s(9170) =< s(9163) s(9171) =< s(9165) s(9172) =< s(9167) s(9173) =< s(9172)*s(9161) s(9174) =< s(9166) s(9175) =< s(9174)*s(9158) s(9176) =< s(9168) s(9177) =< s(9176)*s(9143) with precondition: [V=2,Out=0,V1>=0] * Chain [86]: 19*s(9187)+2*s(9188)+2*s(9189)+1*s(9190)+1*s(9191)+2*s(9193)+19*s(9194)+1*s(9201)+2*s(9206)+2*s(9207)+2*s(9208)+130*s(9209)+20*s(9210)+260*s(9211)+24*s(9212)+20*s(9213)+4*s(9214)+1*s(9215)+1 Such that:s(9215) =< 2 s(9180) =< V1 s(9181) =< 2*V1+1 s(9182) =< V1/2 s(9183) =< V1/3 s(9184) =< 2/3*V1 s(9185) =< 2/3*V1+1/3 s(9186) =< 2/5*V1 s(9187) =< s(9180) s(9188) =< s(9180) s(9189) =< s(9180) s(9190) =< s(9180) s(9191) =< s(9180) s(9192) =< s(9180) s(9193) =< s(9180) s(9185) =< s(9180) s(9185) =< s(9181) s(9190) =< s(9182) s(9194) =< s(9183) s(9189) =< s(9184) s(9190) =< s(9184) s(9188) =< s(9186) s(9195) =< s(9180)+2 s(9196) =< s(9180)+1 s(9197) =< s(9180) s(9198) =< s(9180)+3 s(9190) =< s(9181)*(1/2)+s(9182) s(9191) =< s(9181)*(1/2)+s(9182) s(9192) =< s(9181)*(1/2)+s(9182) s(9189) =< s(9181)*(1/3)+s(9184) s(9190) =< s(9181)*(1/3)+s(9184) s(9191) =< s(9181)*(1/3)+s(9184) s(9192) =< s(9181)*(1/3)+s(9184) s(9188) =< s(9181)*(3/5)+s(9185)*(1/5)+s(9186) s(9189) =< s(9181)*(3/5)+s(9185)*(1/5)+s(9186) s(9190) =< s(9181)*(3/5)+s(9185)*(1/5)+s(9186) s(9191) =< s(9181)*(3/5)+s(9185)*(1/5)+s(9186) s(9192) =< s(9181)*(3/5)+s(9185)*(1/5)+s(9186) s(9194) =< s(9181)*(1/3)+s(9183) s(9187) =< s(9181)*(1/3)+s(9183) s(9199) =< s(9192)*s(9195) s(9200) =< s(9190)*s(9196) s(9201) =< s(9188)*s(9196) s(9202) =< s(9188)*s(9197) s(9203) =< s(9187)*s(9195) s(9204) =< s(9187)*s(9198) s(9205) =< s(9194)*s(9197) s(9206) =< s(9199) s(9207) =< s(9200) s(9208) =< s(9202) s(9209) =< s(9204) s(9210) =< s(9209)*s(9198) s(9211) =< s(9203) s(9212) =< s(9211)*s(9195) s(9213) =< s(9205) s(9214) =< s(9213)*s(9180) with precondition: [V=2,Out=1,V1>=2] * Chain [85]: 57*s(9223)+6*s(9224)+6*s(9225)+3*s(9226)+3*s(9227)+6*s(9229)+57*s(9230)+3*s(9237)+6*s(9242)+6*s(9243)+6*s(9244)+390*s(9245)+60*s(9246)+780*s(9247)+72*s(9248)+60*s(9249)+12*s(9250)+1*s(9286)+1*s(9322)+19*s(9330)+2*s(9331)+2*s(9332)+1*s(9333)+1*s(9334)+2*s(9336)+19*s(9337)+1*s(9344)+2*s(9349)+2*s(9350)+2*s(9351)+130*s(9352)+20*s(9353)+260*s(9354)+24*s(9355)+20*s(9356)+4*s(9357)+1 Such that:s(9286) =< 1 s(9322) =< 2 s(9323) =< V s(9324) =< 2*V+1 s(9325) =< V/2 s(9326) =< V/3 s(9327) =< 2/3*V s(9328) =< 2/3*V+1/3 s(9329) =< 2/5*V aux(411) =< V1 aux(412) =< 2*V1+1 aux(413) =< V1/2 aux(414) =< V1/3 aux(415) =< 2/3*V1 aux(416) =< 2/3*V1+1/3 aux(417) =< 2/5*V1 s(9221) =< aux(416) s(9223) =< aux(411) s(9224) =< aux(411) s(9225) =< aux(411) s(9226) =< aux(411) s(9227) =< aux(411) s(9228) =< aux(411) s(9229) =< aux(411) s(9221) =< aux(411) s(9221) =< aux(412) s(9226) =< aux(413) s(9230) =< aux(414) s(9225) =< aux(415) s(9226) =< aux(415) s(9224) =< aux(417) s(9231) =< aux(411)+2 s(9232) =< aux(411)+1 s(9233) =< aux(411) s(9234) =< aux(411)+3 s(9226) =< aux(412)*(1/2)+aux(413) s(9227) =< aux(412)*(1/2)+aux(413) s(9228) =< aux(412)*(1/2)+aux(413) s(9225) =< aux(412)*(1/3)+aux(415) s(9226) =< aux(412)*(1/3)+aux(415) s(9227) =< aux(412)*(1/3)+aux(415) s(9228) =< aux(412)*(1/3)+aux(415) s(9224) =< aux(412)*(3/5)+s(9221)*(1/5)+aux(417) s(9225) =< aux(412)*(3/5)+s(9221)*(1/5)+aux(417) s(9226) =< aux(412)*(3/5)+s(9221)*(1/5)+aux(417) s(9227) =< aux(412)*(3/5)+s(9221)*(1/5)+aux(417) s(9228) =< aux(412)*(3/5)+s(9221)*(1/5)+aux(417) s(9230) =< aux(412)*(1/3)+aux(414) s(9223) =< aux(412)*(1/3)+aux(414) s(9235) =< s(9228)*s(9231) s(9236) =< s(9226)*s(9232) s(9237) =< s(9224)*s(9232) s(9238) =< s(9224)*s(9233) s(9239) =< s(9223)*s(9231) s(9240) =< s(9223)*s(9234) s(9241) =< s(9230)*s(9233) s(9242) =< s(9235) s(9243) =< s(9236) s(9244) =< s(9238) s(9245) =< s(9240) s(9246) =< s(9245)*s(9234) s(9247) =< s(9239) s(9248) =< s(9247)*s(9231) s(9249) =< s(9241) s(9250) =< s(9249)*aux(411) s(9330) =< s(9323) s(9331) =< s(9323) s(9332) =< s(9323) s(9333) =< s(9323) s(9334) =< s(9323) s(9335) =< s(9323) s(9336) =< s(9323) s(9328) =< s(9323) s(9328) =< s(9324) s(9333) =< s(9325) s(9337) =< s(9326) s(9332) =< s(9327) s(9333) =< s(9327) s(9331) =< s(9329) s(9338) =< s(9323)+2 s(9339) =< s(9323)+1 s(9340) =< s(9323) s(9341) =< s(9323)+3 s(9333) =< s(9324)*(1/2)+s(9325) s(9334) =< s(9324)*(1/2)+s(9325) s(9335) =< s(9324)*(1/2)+s(9325) s(9332) =< s(9324)*(1/3)+s(9327) s(9333) =< s(9324)*(1/3)+s(9327) s(9334) =< s(9324)*(1/3)+s(9327) s(9335) =< s(9324)*(1/3)+s(9327) s(9331) =< s(9324)*(3/5)+s(9328)*(1/5)+s(9329) s(9332) =< s(9324)*(3/5)+s(9328)*(1/5)+s(9329) s(9333) =< s(9324)*(3/5)+s(9328)*(1/5)+s(9329) s(9334) =< s(9324)*(3/5)+s(9328)*(1/5)+s(9329) s(9335) =< s(9324)*(3/5)+s(9328)*(1/5)+s(9329) s(9337) =< s(9324)*(1/3)+s(9326) s(9330) =< s(9324)*(1/3)+s(9326) s(9342) =< s(9335)*s(9338) s(9343) =< s(9333)*s(9339) s(9344) =< s(9331)*s(9339) s(9345) =< s(9331)*s(9340) s(9346) =< s(9330)*s(9338) s(9347) =< s(9330)*s(9341) s(9348) =< s(9337)*s(9340) s(9349) =< s(9342) s(9350) =< s(9343) s(9351) =< s(9345) s(9352) =< s(9347) s(9353) =< s(9352)*s(9341) s(9354) =< s(9346) s(9355) =< s(9354)*s(9338) s(9356) =< s(9348) s(9357) =< s(9356)*s(9323) with precondition: [Out=2,V1>=0,V>=1] #### Cost of chains of fun6(Out): * Chain [92]: 0 with precondition: [Out=0] * Chain [91]: 0 with precondition: [Out=1] #### Cost of chains of fun7(V1,Out): * Chain [94]: 19*s(9585)+2*s(9586)+2*s(9587)+1*s(9588)+1*s(9589)+2*s(9591)+19*s(9592)+1*s(9599)+2*s(9604)+2*s(9605)+2*s(9606)+130*s(9607)+20*s(9608)+260*s(9609)+24*s(9610)+20*s(9611)+4*s(9612)+1 Such that:s(9578) =< V1 s(9579) =< 2*V1+1 s(9580) =< V1/2 s(9581) =< V1/3 s(9582) =< 2/3*V1 s(9583) =< 2/3*V1+1/3 s(9584) =< 2/5*V1 s(9585) =< s(9578) s(9586) =< s(9578) s(9587) =< s(9578) s(9588) =< s(9578) s(9589) =< s(9578) s(9590) =< s(9578) s(9591) =< s(9578) s(9583) =< s(9578) s(9583) =< s(9579) s(9588) =< s(9580) s(9592) =< s(9581) s(9587) =< s(9582) s(9588) =< s(9582) s(9586) =< s(9584) s(9593) =< s(9578)+2 s(9594) =< s(9578)+1 s(9595) =< s(9578) s(9596) =< s(9578)+3 s(9588) =< s(9579)*(1/2)+s(9580) s(9589) =< s(9579)*(1/2)+s(9580) s(9590) =< s(9579)*(1/2)+s(9580) s(9587) =< s(9579)*(1/3)+s(9582) s(9588) =< s(9579)*(1/3)+s(9582) s(9589) =< s(9579)*(1/3)+s(9582) s(9590) =< s(9579)*(1/3)+s(9582) s(9586) =< s(9579)*(3/5)+s(9583)*(1/5)+s(9584) s(9587) =< s(9579)*(3/5)+s(9583)*(1/5)+s(9584) s(9588) =< s(9579)*(3/5)+s(9583)*(1/5)+s(9584) s(9589) =< s(9579)*(3/5)+s(9583)*(1/5)+s(9584) s(9590) =< s(9579)*(3/5)+s(9583)*(1/5)+s(9584) s(9592) =< s(9579)*(1/3)+s(9581) s(9585) =< s(9579)*(1/3)+s(9581) s(9597) =< s(9590)*s(9593) s(9598) =< s(9588)*s(9594) s(9599) =< s(9586)*s(9594) s(9600) =< s(9586)*s(9595) s(9601) =< s(9585)*s(9593) s(9602) =< s(9585)*s(9596) s(9603) =< s(9592)*s(9595) s(9604) =< s(9597) s(9605) =< s(9598) s(9606) =< s(9600) s(9607) =< s(9602) s(9608) =< s(9607)*s(9596) s(9609) =< s(9601) s(9610) =< s(9609)*s(9593) s(9611) =< s(9603) s(9612) =< s(9611)*s(9578) with precondition: [Out=0,V1>=0] * Chain [93]: 19*s(9620)+2*s(9621)+2*s(9622)+1*s(9623)+1*s(9624)+2*s(9626)+19*s(9627)+1*s(9634)+2*s(9639)+2*s(9640)+2*s(9641)+130*s(9642)+20*s(9643)+260*s(9644)+24*s(9645)+20*s(9646)+4*s(9647)+1 Such that:s(9613) =< V1 s(9614) =< 2*V1+1 s(9615) =< V1/2 s(9616) =< V1/3 s(9617) =< 2/3*V1 s(9618) =< 2/3*V1+1/3 s(9619) =< 2/5*V1 s(9620) =< s(9613) s(9621) =< s(9613) s(9622) =< s(9613) s(9623) =< s(9613) s(9624) =< s(9613) s(9625) =< s(9613) s(9626) =< s(9613) s(9618) =< s(9613) s(9618) =< s(9614) s(9623) =< s(9615) s(9627) =< s(9616) s(9622) =< s(9617) s(9623) =< s(9617) s(9621) =< s(9619) s(9628) =< s(9613)+2 s(9629) =< s(9613)+1 s(9630) =< s(9613) s(9631) =< s(9613)+3 s(9623) =< s(9614)*(1/2)+s(9615) s(9624) =< s(9614)*(1/2)+s(9615) s(9625) =< s(9614)*(1/2)+s(9615) s(9622) =< s(9614)*(1/3)+s(9617) s(9623) =< s(9614)*(1/3)+s(9617) s(9624) =< s(9614)*(1/3)+s(9617) s(9625) =< s(9614)*(1/3)+s(9617) s(9621) =< s(9614)*(3/5)+s(9618)*(1/5)+s(9619) s(9622) =< s(9614)*(3/5)+s(9618)*(1/5)+s(9619) s(9623) =< s(9614)*(3/5)+s(9618)*(1/5)+s(9619) s(9624) =< s(9614)*(3/5)+s(9618)*(1/5)+s(9619) s(9625) =< s(9614)*(3/5)+s(9618)*(1/5)+s(9619) s(9627) =< s(9614)*(1/3)+s(9616) s(9620) =< s(9614)*(1/3)+s(9616) s(9632) =< s(9625)*s(9628) s(9633) =< s(9623)*s(9629) s(9634) =< s(9621)*s(9629) s(9635) =< s(9621)*s(9630) s(9636) =< s(9620)*s(9628) s(9637) =< s(9620)*s(9631) s(9638) =< s(9627)*s(9630) s(9639) =< s(9632) s(9640) =< s(9633) s(9641) =< s(9635) s(9642) =< s(9637) s(9643) =< s(9642)*s(9631) s(9644) =< s(9636) s(9645) =< s(9644)*s(9628) s(9646) =< s(9638) s(9647) =< s(9646)*s(9613) with precondition: [Out>=0,V1>=Out+1] #### Cost of chains of fun8(V1,Out): * Chain [97]: 19*s(9655)+2*s(9656)+2*s(9657)+1*s(9658)+1*s(9659)+2*s(9661)+19*s(9662)+1*s(9669)+2*s(9674)+2*s(9675)+2*s(9676)+130*s(9677)+20*s(9678)+260*s(9679)+24*s(9680)+20*s(9681)+4*s(9682)+0 Such that:s(9648) =< V1 s(9649) =< 2*V1+1 s(9650) =< V1/2 s(9651) =< V1/3 s(9652) =< 2/3*V1 s(9653) =< 2/3*V1+1/3 s(9654) =< 2/5*V1 s(9655) =< s(9648) s(9656) =< s(9648) s(9657) =< s(9648) s(9658) =< s(9648) s(9659) =< s(9648) s(9660) =< s(9648) s(9661) =< s(9648) s(9653) =< s(9648) s(9653) =< s(9649) s(9658) =< s(9650) s(9662) =< s(9651) s(9657) =< s(9652) s(9658) =< s(9652) s(9656) =< s(9654) s(9663) =< s(9648)+2 s(9664) =< s(9648)+1 s(9665) =< s(9648) s(9666) =< s(9648)+3 s(9658) =< s(9649)*(1/2)+s(9650) s(9659) =< s(9649)*(1/2)+s(9650) s(9660) =< s(9649)*(1/2)+s(9650) s(9657) =< s(9649)*(1/3)+s(9652) s(9658) =< s(9649)*(1/3)+s(9652) s(9659) =< s(9649)*(1/3)+s(9652) s(9660) =< s(9649)*(1/3)+s(9652) s(9656) =< s(9649)*(3/5)+s(9653)*(1/5)+s(9654) s(9657) =< s(9649)*(3/5)+s(9653)*(1/5)+s(9654) s(9658) =< s(9649)*(3/5)+s(9653)*(1/5)+s(9654) s(9659) =< s(9649)*(3/5)+s(9653)*(1/5)+s(9654) s(9660) =< s(9649)*(3/5)+s(9653)*(1/5)+s(9654) s(9662) =< s(9649)*(1/3)+s(9651) s(9655) =< s(9649)*(1/3)+s(9651) s(9667) =< s(9660)*s(9663) s(9668) =< s(9658)*s(9664) s(9669) =< s(9656)*s(9664) s(9670) =< s(9656)*s(9665) s(9671) =< s(9655)*s(9663) s(9672) =< s(9655)*s(9666) s(9673) =< s(9662)*s(9665) s(9674) =< s(9667) s(9675) =< s(9668) s(9676) =< s(9670) s(9677) =< s(9672) s(9678) =< s(9677)*s(9666) s(9679) =< s(9671) s(9680) =< s(9679)*s(9663) s(9681) =< s(9673) s(9682) =< s(9681)*s(9648) with precondition: [V1>=1,Out>=1,V1+1>=Out] * Chain [96]: 0 with precondition: [Out=0,V1>=0] * Chain [95]: 0 with precondition: [Out=1,V1>=0] #### Cost of chains of start(V1,V,V2): * Chain [98]: 1829*s(9685)+156*s(9688)+887*s(9692)+132*s(9693)+185*s(9733)+1729*s(9746)+182*s(9747)+182*s(9748)+91*s(9749)+91*s(9750)+1729*s(9753)+91*s(9760)+182*s(9765)+182*s(9766)+182*s(9767)+11830*s(9768)+1820*s(9769)+23660*s(9770)+2184*s(9771)+1820*s(9772)+364*s(9773)+1992*s(9799)+232*s(9800)+1026*s(9801)+108*s(9802)+108*s(9803)+54*s(9804)+54*s(9805)+1026*s(9808)+54*s(9815)+108*s(9820)+108*s(9821)+108*s(9822)+7020*s(9823)+1080*s(9824)+14040*s(9825)+1296*s(9826)+1080*s(9827)+216*s(9828)+169*s(9858)+16*s(9859)+1558*s(9861)+164*s(9862)+164*s(9863)+82*s(9864)+82*s(9865)+1558*s(9868)+82*s(9875)+164*s(9880)+164*s(9881)+164*s(9882)+10660*s(9883)+1640*s(9884)+21320*s(9885)+1968*s(9886)+1640*s(9887)+328*s(9888)+19 Such that:aux(438) =< 1 aux(439) =< 2 aux(440) =< V1 aux(441) =< 2*V1+1 aux(442) =< V1/2 aux(443) =< V1/3 aux(444) =< 2/3*V1 aux(445) =< 2/3*V1+1/3 aux(446) =< 2/5*V1 aux(447) =< V aux(448) =< 2*V+1 aux(449) =< V/2 aux(450) =< V/3 aux(451) =< 2/3*V aux(452) =< 2/3*V+1/3 aux(453) =< 2/5*V aux(454) =< V2 aux(455) =< 2*V2+1 aux(456) =< V2/2 aux(457) =< V2/3 aux(458) =< 2/3*V2 aux(459) =< 2/3*V2+1/3 aux(460) =< 2/5*V2 s(9858) =< aux(438) s(9799) =< aux(439) s(9733) =< aux(440) s(9744) =< aux(445) s(9692) =< aux(447) s(9860) =< aux(452) s(9798) =< aux(459) s(9800) =< s(9799)*aux(439) s(9801) =< aux(454) s(9802) =< aux(454) s(9803) =< aux(454) s(9804) =< aux(454) s(9805) =< aux(454) s(9806) =< aux(454) s(9685) =< aux(454) s(9798) =< aux(454) s(9798) =< aux(455) s(9804) =< aux(456) s(9808) =< aux(457) s(9803) =< aux(458) s(9804) =< aux(458) s(9802) =< aux(460) s(9809) =< aux(454)+2 s(9810) =< aux(454)+1 s(9811) =< aux(454) s(9812) =< aux(454)+3 s(9804) =< aux(455)*(1/2)+aux(456) s(9805) =< aux(455)*(1/2)+aux(456) s(9806) =< aux(455)*(1/2)+aux(456) s(9803) =< aux(455)*(1/3)+aux(458) s(9804) =< aux(455)*(1/3)+aux(458) s(9805) =< aux(455)*(1/3)+aux(458) s(9806) =< aux(455)*(1/3)+aux(458) s(9802) =< aux(455)*(3/5)+s(9798)*(1/5)+aux(460) s(9803) =< aux(455)*(3/5)+s(9798)*(1/5)+aux(460) s(9804) =< aux(455)*(3/5)+s(9798)*(1/5)+aux(460) s(9805) =< aux(455)*(3/5)+s(9798)*(1/5)+aux(460) s(9806) =< aux(455)*(3/5)+s(9798)*(1/5)+aux(460) s(9808) =< aux(455)*(1/3)+aux(457) s(9801) =< aux(455)*(1/3)+aux(457) s(9813) =< s(9806)*s(9809) s(9814) =< s(9804)*s(9810) s(9815) =< s(9802)*s(9810) s(9816) =< s(9802)*s(9811) s(9817) =< s(9801)*s(9809) s(9818) =< s(9801)*s(9812) s(9819) =< s(9808)*s(9811) s(9820) =< s(9813) s(9821) =< s(9814) s(9822) =< s(9816) s(9823) =< s(9818) s(9824) =< s(9823)*s(9812) s(9825) =< s(9817) s(9826) =< s(9825)*s(9809) s(9827) =< s(9819) s(9828) =< s(9827)*aux(454) s(9746) =< aux(440) s(9747) =< aux(440) s(9748) =< aux(440) s(9749) =< aux(440) s(9750) =< aux(440) s(9751) =< aux(440) s(9744) =< aux(440) s(9744) =< aux(441) s(9749) =< aux(442) s(9753) =< aux(443) s(9748) =< aux(444) s(9749) =< aux(444) s(9747) =< aux(446) s(9754) =< aux(440)+2 s(9755) =< aux(440)+1 s(9756) =< aux(440) s(9757) =< aux(440)+3 s(9749) =< aux(441)*(1/2)+aux(442) s(9750) =< aux(441)*(1/2)+aux(442) s(9751) =< aux(441)*(1/2)+aux(442) s(9748) =< aux(441)*(1/3)+aux(444) s(9749) =< aux(441)*(1/3)+aux(444) s(9750) =< aux(441)*(1/3)+aux(444) s(9751) =< aux(441)*(1/3)+aux(444) s(9747) =< aux(441)*(3/5)+s(9744)*(1/5)+aux(446) s(9748) =< aux(441)*(3/5)+s(9744)*(1/5)+aux(446) s(9749) =< aux(441)*(3/5)+s(9744)*(1/5)+aux(446) s(9750) =< aux(441)*(3/5)+s(9744)*(1/5)+aux(446) s(9751) =< aux(441)*(3/5)+s(9744)*(1/5)+aux(446) s(9753) =< aux(441)*(1/3)+aux(443) s(9746) =< aux(441)*(1/3)+aux(443) s(9758) =< s(9751)*s(9754) s(9759) =< s(9749)*s(9755) s(9760) =< s(9747)*s(9755) s(9761) =< s(9747)*s(9756) s(9762) =< s(9746)*s(9754) s(9763) =< s(9746)*s(9757) s(9764) =< s(9753)*s(9756) s(9765) =< s(9758) s(9766) =< s(9759) s(9767) =< s(9761) s(9768) =< s(9763) s(9769) =< s(9768)*s(9757) s(9770) =< s(9762) s(9771) =< s(9770)*s(9754) s(9772) =< s(9764) s(9773) =< s(9772)*aux(440) s(9688) =< s(9685)*aux(454) s(9859) =< s(9858)*aux(438) s(9861) =< aux(447) s(9862) =< aux(447) s(9863) =< aux(447) s(9864) =< aux(447) s(9865) =< aux(447) s(9866) =< aux(447) s(9860) =< aux(447) s(9860) =< aux(448) s(9864) =< aux(449) s(9868) =< aux(450) s(9863) =< aux(451) s(9864) =< aux(451) s(9862) =< aux(453) s(9869) =< aux(447)+2 s(9870) =< aux(447)+1 s(9871) =< aux(447) s(9872) =< aux(447)+3 s(9864) =< aux(448)*(1/2)+aux(449) s(9865) =< aux(448)*(1/2)+aux(449) s(9866) =< aux(448)*(1/2)+aux(449) s(9863) =< aux(448)*(1/3)+aux(451) s(9864) =< aux(448)*(1/3)+aux(451) s(9865) =< aux(448)*(1/3)+aux(451) s(9866) =< aux(448)*(1/3)+aux(451) s(9862) =< aux(448)*(3/5)+s(9860)*(1/5)+aux(453) s(9863) =< aux(448)*(3/5)+s(9860)*(1/5)+aux(453) s(9864) =< aux(448)*(3/5)+s(9860)*(1/5)+aux(453) s(9865) =< aux(448)*(3/5)+s(9860)*(1/5)+aux(453) s(9866) =< aux(448)*(3/5)+s(9860)*(1/5)+aux(453) s(9868) =< aux(448)*(1/3)+aux(450) s(9861) =< aux(448)*(1/3)+aux(450) s(9873) =< s(9866)*s(9869) s(9874) =< s(9864)*s(9870) s(9875) =< s(9862)*s(9870) s(9876) =< s(9862)*s(9871) s(9877) =< s(9861)*s(9869) s(9878) =< s(9861)*s(9872) s(9879) =< s(9868)*s(9871) s(9880) =< s(9873) s(9881) =< s(9874) s(9882) =< s(9876) s(9883) =< s(9878) s(9884) =< s(9883)*s(9872) s(9885) =< s(9877) s(9886) =< s(9885)*s(9869) s(9887) =< s(9879) s(9888) =< s(9887)*aux(447) s(9693) =< s(9692)*aux(447) with precondition: [] Closed-form bounds of start(V1,V,V2): ------------------------------------- * Chain [98] with precondition: [] - Upper bound: nat(V1)*111023+5116+nat(V1)*55783*nat(V1)+nat(V1)*4004*nat(V1)*nat(V1)+nat(V1)*364*nat(V1)*nat(V1/3)+nat(V1)*1820*nat(V1/3)+nat(V)*100763+nat(V)*50398*nat(V)+nat(V)*3608*nat(V)*nat(V)+nat(V)*328*nat(V)*nat(V/3)+nat(V)*1640*nat(V/3)+nat(V2)*67601+nat(V2)*33258*nat(V2)+nat(V2)*2376*nat(V2)*nat(V2)+nat(V2)*216*nat(V2)*nat(V2/3)+nat(V2)*1080*nat(V2/3)+nat(V1/3)*1729+nat(V/3)*1558+nat(V2/3)*1026 - Complexity: n^3 ### Maximum cost of start(V1,V,V2): nat(V1)*111023+5116+nat(V1)*55783*nat(V1)+nat(V1)*4004*nat(V1)*nat(V1)+nat(V1)*364*nat(V1)*nat(V1/3)+nat(V1)*1820*nat(V1/3)+nat(V)*100763+nat(V)*50398*nat(V)+nat(V)*3608*nat(V)*nat(V)+nat(V)*328*nat(V)*nat(V/3)+nat(V)*1640*nat(V/3)+nat(V2)*67601+nat(V2)*33258*nat(V2)+nat(V2)*2376*nat(V2)*nat(V2)+nat(V2)*216*nat(V2)*nat(V2/3)+nat(V2)*1080*nat(V2/3)+nat(V1/3)*1729+nat(V/3)*1558+nat(V2/3)*1026 Asymptotic class: n^3 * Total analysis performed in 49891 ms. ---------------------------------------- (14) BOUNDS(1, n^3) ---------------------------------------- (15) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (16) Obligation: Analyzing the following TRS for decreasing loops: 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: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(neq(x, 0), y, y) cond2(false, x, y) -> cond1(neq(x, 0), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) neq(0, 0) -> false neq(0, s(x)) -> true neq(s(x), 0) -> true neq(s(x), s(y)) -> neq(x, y) p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(0) -> 0 encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (17) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence neq(s(x), s(y)) ->^+ neq(x, y) gives rise to a decreasing loop by considering the right hand sides subterm at position []. The pumping substitution is [x / s(x), y / s(y)]. The result substitution is [ ]. ---------------------------------------- (18) Complex Obligation (BEST) ---------------------------------------- (19) Obligation: Proved the lower bound n^1 for the following 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: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(neq(x, 0), y, y) cond2(false, x, y) -> cond1(neq(x, 0), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) neq(0, 0) -> false neq(0, s(x)) -> true neq(s(x), 0) -> true neq(s(x), s(y)) -> neq(x, y) p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(0) -> 0 encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (20) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (21) BOUNDS(n^1, INF) ---------------------------------------- (22) Obligation: Analyzing the following TRS for decreasing loops: 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: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(neq(x, 0), y, y) cond2(false, x, y) -> cond1(neq(x, 0), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) neq(0, 0) -> false neq(0, s(x)) -> true neq(s(x), 0) -> true neq(s(x), s(y)) -> neq(x, y) p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(0) -> 0 encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_neq(x_1, x_2)) -> neq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_neq(x_1, x_2) -> neq(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST