/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3).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), 254 ms] (4) CpxRelTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 32.8 s] (14) BOUNDS(1, n^3) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRelTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 0 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 245 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 127 ms] (28) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: p(0) -> 0 p(s(x)) -> x le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) minus(x, y) -> if(le(x, y), x, y) if(true, x, y) -> 0 if(false, x, y) -> s(minus(p(x), y)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: p(0) -> 0 p(s(x)) -> x le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) minus(x, y) -> if(le(x, y), x, y) if(true, x, y) -> 0 if(false, x, y) -> s(minus(p(x), y)) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: p(0) -> 0 p(s(x)) -> x le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) minus(x, y) -> if(le(x, y), x, y) if(true, x, y) -> 0 if(false, x, y) -> s(minus(p(x), y)) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). The TRS R consists of the following rules: p(0) -> 0 [1] p(s(x)) -> x [1] le(0, y) -> true [1] le(s(x), 0) -> false [1] le(s(x), s(y)) -> le(x, y) [1] minus(x, y) -> if(le(x, y), x, y) [1] if(true, x, y) -> 0 [1] if(false, x, y) -> s(minus(p(x), y)) [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) [0] encode_true -> true [0] encode_false -> false [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: p(0) -> 0 [1] p(s(x)) -> x [1] le(0, y) -> true [1] le(s(x), 0) -> false [1] le(s(x), s(y)) -> le(x, y) [1] minus(x, y) -> if(le(x, y), x, y) [1] if(true, x, y) -> 0 [1] if(false, x, y) -> s(minus(p(x), y)) [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) [0] encode_true -> true [0] encode_false -> false [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] The TRS has the following type information: p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if 0 :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if s :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if true :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if false :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if minus :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encArg :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if cons_p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if cons_le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if cons_minus :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if cons_if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_0 :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_s :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_true :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_false :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_minus :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if 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_p(v0) -> null_encode_p [0] encode_0 -> null_encode_0 [0] encode_s(v0) -> null_encode_s [0] encode_le(v0, v1) -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_minus(v0, v1) -> null_encode_minus [0] encode_if(v0, v1, v2) -> null_encode_if [0] p(v0) -> null_p [0] le(v0, v1) -> null_le [0] if(v0, v1, v2) -> null_if [0] And the following fresh constants: null_encArg, null_encode_p, null_encode_0, null_encode_s, null_encode_le, null_encode_true, null_encode_false, null_encode_minus, null_encode_if, null_p, null_le, null_if ---------------------------------------- (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: p(0) -> 0 [1] p(s(x)) -> x [1] le(0, y) -> true [1] le(s(x), 0) -> false [1] le(s(x), s(y)) -> le(x, y) [1] minus(x, y) -> if(le(x, y), x, y) [1] if(true, x, y) -> 0 [1] if(false, x, y) -> s(minus(p(x), y)) [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) [0] encode_true -> true [0] encode_false -> false [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(v0) -> null_encArg [0] encode_p(v0) -> null_encode_p [0] encode_0 -> null_encode_0 [0] encode_s(v0) -> null_encode_s [0] encode_le(v0, v1) -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_minus(v0, v1) -> null_encode_minus [0] encode_if(v0, v1, v2) -> null_encode_if [0] p(v0) -> null_p [0] le(v0, v1) -> null_le [0] if(v0, v1, v2) -> null_if [0] The TRS has the following type information: p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if 0 :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if s :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if true :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if false :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if minus :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if encArg :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if cons_p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if cons_le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if cons_minus :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if cons_if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if encode_p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if encode_0 :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if encode_s :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if encode_le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if encode_true :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if encode_false :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if encode_minus :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if encode_if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if null_encArg :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if null_encode_p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if null_encode_0 :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if null_encode_s :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if null_encode_le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if null_encode_true :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if null_encode_false :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if null_encode_minus :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if null_encode_if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if null_p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if null_le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if null_if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_if Rewrite Strategy: INNERMOST ---------------------------------------- (11) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 true => 2 false => 1 null_encArg => 0 null_encode_p => 0 null_encode_0 => 0 null_encode_s => 0 null_encode_le => 0 null_encode_true => 0 null_encode_false => 0 null_encode_minus => 0 null_encode_if => 0 null_p => 0 null_le => 0 null_if => 0 ---------------------------------------- (12) Obligation: Complexity RNTS consisting of the following rules: encArg(z) -{ 0 }-> p(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> minus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> le(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encArg(z) -{ 0 }-> 2 :|: z = 2 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0 encode_0 -{ 0 }-> 0 :|: encode_false -{ 0 }-> 1 :|: encode_false -{ 0 }-> 0 :|: encode_if(z, z', z'') -{ 0 }-> if(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_if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_le(z, z') -{ 0 }-> le(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_le(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_minus(z, z') -{ 0 }-> minus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_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 :|: if(z, z', z'') -{ 1 }-> 0 :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0 if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 if(z, z', z'') -{ 1 }-> 1 + minus(p(x), y) :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0 le(z, z') -{ 1 }-> le(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x le(z, z') -{ 1 }-> 2 :|: y >= 0, z = 0, z' = y le(z, z') -{ 1 }-> 1 :|: x >= 0, z = 1 + x, z' = 0 le(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 minus(z, z') -{ 1 }-> if(le(x, y), x, y) :|: x >= 0, y >= 0, z = x, z' = y 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(V, V2, V11),0,[p(V, Out)],[V >= 0]). eq(start(V, V2, V11),0,[le(V, V2, Out)],[V >= 0,V2 >= 0]). eq(start(V, V2, V11),0,[minus(V, V2, Out)],[V >= 0,V2 >= 0]). eq(start(V, V2, V11),0,[if(V, V2, V11, Out)],[V >= 0,V2 >= 0,V11 >= 0]). eq(start(V, V2, V11),0,[encArg(V, Out)],[V >= 0]). eq(start(V, V2, V11),0,[fun(V, Out)],[V >= 0]). eq(start(V, V2, V11),0,[fun1(Out)],[]). eq(start(V, V2, V11),0,[fun2(V, Out)],[V >= 0]). eq(start(V, V2, V11),0,[fun3(V, V2, Out)],[V >= 0,V2 >= 0]). eq(start(V, V2, V11),0,[fun4(Out)],[]). eq(start(V, V2, V11),0,[fun5(Out)],[]). eq(start(V, V2, V11),0,[fun6(V, V2, Out)],[V >= 0,V2 >= 0]). eq(start(V, V2, V11),0,[fun7(V, V2, V11, Out)],[V >= 0,V2 >= 0,V11 >= 0]). eq(p(V, Out),1,[],[Out = 0,V = 0]). eq(p(V, Out),1,[],[Out = V1,V1 >= 0,V = 1 + V1]). eq(le(V, V2, Out),1,[],[Out = 2,V3 >= 0,V = 0,V2 = V3]). eq(le(V, V2, Out),1,[],[Out = 1,V4 >= 0,V = 1 + V4,V2 = 0]). eq(le(V, V2, Out),1,[le(V5, V6, Ret)],[Out = Ret,V2 = 1 + V6,V5 >= 0,V6 >= 0,V = 1 + V5]). eq(minus(V, V2, Out),1,[le(V7, V8, Ret0),if(Ret0, V7, V8, Ret1)],[Out = Ret1,V7 >= 0,V8 >= 0,V = V7,V2 = V8]). eq(if(V, V2, V11, Out),1,[],[Out = 0,V = 2,V2 = V9,V11 = V10,V9 >= 0,V10 >= 0]). eq(if(V, V2, V11, Out),1,[p(V13, Ret10),minus(Ret10, V12, Ret11)],[Out = 1 + Ret11,V2 = V13,V11 = V12,V = 1,V13 >= 0,V12 >= 0]). eq(encArg(V, Out),0,[],[Out = 0,V = 0]). eq(encArg(V, Out),0,[encArg(V14, Ret12)],[Out = 1 + Ret12,V = 1 + V14,V14 >= 0]). eq(encArg(V, Out),0,[],[Out = 2,V = 2]). eq(encArg(V, Out),0,[],[Out = 1,V = 1]). eq(encArg(V, Out),0,[encArg(V15, Ret01),p(Ret01, Ret2)],[Out = Ret2,V = 1 + V15,V15 >= 0]). eq(encArg(V, Out),0,[encArg(V16, Ret02),encArg(V17, Ret13),le(Ret02, Ret13, Ret3)],[Out = Ret3,V16 >= 0,V = 1 + V16 + V17,V17 >= 0]). eq(encArg(V, Out),0,[encArg(V19, Ret03),encArg(V18, Ret14),minus(Ret03, Ret14, Ret4)],[Out = Ret4,V19 >= 0,V = 1 + V18 + V19,V18 >= 0]). eq(encArg(V, Out),0,[encArg(V22, Ret04),encArg(V21, Ret15),encArg(V20, Ret21),if(Ret04, Ret15, Ret21, Ret5)],[Out = Ret5,V22 >= 0,V = 1 + V20 + V21 + V22,V20 >= 0,V21 >= 0]). eq(fun(V, Out),0,[encArg(V23, Ret05),p(Ret05, Ret6)],[Out = Ret6,V23 >= 0,V = V23]). eq(fun1(Out),0,[],[Out = 0]). eq(fun2(V, Out),0,[encArg(V24, Ret16)],[Out = 1 + Ret16,V24 >= 0,V = V24]). eq(fun3(V, V2, Out),0,[encArg(V26, Ret06),encArg(V25, Ret17),le(Ret06, Ret17, Ret7)],[Out = Ret7,V26 >= 0,V25 >= 0,V = V26,V2 = V25]). eq(fun4(Out),0,[],[Out = 2]). eq(fun5(Out),0,[],[Out = 1]). eq(fun6(V, V2, Out),0,[encArg(V28, Ret07),encArg(V27, Ret18),minus(Ret07, Ret18, Ret8)],[Out = Ret8,V28 >= 0,V27 >= 0,V = V28,V2 = V27]). eq(fun7(V, V2, V11, Out),0,[encArg(V29, Ret08),encArg(V31, Ret19),encArg(V30, Ret22),if(Ret08, Ret19, Ret22, Ret9)],[Out = Ret9,V29 >= 0,V30 >= 0,V31 >= 0,V = V29,V2 = V31,V11 = V30]). eq(encArg(V, Out),0,[],[Out = 0,V32 >= 0,V = V32]). eq(fun(V, Out),0,[],[Out = 0,V33 >= 0,V = V33]). eq(fun2(V, Out),0,[],[Out = 0,V34 >= 0,V = V34]). eq(fun3(V, V2, Out),0,[],[Out = 0,V35 >= 0,V36 >= 0,V = V35,V2 = V36]). eq(fun4(Out),0,[],[Out = 0]). eq(fun5(Out),0,[],[Out = 0]). eq(fun6(V, V2, Out),0,[],[Out = 0,V37 >= 0,V38 >= 0,V = V37,V2 = V38]). eq(fun7(V, V2, V11, Out),0,[],[Out = 0,V39 >= 0,V11 = V41,V40 >= 0,V = V39,V2 = V40,V41 >= 0]). eq(p(V, Out),0,[],[Out = 0,V42 >= 0,V = V42]). eq(le(V, V2, Out),0,[],[Out = 0,V43 >= 0,V44 >= 0,V = V43,V2 = V44]). eq(if(V, V2, V11, Out),0,[],[Out = 0,V45 >= 0,V11 = V47,V46 >= 0,V = V45,V2 = V46,V47 >= 0]). input_output_vars(p(V,Out),[V],[Out]). input_output_vars(le(V,V2,Out),[V,V2],[Out]). input_output_vars(minus(V,V2,Out),[V,V2],[Out]). input_output_vars(if(V,V2,V11,Out),[V,V2,V11],[Out]). input_output_vars(encArg(V,Out),[V],[Out]). input_output_vars(fun(V,Out),[V],[Out]). input_output_vars(fun1(Out),[],[Out]). input_output_vars(fun2(V,Out),[V],[Out]). input_output_vars(fun3(V,V2,Out),[V,V2],[Out]). input_output_vars(fun4(Out),[],[Out]). input_output_vars(fun5(Out),[],[Out]). input_output_vars(fun6(V,V2,Out),[V,V2],[Out]). input_output_vars(fun7(V,V2,V11,Out),[V,V2,V11],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [le/3] 1. non_recursive : [p/2] 2. recursive : [if/4,minus/3] 3. recursive [non_tail,multiple] : [encArg/2] 4. non_recursive : [fun/2] 5. non_recursive : [fun1/1] 6. non_recursive : [fun2/2] 7. non_recursive : [fun3/3] 8. non_recursive : [fun4/1] 9. non_recursive : [fun5/1] 10. non_recursive : [fun6/3] 11. non_recursive : [fun7/4] 12. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into le/3 1. SCC is partially evaluated into p/2 2. SCC is partially evaluated into minus/3 3. SCC is partially evaluated into encArg/2 4. SCC is partially evaluated into fun/2 5. SCC is completely evaluated into other SCCs 6. SCC is partially evaluated into fun2/2 7. SCC is partially evaluated into fun3/3 8. SCC is partially evaluated into fun4/1 9. SCC is partially evaluated into fun5/1 10. SCC is partially evaluated into fun6/3 11. SCC is partially evaluated into fun7/4 12. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations le/3 * CE 24 is refined into CE [51] * CE 22 is refined into CE [52] * CE 21 is refined into CE [53] * CE 23 is refined into CE [54] ### Cost equations --> "Loop" of le/3 * CEs [54] --> Loop 26 * CEs [51] --> Loop 27 * CEs [52] --> Loop 28 * CEs [53] --> Loop 29 ### Ranking functions of CR le(V,V2,Out) * RF of phase [26]: [V,V2] #### Partial ranking functions of CR le(V,V2,Out) * Partial RF of phase [26]: - RF of loop [26:1]: V V2 ### Specialization of cost equations p/2 * CE 16 is refined into CE [55] * CE 15 is refined into CE [56] * CE 17 is refined into CE [57] ### Cost equations --> "Loop" of p/2 * CEs [55] --> Loop 30 * CEs [56,57] --> Loop 31 ### Ranking functions of CR p(V,Out) #### Partial ranking functions of CR p(V,Out) ### Specialization of cost equations minus/3 * CE 18 is refined into CE [58,59,60,61,62] * CE 20 is refined into CE [63,64] * CE 19 is refined into CE [65,66,67,68] ### Cost equations --> "Loop" of minus/3 * CEs [68] --> Loop 32 * CEs [67] --> Loop 33 * CEs [66] --> Loop 34 * CEs [65] --> Loop 35 * CEs [59] --> Loop 36 * CEs [58,60,61,62,63,64] --> Loop 37 ### Ranking functions of CR minus(V,V2,Out) * RF of phase [32]: [V-1,V-V2] * RF of phase [34]: [V] #### Partial ranking functions of CR minus(V,V2,Out) * Partial RF of phase [32]: - RF of loop [32:1]: V-1 V-V2 * Partial RF of phase [34]: - RF of loop [34:1]: V ### Specialization of cost equations encArg/2 * CE 28 is refined into CE [69] * CE 30 is refined into CE [70] * CE 31 is refined into CE [71] * CE 33 is refined into CE [72,73,74,75,76] * CE 34 is refined into CE [77,78,79] * CE 29 is refined into CE [80] * CE 32 is refined into CE [81,82] * CE 26 is refined into CE [83,84,85,86] * CE 25 is refined into CE [87] * CE 27 is refined into CE [88] ### Cost equations --> "Loop" of encArg/2 * CEs [86] --> Loop 38 * CEs [85] --> Loop 39 * CEs [83,84] --> Loop 40 * CEs [87,88] --> Loop 41 * CEs [80] --> Loop 42 * CEs [82] --> Loop 43 * CEs [81] --> Loop 44 * CEs [76] --> Loop 45 * CEs [72] --> Loop 46 * CEs [75,79] --> Loop 47 * CEs [73,78] --> Loop 48 * CEs [74,77] --> Loop 49 * CEs [69] --> Loop 50 * CEs [70] --> Loop 51 * CEs [71] --> Loop 52 ### Ranking functions of CR encArg(V,Out) * RF of phase [38,39,40,41,42,43,44,45,46,47,48,49]: [V] #### Partial ranking functions of CR encArg(V,Out) * Partial RF of phase [38,39,40,41,42,43,44,45,46,47,48,49]: - RF of loop [38:1,38:2,38:3,39:1,39:2,39:3,40:1,40:2,40:3,41:1,41:2,41:3,42:1,43:1,44:1,45:1,45:2,46:1,46:2,47:1,47:2,48:1,48:2,49:1,49:2]: V ### Specialization of cost equations fun/2 * CE 35 is refined into CE [89,90,91,92,93] * CE 36 is refined into CE [94] ### Cost equations --> "Loop" of fun/2 * CEs [90,92] --> Loop 53 * CEs [89,91,93,94] --> Loop 54 ### Ranking functions of CR fun(V,Out) #### Partial ranking functions of CR fun(V,Out) ### Specialization of cost equations fun2/2 * CE 37 is refined into CE [95,96,97] * CE 38 is refined into CE [98] ### Cost equations --> "Loop" of fun2/2 * CEs [97] --> Loop 55 * CEs [98] --> Loop 56 * CEs [95,96] --> Loop 57 ### Ranking functions of CR fun2(V,Out) #### Partial ranking functions of CR fun2(V,Out) ### Specialization of cost equations fun3/3 * CE 39 is refined into CE [99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124] * CE 40 is refined into CE [125] ### Cost equations --> "Loop" of fun3/3 * CEs [104,107,121] --> Loop 58 * CEs [106] --> Loop 59 * CEs [105,122] --> Loop 60 * CEs [100,102,109,111,113,117] --> Loop 61 * CEs [99,103,108,114,116,119,123] --> Loop 62 * CEs [101,110,112,115,118,120,124,125] --> Loop 63 ### Ranking functions of CR fun3(V,V2,Out) #### Partial ranking functions of CR fun3(V,V2,Out) ### Specialization of cost equations fun4/1 * CE 41 is refined into CE [126] * CE 42 is refined into CE [127] ### Cost equations --> "Loop" of fun4/1 * CEs [126] --> Loop 64 * CEs [127] --> Loop 65 ### Ranking functions of CR fun4(Out) #### Partial ranking functions of CR fun4(Out) ### Specialization of cost equations fun5/1 * CE 43 is refined into CE [128] * CE 44 is refined into CE [129] ### Cost equations --> "Loop" of fun5/1 * CEs [128] --> Loop 66 * CEs [129] --> Loop 67 ### Ranking functions of CR fun5(Out) #### Partial ranking functions of CR fun5(Out) ### Specialization of cost equations fun6/3 * CE 45 is refined into CE [130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145] * CE 46 is refined into CE [146] ### Cost equations --> "Loop" of fun6/3 * CEs [134] --> Loop 68 * CEs [133,144] --> Loop 69 * CEs [131,132,136,138,139,142] --> Loop 70 * CEs [130,135,137,140,141,143,145,146] --> Loop 71 ### Ranking functions of CR fun6(V,V2,Out) #### Partial ranking functions of CR fun6(V,V2,Out) ### Specialization of cost equations fun7/4 * CE 47 is refined into CE [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] * CE 48 is refined into CE [174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194] * CE 49 is refined into CE [195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212] * CE 50 is refined into CE [213] ### Cost equations --> "Loop" of fun7/4 * CEs [180] --> Loop 72 * CEs [178,179,193] --> Loop 73 * CEs [176,177,183,186,191] --> Loop 74 * CEs [174,175,181,182,184,185,187,188,189,190,192,194] --> Loop 75 * CEs [150,151,152,168,169,170,198,199,200] --> Loop 76 * CEs [148,154,157,163,166,172,196,202,205,211] --> Loop 77 * CEs [147,149,153,155,156,158,159,160,161,162,164,165,167,171,173,195,197,201,203,204,206,207,208,209,210,212,213] --> Loop 78 ### Ranking functions of CR fun7(V,V2,V11,Out) #### Partial ranking functions of CR fun7(V,V2,V11,Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [214] * CE 2 is refined into CE [215,216,217,218] * CE 3 is refined into CE [219] * CE 4 is refined into CE [220,221] * CE 5 is refined into CE [222,223,224,225,226] * CE 6 is refined into CE [227,228,229] * CE 7 is refined into CE [230,231,232] * CE 8 is refined into CE [233,234] * CE 9 is refined into CE [235,236,237] * CE 10 is refined into CE [238,239,240] * CE 11 is refined into CE [241,242] * CE 12 is refined into CE [243,244] * CE 13 is refined into CE [245,246] * CE 14 is refined into CE [247,248,249,250] ### Cost equations --> "Loop" of start/3 * CEs [214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250] --> Loop 79 ### Ranking functions of CR start(V,V2,V11) #### Partial ranking functions of CR start(V,V2,V11) Computing Bounds ===================================== #### Cost of chains of le(V,V2,Out): * Chain [[26],29]: 1*it(26)+1 Such that:it(26) =< V with precondition: [Out=2,V>=1,V2>=V] * Chain [[26],28]: 1*it(26)+1 Such that:it(26) =< V2 with precondition: [Out=1,V2>=1,V>=V2+1] * Chain [[26],27]: 1*it(26)+0 Such that:it(26) =< V2 with precondition: [Out=0,V>=1,V2>=1] * Chain [29]: 1 with precondition: [V=0,Out=2,V2>=0] * Chain [28]: 1 with precondition: [V2=0,Out=1,V>=1] * Chain [27]: 0 with precondition: [Out=0,V>=0,V2>=0] #### Cost of chains of p(V,Out): * Chain [31]: 1 with precondition: [Out=0,V>=0] * Chain [30]: 1 with precondition: [V=Out+1,V>=1] #### Cost of chains of minus(V,V2,Out): * Chain [[34],37]: 4*it(34)+2*s(4)+3 Such that:aux(1) =< V-Out it(34) =< Out s(4) =< aux(1) with precondition: [V2=0,Out>=1,V>=Out] * Chain [[34],36]: 4*it(34)+2 Such that:it(34) =< Out with precondition: [V2=0,Out>=1,V>=Out+1] * Chain [[34],35,37]: 4*it(34)+7 Such that:it(34) =< Out with precondition: [V2=0,Out>=2,V>=Out] * Chain [[32],37]: 4*it(32)+2*s(2)+2*s(4)+1*s(8)+3 Such that:aux(1) =< V-Out it(32) =< Out aux(5) =< V2 s(4) =< aux(1) s(2) =< aux(5) s(8) =< it(32)*aux(5) with precondition: [V2>=1,Out>=1,V>=Out+V2] * Chain [[32],33,37]: 4*it(32)+3*s(2)+1*s(8)+7 Such that:it(32) =< Out aux(7) =< V2 s(2) =< aux(7) s(8) =< it(32)*aux(7) with precondition: [V2>=1,Out>=2,V>=Out+V2] * Chain [37]: 2*s(2)+2*s(4)+3 Such that:aux(1) =< V aux(2) =< V2 s(4) =< aux(1) s(2) =< aux(2) with precondition: [Out=0,V>=0,V2>=0] * Chain [36]: 2 with precondition: [V2=0,Out=0,V>=1] * Chain [35,37]: 7 with precondition: [V2=0,Out=1,V>=1] * Chain [33,37]: 3*s(2)+7 Such that:aux(6) =< V2 s(2) =< aux(6) with precondition: [Out=1,V2>=1,V>=V2+1] #### Cost of chains of encArg(V,Out): * Chain [52]: 0 with precondition: [V=1,Out=1] * Chain [51]: 0 with precondition: [V=2,Out=2] * Chain [50]: 0 with precondition: [Out=0,V>=0] * Chain [multiple([38,39,40,41,42,43,44,45,46,47,48,49],[[52],[51],[50]])]: 9*it(38)+9*it(39)+5*it(40)+1*it(41)+2*it(43)+1*it(45)+1*it(46)+7*it(47)+7*it(48)+3*it(49)+18*s(89)+2*s(90)+14*s(92)+6*s(94)+1*s(98)+1*s(99)+18*s(100)+2*s(101)+14*s(103)+1*s(105)+2*s(106)+2*s(107)+0 Such that:s(38) =< 2*V aux(33) =< V aux(34) =< 2*V+1 aux(35) =< V/2 aux(36) =< 2/3*V aux(37) =< 3/4*V aux(38) =< 3/8*V aux(39) =< 4/5*V aux(40) =< 4/7*V it(41) =< aux(33) it(43) =< aux(33) it(45) =< aux(33) it(46) =< aux(33) it(47) =< aux(33) it(48) =< aux(33) it(49) =< aux(33) it([50]) =< aux(34) it(39) =< aux(35) it(45) =< aux(36) it(47) =< aux(36) it(40) =< aux(37) it(38) =< aux(38) it(48) =< aux(39) it(47) =< aux(40) aux(17) =< s(38) aux(29) =< s(38)+2 aux(27) =< s(38)-2 aux(26) =< s(38)+1 aux(19) =< s(38)-1 it(48) =< it([50])*(1/5)+aux(39) it(49) =< it([50])*(1/5)+aux(39) it(47) =< it([50])*(3/7)+aux(40) it(48) =< it([50])*(3/7)+aux(40) it(49) =< it([50])*(3/7)+aux(40) it(45) =< it([50])*(1/3)+aux(36) it(46) =< it([50])*(1/3)+aux(36) it(47) =< it([50])*(1/3)+aux(36) it(48) =< it([50])*(1/3)+aux(36) it(49) =< it([50])*(1/3)+aux(36) it(40) =< it([50])*(1/8)+aux(37) it(41) =< it([50])*(1/8)+aux(37) it(39) =< it([50])*(1/4)+aux(35) it(40) =< it([50])*(1/4)+aux(35) it(41) =< it([50])*(1/4)+aux(35) it(38) =< it([50])*(5/16)+aux(38) it(39) =< it([50])*(5/16)+aux(38) it(40) =< it([50])*(5/16)+aux(38) it(41) =< it([50])*(5/16)+aux(38) s(105) =< it(49)*aux(17) s(109) =< it(49)*aux(17) s(108) =< it(49)*aux(29) s(104) =< it(48)*aux(29) s(99) =< it(47)*aux(27) s(102) =< it(47)*aux(26) s(98) =< it(45)*aux(19) s(96) =< it(40)*aux(19) s(93) =< it(39)*aux(19) s(91) =< it(38)*aux(17) s(106) =< s(109) s(107) =< s(108) s(103) =< s(104) s(100) =< s(102) s(101) =< s(100)*aux(26) s(94) =< s(96) s(92) =< s(93) s(89) =< s(91) s(90) =< s(89)*s(38) with precondition: [V>=1,Out>=0,2*V>=Out] #### Cost of chains of fun(V,Out): * Chain [54]: 1*s(163)+2*s(164)+1*s(165)+1*s(166)+7*s(167)+7*s(168)+3*s(169)+9*s(170)+5*s(171)+9*s(172)+1*s(178)+1*s(182)+1*s(184)+2*s(188)+2*s(189)+14*s(190)+18*s(191)+2*s(192)+6*s(193)+14*s(194)+18*s(195)+2*s(196)+1 Such that:s(154) =< V s(155) =< 2*V s(156) =< 2*V+1 s(157) =< V/2 s(158) =< 2/3*V s(159) =< 3/4*V s(160) =< 3/8*V s(161) =< 4/5*V s(162) =< 4/7*V s(163) =< s(154) s(164) =< s(154) s(165) =< s(154) s(166) =< s(154) s(167) =< s(154) s(168) =< s(154) s(169) =< s(154) s(170) =< s(157) s(165) =< s(158) s(167) =< s(158) s(171) =< s(159) s(172) =< s(160) s(168) =< s(161) s(167) =< s(162) s(173) =< s(155) s(174) =< s(155)+2 s(175) =< s(155)-2 s(176) =< s(155)+1 s(177) =< s(155)-1 s(168) =< s(156)*(1/5)+s(161) s(169) =< s(156)*(1/5)+s(161) s(167) =< s(156)*(3/7)+s(162) s(168) =< s(156)*(3/7)+s(162) s(169) =< s(156)*(3/7)+s(162) s(165) =< s(156)*(1/3)+s(158) s(166) =< s(156)*(1/3)+s(158) s(167) =< s(156)*(1/3)+s(158) s(168) =< s(156)*(1/3)+s(158) s(169) =< s(156)*(1/3)+s(158) s(171) =< s(156)*(1/8)+s(159) s(163) =< s(156)*(1/8)+s(159) s(170) =< s(156)*(1/4)+s(157) s(171) =< s(156)*(1/4)+s(157) s(163) =< s(156)*(1/4)+s(157) s(172) =< s(156)*(5/16)+s(160) s(170) =< s(156)*(5/16)+s(160) s(171) =< s(156)*(5/16)+s(160) s(163) =< s(156)*(5/16)+s(160) s(178) =< s(169)*s(173) s(179) =< s(169)*s(173) s(180) =< s(169)*s(174) s(181) =< s(168)*s(174) s(182) =< s(167)*s(175) s(183) =< s(167)*s(176) s(184) =< s(165)*s(177) s(185) =< s(171)*s(177) s(186) =< s(170)*s(177) s(187) =< s(172)*s(173) s(188) =< s(179) s(189) =< s(180) s(190) =< s(181) s(191) =< s(183) s(192) =< s(191)*s(176) s(193) =< s(185) s(194) =< s(186) s(195) =< s(187) s(196) =< s(195)*s(155) with precondition: [Out=0,V>=0] * Chain [53]: 1*s(206)+2*s(207)+1*s(208)+1*s(209)+7*s(210)+7*s(211)+3*s(212)+9*s(213)+5*s(214)+9*s(215)+1*s(221)+1*s(225)+1*s(227)+2*s(231)+2*s(232)+14*s(233)+18*s(234)+2*s(235)+6*s(236)+14*s(237)+18*s(238)+2*s(239)+1 Such that:s(197) =< V s(198) =< 2*V s(199) =< 2*V+1 s(200) =< V/2 s(201) =< 2/3*V s(202) =< 3/4*V s(203) =< 3/8*V s(204) =< 4/5*V s(205) =< 4/7*V s(206) =< s(197) s(207) =< s(197) s(208) =< s(197) s(209) =< s(197) s(210) =< s(197) s(211) =< s(197) s(212) =< s(197) s(213) =< s(200) s(208) =< s(201) s(210) =< s(201) s(214) =< s(202) s(215) =< s(203) s(211) =< s(204) s(210) =< s(205) s(216) =< s(198) s(217) =< s(198)+2 s(218) =< s(198)-2 s(219) =< s(198)+1 s(220) =< s(198)-1 s(211) =< s(199)*(1/5)+s(204) s(212) =< s(199)*(1/5)+s(204) s(210) =< s(199)*(3/7)+s(205) s(211) =< s(199)*(3/7)+s(205) s(212) =< s(199)*(3/7)+s(205) s(208) =< s(199)*(1/3)+s(201) s(209) =< s(199)*(1/3)+s(201) s(210) =< s(199)*(1/3)+s(201) s(211) =< s(199)*(1/3)+s(201) s(212) =< s(199)*(1/3)+s(201) s(214) =< s(199)*(1/8)+s(202) s(206) =< s(199)*(1/8)+s(202) s(213) =< s(199)*(1/4)+s(200) s(214) =< s(199)*(1/4)+s(200) s(206) =< s(199)*(1/4)+s(200) s(215) =< s(199)*(5/16)+s(203) s(213) =< s(199)*(5/16)+s(203) s(214) =< s(199)*(5/16)+s(203) s(206) =< s(199)*(5/16)+s(203) s(221) =< s(212)*s(216) s(222) =< s(212)*s(216) s(223) =< s(212)*s(217) s(224) =< s(211)*s(217) s(225) =< s(210)*s(218) s(226) =< s(210)*s(219) s(227) =< s(208)*s(220) s(228) =< s(214)*s(220) s(229) =< s(213)*s(220) s(230) =< s(215)*s(216) s(231) =< s(222) s(232) =< s(223) s(233) =< s(224) s(234) =< s(226) s(235) =< s(234)*s(219) s(236) =< s(228) s(237) =< s(229) s(238) =< s(230) s(239) =< s(238)*s(198) with precondition: [V>=1,Out>=0,2*V>=Out+1] #### Cost of chains of fun2(V,Out): * Chain [57]: 1*s(249)+2*s(250)+1*s(251)+1*s(252)+7*s(253)+7*s(254)+3*s(255)+9*s(256)+5*s(257)+9*s(258)+1*s(264)+1*s(268)+1*s(270)+2*s(274)+2*s(275)+14*s(276)+18*s(277)+2*s(278)+6*s(279)+14*s(280)+18*s(281)+2*s(282)+0 Such that:s(240) =< V s(241) =< 2*V s(242) =< 2*V+1 s(243) =< V/2 s(244) =< 2/3*V s(245) =< 3/4*V s(246) =< 3/8*V s(247) =< 4/5*V s(248) =< 4/7*V s(249) =< s(240) s(250) =< s(240) s(251) =< s(240) s(252) =< s(240) s(253) =< s(240) s(254) =< s(240) s(255) =< s(240) s(256) =< s(243) s(251) =< s(244) s(253) =< s(244) s(257) =< s(245) s(258) =< s(246) s(254) =< s(247) s(253) =< s(248) s(259) =< s(241) s(260) =< s(241)+2 s(261) =< s(241)-2 s(262) =< s(241)+1 s(263) =< s(241)-1 s(254) =< s(242)*(1/5)+s(247) s(255) =< s(242)*(1/5)+s(247) s(253) =< s(242)*(3/7)+s(248) s(254) =< s(242)*(3/7)+s(248) s(255) =< s(242)*(3/7)+s(248) s(251) =< s(242)*(1/3)+s(244) s(252) =< s(242)*(1/3)+s(244) s(253) =< s(242)*(1/3)+s(244) s(254) =< s(242)*(1/3)+s(244) s(255) =< s(242)*(1/3)+s(244) s(257) =< s(242)*(1/8)+s(245) s(249) =< s(242)*(1/8)+s(245) s(256) =< s(242)*(1/4)+s(243) s(257) =< s(242)*(1/4)+s(243) s(249) =< s(242)*(1/4)+s(243) s(258) =< s(242)*(5/16)+s(246) s(256) =< s(242)*(5/16)+s(246) s(257) =< s(242)*(5/16)+s(246) s(249) =< s(242)*(5/16)+s(246) s(264) =< s(255)*s(259) s(265) =< s(255)*s(259) s(266) =< s(255)*s(260) s(267) =< s(254)*s(260) s(268) =< s(253)*s(261) s(269) =< s(253)*s(262) s(270) =< s(251)*s(263) s(271) =< s(257)*s(263) s(272) =< s(256)*s(263) s(273) =< s(258)*s(259) s(274) =< s(265) s(275) =< s(266) s(276) =< s(267) s(277) =< s(269) s(278) =< s(277)*s(262) s(279) =< s(271) s(280) =< s(272) s(281) =< s(273) s(282) =< s(281)*s(241) with precondition: [V>=1,Out>=1,2*V+1>=Out] * Chain [56]: 0 with precondition: [Out=0,V>=0] * Chain [55]: 0 with precondition: [Out=1,V>=0] #### Cost of chains of fun3(V,V2,Out): * Chain [63]: 2*s(292)+4*s(293)+2*s(294)+2*s(295)+14*s(296)+14*s(297)+6*s(298)+18*s(299)+10*s(300)+18*s(301)+2*s(307)+2*s(311)+2*s(313)+4*s(317)+4*s(318)+28*s(319)+36*s(320)+4*s(321)+12*s(322)+28*s(323)+36*s(324)+4*s(325)+3*s(335)+6*s(336)+3*s(337)+3*s(338)+21*s(339)+21*s(340)+9*s(341)+27*s(342)+15*s(343)+27*s(344)+3*s(350)+3*s(354)+3*s(356)+6*s(360)+6*s(361)+42*s(362)+54*s(363)+6*s(364)+18*s(365)+42*s(366)+54*s(367)+6*s(368)+3*s(369)+1*s(458)+0 Such that:s(458) =< 2 aux(44) =< V aux(45) =< 2*V aux(46) =< 2*V+1 aux(47) =< V/2 aux(48) =< 2/3*V aux(49) =< 3/4*V aux(50) =< 3/8*V aux(51) =< 4/5*V aux(52) =< 4/7*V aux(53) =< V2 aux(54) =< 2*V2 aux(55) =< 2*V2+1 aux(56) =< V2/2 aux(57) =< 2/3*V2 aux(58) =< 3/4*V2 aux(59) =< 3/8*V2 aux(60) =< 4/5*V2 aux(61) =< 4/7*V2 s(369) =< aux(54) s(335) =< aux(53) s(336) =< aux(53) s(337) =< aux(53) s(338) =< aux(53) s(339) =< aux(53) s(340) =< aux(53) s(341) =< aux(53) s(342) =< aux(56) s(337) =< aux(57) s(339) =< aux(57) s(343) =< aux(58) s(344) =< aux(59) s(340) =< aux(60) s(339) =< aux(61) s(345) =< aux(54) s(346) =< aux(54)+2 s(347) =< aux(54)-2 s(348) =< aux(54)+1 s(349) =< aux(54)-1 s(340) =< aux(55)*(1/5)+aux(60) s(341) =< aux(55)*(1/5)+aux(60) s(339) =< aux(55)*(3/7)+aux(61) s(340) =< aux(55)*(3/7)+aux(61) s(341) =< aux(55)*(3/7)+aux(61) s(337) =< aux(55)*(1/3)+aux(57) s(338) =< aux(55)*(1/3)+aux(57) s(339) =< aux(55)*(1/3)+aux(57) s(340) =< aux(55)*(1/3)+aux(57) s(341) =< aux(55)*(1/3)+aux(57) s(343) =< aux(55)*(1/8)+aux(58) s(335) =< aux(55)*(1/8)+aux(58) s(342) =< aux(55)*(1/4)+aux(56) s(343) =< aux(55)*(1/4)+aux(56) s(335) =< aux(55)*(1/4)+aux(56) s(344) =< aux(55)*(5/16)+aux(59) s(342) =< aux(55)*(5/16)+aux(59) s(343) =< aux(55)*(5/16)+aux(59) s(335) =< aux(55)*(5/16)+aux(59) s(350) =< s(341)*s(345) s(351) =< s(341)*s(345) s(352) =< s(341)*s(346) s(353) =< s(340)*s(346) s(354) =< s(339)*s(347) s(355) =< s(339)*s(348) s(356) =< s(337)*s(349) s(357) =< s(343)*s(349) s(358) =< s(342)*s(349) s(359) =< s(344)*s(345) s(360) =< s(351) s(361) =< s(352) s(362) =< s(353) s(363) =< s(355) s(364) =< s(363)*s(348) s(365) =< s(357) s(366) =< s(358) s(367) =< s(359) s(368) =< s(367)*aux(54) s(292) =< aux(44) s(293) =< aux(44) s(294) =< aux(44) s(295) =< aux(44) s(296) =< aux(44) s(297) =< aux(44) s(298) =< aux(44) s(299) =< aux(47) s(294) =< aux(48) s(296) =< aux(48) s(300) =< aux(49) s(301) =< aux(50) s(297) =< aux(51) s(296) =< aux(52) s(302) =< aux(45) s(303) =< aux(45)+2 s(304) =< aux(45)-2 s(305) =< aux(45)+1 s(306) =< aux(45)-1 s(297) =< aux(46)*(1/5)+aux(51) s(298) =< aux(46)*(1/5)+aux(51) s(296) =< aux(46)*(3/7)+aux(52) s(297) =< aux(46)*(3/7)+aux(52) s(298) =< aux(46)*(3/7)+aux(52) s(294) =< aux(46)*(1/3)+aux(48) s(295) =< aux(46)*(1/3)+aux(48) s(296) =< aux(46)*(1/3)+aux(48) s(297) =< aux(46)*(1/3)+aux(48) s(298) =< aux(46)*(1/3)+aux(48) s(300) =< aux(46)*(1/8)+aux(49) s(292) =< aux(46)*(1/8)+aux(49) s(299) =< aux(46)*(1/4)+aux(47) s(300) =< aux(46)*(1/4)+aux(47) s(292) =< aux(46)*(1/4)+aux(47) s(301) =< aux(46)*(5/16)+aux(50) s(299) =< aux(46)*(5/16)+aux(50) s(300) =< aux(46)*(5/16)+aux(50) s(292) =< aux(46)*(5/16)+aux(50) s(307) =< s(298)*s(302) s(308) =< s(298)*s(302) s(309) =< s(298)*s(303) s(310) =< s(297)*s(303) s(311) =< s(296)*s(304) s(312) =< s(296)*s(305) s(313) =< s(294)*s(306) s(314) =< s(300)*s(306) s(315) =< s(299)*s(306) s(316) =< s(301)*s(302) s(317) =< s(308) s(318) =< s(309) s(319) =< s(310) s(320) =< s(312) s(321) =< s(320)*s(305) s(322) =< s(314) s(323) =< s(315) s(324) =< s(316) s(325) =< s(324)*aux(45) with precondition: [Out=0,V>=0,V2>=0] * Chain [62]: 3*s(514)+6*s(515)+3*s(516)+3*s(517)+21*s(518)+21*s(519)+9*s(520)+27*s(521)+15*s(522)+27*s(523)+3*s(529)+3*s(533)+3*s(535)+6*s(539)+6*s(540)+42*s(541)+54*s(542)+6*s(543)+18*s(544)+42*s(545)+54*s(546)+6*s(547)+4*s(557)+8*s(558)+4*s(559)+4*s(560)+28*s(561)+28*s(562)+12*s(563)+36*s(564)+20*s(565)+36*s(566)+4*s(572)+4*s(576)+4*s(578)+8*s(582)+8*s(583)+56*s(584)+72*s(585)+8*s(586)+24*s(587)+56*s(588)+72*s(589)+8*s(590)+1*s(677)+2*s(764)+1 Such that:aux(63) =< 2 aux(64) =< V aux(65) =< 2*V aux(66) =< 2*V+1 aux(67) =< V/2 aux(68) =< 2/3*V aux(69) =< 3/4*V aux(70) =< 3/8*V aux(71) =< 4/5*V aux(72) =< 4/7*V aux(73) =< V2 aux(74) =< 2*V2 aux(75) =< 2*V2+1 aux(76) =< V2/2 aux(77) =< 2/3*V2 aux(78) =< 3/4*V2 aux(79) =< 3/8*V2 aux(80) =< 4/5*V2 aux(81) =< 4/7*V2 s(764) =< aux(63) s(557) =< aux(73) s(558) =< aux(73) s(559) =< aux(73) s(560) =< aux(73) s(561) =< aux(73) s(562) =< aux(73) s(563) =< aux(73) s(564) =< aux(76) s(559) =< aux(77) s(561) =< aux(77) s(565) =< aux(78) s(566) =< aux(79) s(562) =< aux(80) s(561) =< aux(81) s(567) =< aux(74) s(568) =< aux(74)+2 s(569) =< aux(74)-2 s(570) =< aux(74)+1 s(571) =< aux(74)-1 s(562) =< aux(75)*(1/5)+aux(80) s(563) =< aux(75)*(1/5)+aux(80) s(561) =< aux(75)*(3/7)+aux(81) s(562) =< aux(75)*(3/7)+aux(81) s(563) =< aux(75)*(3/7)+aux(81) s(559) =< aux(75)*(1/3)+aux(77) s(560) =< aux(75)*(1/3)+aux(77) s(561) =< aux(75)*(1/3)+aux(77) s(562) =< aux(75)*(1/3)+aux(77) s(563) =< aux(75)*(1/3)+aux(77) s(565) =< aux(75)*(1/8)+aux(78) s(557) =< aux(75)*(1/8)+aux(78) s(564) =< aux(75)*(1/4)+aux(76) s(565) =< aux(75)*(1/4)+aux(76) s(557) =< aux(75)*(1/4)+aux(76) s(566) =< aux(75)*(5/16)+aux(79) s(564) =< aux(75)*(5/16)+aux(79) s(565) =< aux(75)*(5/16)+aux(79) s(557) =< aux(75)*(5/16)+aux(79) s(572) =< s(563)*s(567) s(573) =< s(563)*s(567) s(574) =< s(563)*s(568) s(575) =< s(562)*s(568) s(576) =< s(561)*s(569) s(577) =< s(561)*s(570) s(578) =< s(559)*s(571) s(579) =< s(565)*s(571) s(580) =< s(564)*s(571) s(581) =< s(566)*s(567) s(582) =< s(573) s(583) =< s(574) s(584) =< s(575) s(585) =< s(577) s(586) =< s(585)*s(570) s(587) =< s(579) s(588) =< s(580) s(589) =< s(581) s(590) =< s(589)*aux(74) s(514) =< aux(64) s(515) =< aux(64) s(516) =< aux(64) s(517) =< aux(64) s(518) =< aux(64) s(519) =< aux(64) s(520) =< aux(64) s(521) =< aux(67) s(516) =< aux(68) s(518) =< aux(68) s(522) =< aux(69) s(523) =< aux(70) s(519) =< aux(71) s(518) =< aux(72) s(524) =< aux(65) s(525) =< aux(65)+2 s(526) =< aux(65)-2 s(527) =< aux(65)+1 s(528) =< aux(65)-1 s(519) =< aux(66)*(1/5)+aux(71) s(520) =< aux(66)*(1/5)+aux(71) s(518) =< aux(66)*(3/7)+aux(72) s(519) =< aux(66)*(3/7)+aux(72) s(520) =< aux(66)*(3/7)+aux(72) s(516) =< aux(66)*(1/3)+aux(68) s(517) =< aux(66)*(1/3)+aux(68) s(518) =< aux(66)*(1/3)+aux(68) s(519) =< aux(66)*(1/3)+aux(68) s(520) =< aux(66)*(1/3)+aux(68) s(522) =< aux(66)*(1/8)+aux(69) s(514) =< aux(66)*(1/8)+aux(69) s(521) =< aux(66)*(1/4)+aux(67) s(522) =< aux(66)*(1/4)+aux(67) s(514) =< aux(66)*(1/4)+aux(67) s(523) =< aux(66)*(5/16)+aux(70) s(521) =< aux(66)*(5/16)+aux(70) s(522) =< aux(66)*(5/16)+aux(70) s(514) =< aux(66)*(5/16)+aux(70) s(529) =< s(520)*s(524) s(530) =< s(520)*s(524) s(531) =< s(520)*s(525) s(532) =< s(519)*s(525) s(533) =< s(518)*s(526) s(534) =< s(518)*s(527) s(535) =< s(516)*s(528) s(536) =< s(522)*s(528) s(537) =< s(521)*s(528) s(538) =< s(523)*s(524) s(539) =< s(530) s(540) =< s(531) s(541) =< s(532) s(542) =< s(534) s(543) =< s(542)*s(527) s(544) =< s(536) s(545) =< s(537) s(546) =< s(538) s(547) =< s(546)*aux(65) s(677) =< aux(74) with precondition: [Out=2,V>=0,V2>=0] * Chain [61]: 3*s(818)+6*s(819)+3*s(820)+3*s(821)+21*s(822)+21*s(823)+9*s(824)+27*s(825)+15*s(826)+27*s(827)+3*s(833)+3*s(837)+3*s(839)+6*s(843)+6*s(844)+42*s(845)+54*s(846)+6*s(847)+18*s(848)+42*s(849)+54*s(850)+6*s(851)+4*s(861)+8*s(862)+4*s(863)+4*s(864)+28*s(865)+28*s(866)+12*s(867)+36*s(868)+20*s(869)+36*s(870)+4*s(876)+4*s(880)+4*s(882)+8*s(886)+8*s(887)+56*s(888)+72*s(889)+8*s(890)+24*s(891)+56*s(892)+72*s(893)+8*s(894)+1*s(981)+1*s(1111)+1 Such that:s(1111) =< 1 aux(83) =< V aux(84) =< 2*V aux(85) =< 2*V+1 aux(86) =< V/2 aux(87) =< 2/3*V aux(88) =< 3/4*V aux(89) =< 3/8*V aux(90) =< 4/5*V aux(91) =< 4/7*V aux(92) =< V2 aux(93) =< 2*V2 aux(94) =< 2*V2+1 aux(95) =< V2/2 aux(96) =< 2/3*V2 aux(97) =< 3/4*V2 aux(98) =< 3/8*V2 aux(99) =< 4/5*V2 aux(100) =< 4/7*V2 s(861) =< aux(92) s(862) =< aux(92) s(863) =< aux(92) s(864) =< aux(92) s(865) =< aux(92) s(866) =< aux(92) s(867) =< aux(92) s(868) =< aux(95) s(863) =< aux(96) s(865) =< aux(96) s(869) =< aux(97) s(870) =< aux(98) s(866) =< aux(99) s(865) =< aux(100) s(871) =< aux(93) s(872) =< aux(93)+2 s(873) =< aux(93)-2 s(874) =< aux(93)+1 s(875) =< aux(93)-1 s(866) =< aux(94)*(1/5)+aux(99) s(867) =< aux(94)*(1/5)+aux(99) s(865) =< aux(94)*(3/7)+aux(100) s(866) =< aux(94)*(3/7)+aux(100) s(867) =< aux(94)*(3/7)+aux(100) s(863) =< aux(94)*(1/3)+aux(96) s(864) =< aux(94)*(1/3)+aux(96) s(865) =< aux(94)*(1/3)+aux(96) s(866) =< aux(94)*(1/3)+aux(96) s(867) =< aux(94)*(1/3)+aux(96) s(869) =< aux(94)*(1/8)+aux(97) s(861) =< aux(94)*(1/8)+aux(97) s(868) =< aux(94)*(1/4)+aux(95) s(869) =< aux(94)*(1/4)+aux(95) s(861) =< aux(94)*(1/4)+aux(95) s(870) =< aux(94)*(5/16)+aux(98) s(868) =< aux(94)*(5/16)+aux(98) s(869) =< aux(94)*(5/16)+aux(98) s(861) =< aux(94)*(5/16)+aux(98) s(876) =< s(867)*s(871) s(877) =< s(867)*s(871) s(878) =< s(867)*s(872) s(879) =< s(866)*s(872) s(880) =< s(865)*s(873) s(881) =< s(865)*s(874) s(882) =< s(863)*s(875) s(883) =< s(869)*s(875) s(884) =< s(868)*s(875) s(885) =< s(870)*s(871) s(886) =< s(877) s(887) =< s(878) s(888) =< s(879) s(889) =< s(881) s(890) =< s(889)*s(874) s(891) =< s(883) s(892) =< s(884) s(893) =< s(885) s(894) =< s(893)*aux(93) s(818) =< aux(83) s(819) =< aux(83) s(820) =< aux(83) s(821) =< aux(83) s(822) =< aux(83) s(823) =< aux(83) s(824) =< aux(83) s(825) =< aux(86) s(820) =< aux(87) s(822) =< aux(87) s(826) =< aux(88) s(827) =< aux(89) s(823) =< aux(90) s(822) =< aux(91) s(828) =< aux(84) s(829) =< aux(84)+2 s(830) =< aux(84)-2 s(831) =< aux(84)+1 s(832) =< aux(84)-1 s(823) =< aux(85)*(1/5)+aux(90) s(824) =< aux(85)*(1/5)+aux(90) s(822) =< aux(85)*(3/7)+aux(91) s(823) =< aux(85)*(3/7)+aux(91) s(824) =< aux(85)*(3/7)+aux(91) s(820) =< aux(85)*(1/3)+aux(87) s(821) =< aux(85)*(1/3)+aux(87) s(822) =< aux(85)*(1/3)+aux(87) s(823) =< aux(85)*(1/3)+aux(87) s(824) =< aux(85)*(1/3)+aux(87) s(826) =< aux(85)*(1/8)+aux(88) s(818) =< aux(85)*(1/8)+aux(88) s(825) =< aux(85)*(1/4)+aux(86) s(826) =< aux(85)*(1/4)+aux(86) s(818) =< aux(85)*(1/4)+aux(86) s(827) =< aux(85)*(5/16)+aux(89) s(825) =< aux(85)*(5/16)+aux(89) s(826) =< aux(85)*(5/16)+aux(89) s(818) =< aux(85)*(5/16)+aux(89) s(833) =< s(824)*s(828) s(834) =< s(824)*s(828) s(835) =< s(824)*s(829) s(836) =< s(823)*s(829) s(837) =< s(822)*s(830) s(838) =< s(822)*s(831) s(839) =< s(820)*s(832) s(840) =< s(826)*s(832) s(841) =< s(825)*s(832) s(842) =< s(827)*s(828) s(843) =< s(834) s(844) =< s(835) s(845) =< s(836) s(846) =< s(838) s(847) =< s(846)*s(831) s(848) =< s(840) s(849) =< s(841) s(850) =< s(842) s(851) =< s(850)*aux(84) s(981) =< aux(84) with precondition: [Out=1,V>=1,V2>=0] * Chain [60]: 1*s(1121)+2*s(1122)+1*s(1123)+1*s(1124)+7*s(1125)+7*s(1126)+3*s(1127)+9*s(1128)+5*s(1129)+9*s(1130)+1*s(1136)+1*s(1140)+1*s(1142)+2*s(1146)+2*s(1147)+14*s(1148)+18*s(1149)+2*s(1150)+6*s(1151)+14*s(1152)+18*s(1153)+2*s(1154)+2*s(1155)+0 Such that:s(1112) =< V s(1113) =< 2*V s(1114) =< 2*V+1 s(1115) =< V/2 s(1116) =< 2/3*V s(1117) =< 3/4*V s(1118) =< 3/8*V s(1119) =< 4/5*V s(1120) =< 4/7*V aux(101) =< 2 s(1155) =< aux(101) s(1121) =< s(1112) s(1122) =< s(1112) s(1123) =< s(1112) s(1124) =< s(1112) s(1125) =< s(1112) s(1126) =< s(1112) s(1127) =< s(1112) s(1128) =< s(1115) s(1123) =< s(1116) s(1125) =< s(1116) s(1129) =< s(1117) s(1130) =< s(1118) s(1126) =< s(1119) s(1125) =< s(1120) s(1131) =< s(1113) s(1132) =< s(1113)+2 s(1133) =< s(1113)-2 s(1134) =< s(1113)+1 s(1135) =< s(1113)-1 s(1126) =< s(1114)*(1/5)+s(1119) s(1127) =< s(1114)*(1/5)+s(1119) s(1125) =< s(1114)*(3/7)+s(1120) s(1126) =< s(1114)*(3/7)+s(1120) s(1127) =< s(1114)*(3/7)+s(1120) s(1123) =< s(1114)*(1/3)+s(1116) s(1124) =< s(1114)*(1/3)+s(1116) s(1125) =< s(1114)*(1/3)+s(1116) s(1126) =< s(1114)*(1/3)+s(1116) s(1127) =< s(1114)*(1/3)+s(1116) s(1129) =< s(1114)*(1/8)+s(1117) s(1121) =< s(1114)*(1/8)+s(1117) s(1128) =< s(1114)*(1/4)+s(1115) s(1129) =< s(1114)*(1/4)+s(1115) s(1121) =< s(1114)*(1/4)+s(1115) s(1130) =< s(1114)*(5/16)+s(1118) s(1128) =< s(1114)*(5/16)+s(1118) s(1129) =< s(1114)*(5/16)+s(1118) s(1121) =< s(1114)*(5/16)+s(1118) s(1136) =< s(1127)*s(1131) s(1137) =< s(1127)*s(1131) s(1138) =< s(1127)*s(1132) s(1139) =< s(1126)*s(1132) s(1140) =< s(1125)*s(1133) s(1141) =< s(1125)*s(1134) s(1142) =< s(1123)*s(1135) s(1143) =< s(1129)*s(1135) s(1144) =< s(1128)*s(1135) s(1145) =< s(1130)*s(1131) s(1146) =< s(1137) s(1147) =< s(1138) s(1148) =< s(1139) s(1149) =< s(1141) s(1150) =< s(1149)*s(1134) s(1151) =< s(1143) s(1152) =< s(1144) s(1153) =< s(1145) s(1154) =< s(1153)*s(1113) with precondition: [V2=2,Out=0,V>=0] * Chain [59]: 1*s(1166)+2*s(1167)+1*s(1168)+1*s(1169)+7*s(1170)+7*s(1171)+3*s(1172)+9*s(1173)+5*s(1174)+9*s(1175)+1*s(1181)+1*s(1185)+1*s(1187)+2*s(1191)+2*s(1192)+14*s(1193)+18*s(1194)+2*s(1195)+6*s(1196)+14*s(1197)+18*s(1198)+2*s(1199)+1*s(1200)+1 Such that:s(1200) =< 2 s(1157) =< V s(1158) =< 2*V s(1159) =< 2*V+1 s(1160) =< V/2 s(1161) =< 2/3*V s(1162) =< 3/4*V s(1163) =< 3/8*V s(1164) =< 4/5*V s(1165) =< 4/7*V s(1166) =< s(1157) s(1167) =< s(1157) s(1168) =< s(1157) s(1169) =< s(1157) s(1170) =< s(1157) s(1171) =< s(1157) s(1172) =< s(1157) s(1173) =< s(1160) s(1168) =< s(1161) s(1170) =< s(1161) s(1174) =< s(1162) s(1175) =< s(1163) s(1171) =< s(1164) s(1170) =< s(1165) s(1176) =< s(1158) s(1177) =< s(1158)+2 s(1178) =< s(1158)-2 s(1179) =< s(1158)+1 s(1180) =< s(1158)-1 s(1171) =< s(1159)*(1/5)+s(1164) s(1172) =< s(1159)*(1/5)+s(1164) s(1170) =< s(1159)*(3/7)+s(1165) s(1171) =< s(1159)*(3/7)+s(1165) s(1172) =< s(1159)*(3/7)+s(1165) s(1168) =< s(1159)*(1/3)+s(1161) s(1169) =< s(1159)*(1/3)+s(1161) s(1170) =< s(1159)*(1/3)+s(1161) s(1171) =< s(1159)*(1/3)+s(1161) s(1172) =< s(1159)*(1/3)+s(1161) s(1174) =< s(1159)*(1/8)+s(1162) s(1166) =< s(1159)*(1/8)+s(1162) s(1173) =< s(1159)*(1/4)+s(1160) s(1174) =< s(1159)*(1/4)+s(1160) s(1166) =< s(1159)*(1/4)+s(1160) s(1175) =< s(1159)*(5/16)+s(1163) s(1173) =< s(1159)*(5/16)+s(1163) s(1174) =< s(1159)*(5/16)+s(1163) s(1166) =< s(1159)*(5/16)+s(1163) s(1181) =< s(1172)*s(1176) s(1182) =< s(1172)*s(1176) s(1183) =< s(1172)*s(1177) s(1184) =< s(1171)*s(1177) s(1185) =< s(1170)*s(1178) s(1186) =< s(1170)*s(1179) s(1187) =< s(1168)*s(1180) s(1188) =< s(1174)*s(1180) s(1189) =< s(1173)*s(1180) s(1190) =< s(1175)*s(1176) s(1191) =< s(1182) s(1192) =< s(1183) s(1193) =< s(1184) s(1194) =< s(1186) s(1195) =< s(1194)*s(1179) s(1196) =< s(1188) s(1197) =< s(1189) s(1198) =< s(1190) s(1199) =< s(1198)*s(1158) with precondition: [V2=2,Out=1,2*V>=3] * Chain [58]: 2*s(1210)+4*s(1211)+2*s(1212)+2*s(1213)+14*s(1214)+14*s(1215)+6*s(1216)+18*s(1217)+10*s(1218)+18*s(1219)+2*s(1225)+2*s(1229)+2*s(1231)+4*s(1235)+4*s(1236)+28*s(1237)+36*s(1238)+4*s(1239)+12*s(1240)+28*s(1241)+36*s(1242)+4*s(1243)+1*s(1287)+1 Such that:s(1287) =< 2 aux(102) =< V aux(103) =< 2*V aux(104) =< 2*V+1 aux(105) =< V/2 aux(106) =< 2/3*V aux(107) =< 3/4*V aux(108) =< 3/8*V aux(109) =< 4/5*V aux(110) =< 4/7*V s(1210) =< aux(102) s(1211) =< aux(102) s(1212) =< aux(102) s(1213) =< aux(102) s(1214) =< aux(102) s(1215) =< aux(102) s(1216) =< aux(102) s(1217) =< aux(105) s(1212) =< aux(106) s(1214) =< aux(106) s(1218) =< aux(107) s(1219) =< aux(108) s(1215) =< aux(109) s(1214) =< aux(110) s(1220) =< aux(103) s(1221) =< aux(103)+2 s(1222) =< aux(103)-2 s(1223) =< aux(103)+1 s(1224) =< aux(103)-1 s(1215) =< aux(104)*(1/5)+aux(109) s(1216) =< aux(104)*(1/5)+aux(109) s(1214) =< aux(104)*(3/7)+aux(110) s(1215) =< aux(104)*(3/7)+aux(110) s(1216) =< aux(104)*(3/7)+aux(110) s(1212) =< aux(104)*(1/3)+aux(106) s(1213) =< aux(104)*(1/3)+aux(106) s(1214) =< aux(104)*(1/3)+aux(106) s(1215) =< aux(104)*(1/3)+aux(106) s(1216) =< aux(104)*(1/3)+aux(106) s(1218) =< aux(104)*(1/8)+aux(107) s(1210) =< aux(104)*(1/8)+aux(107) s(1217) =< aux(104)*(1/4)+aux(105) s(1218) =< aux(104)*(1/4)+aux(105) s(1210) =< aux(104)*(1/4)+aux(105) s(1219) =< aux(104)*(5/16)+aux(108) s(1217) =< aux(104)*(5/16)+aux(108) s(1218) =< aux(104)*(5/16)+aux(108) s(1210) =< aux(104)*(5/16)+aux(108) s(1225) =< s(1216)*s(1220) s(1226) =< s(1216)*s(1220) s(1227) =< s(1216)*s(1221) s(1228) =< s(1215)*s(1221) s(1229) =< s(1214)*s(1222) s(1230) =< s(1214)*s(1223) s(1231) =< s(1212)*s(1224) s(1232) =< s(1218)*s(1224) s(1233) =< s(1217)*s(1224) s(1234) =< s(1219)*s(1220) s(1235) =< s(1226) s(1236) =< s(1227) s(1237) =< s(1228) s(1238) =< s(1230) s(1239) =< s(1238)*s(1223) s(1240) =< s(1232) s(1241) =< s(1233) s(1242) =< s(1234) s(1243) =< s(1242)*aux(103) with precondition: [V2=2,Out=2,V>=0] #### Cost of chains of fun4(Out): * Chain [65]: 0 with precondition: [Out=0] * Chain [64]: 0 with precondition: [Out=2] #### Cost of chains of fun5(Out): * Chain [67]: 0 with precondition: [Out=0] * Chain [66]: 0 with precondition: [Out=1] #### Cost of chains of fun6(V,V2,Out): * Chain [71]: 2*s(1695)+4*s(1696)+2*s(1697)+2*s(1698)+14*s(1699)+14*s(1700)+6*s(1701)+18*s(1702)+10*s(1703)+18*s(1704)+2*s(1710)+2*s(1714)+2*s(1716)+4*s(1720)+4*s(1721)+28*s(1722)+36*s(1723)+4*s(1724)+12*s(1725)+28*s(1726)+36*s(1727)+4*s(1728)+3*s(1738)+6*s(1739)+3*s(1740)+3*s(1741)+21*s(1742)+21*s(1743)+9*s(1744)+27*s(1745)+15*s(1746)+27*s(1747)+3*s(1753)+3*s(1757)+3*s(1759)+6*s(1763)+6*s(1764)+42*s(1765)+54*s(1766)+6*s(1767)+18*s(1768)+42*s(1769)+54*s(1770)+6*s(1771)+4*s(1774)+6*s(1775)+8*s(1868)+3 Such that:aux(147) =< 2 aux(148) =< V aux(149) =< 2*V aux(150) =< 2*V+1 aux(151) =< V/2 aux(152) =< 2/3*V aux(153) =< 3/4*V aux(154) =< 3/8*V aux(155) =< 4/5*V aux(156) =< 4/7*V aux(157) =< V2 aux(158) =< 2*V2 aux(159) =< 2*V2+1 aux(160) =< V2/2 aux(161) =< 2/3*V2 aux(162) =< 3/4*V2 aux(163) =< 3/8*V2 aux(164) =< 4/5*V2 aux(165) =< 4/7*V2 s(1868) =< aux(147) s(1775) =< aux(158) s(1738) =< aux(157) s(1739) =< aux(157) s(1740) =< aux(157) s(1741) =< aux(157) s(1742) =< aux(157) s(1743) =< aux(157) s(1744) =< aux(157) s(1745) =< aux(160) s(1740) =< aux(161) s(1742) =< aux(161) s(1746) =< aux(162) s(1747) =< aux(163) s(1743) =< aux(164) s(1742) =< aux(165) s(1748) =< aux(158) s(1749) =< aux(158)+2 s(1750) =< aux(158)-2 s(1751) =< aux(158)+1 s(1752) =< aux(158)-1 s(1743) =< aux(159)*(1/5)+aux(164) s(1744) =< aux(159)*(1/5)+aux(164) s(1742) =< aux(159)*(3/7)+aux(165) s(1743) =< aux(159)*(3/7)+aux(165) s(1744) =< aux(159)*(3/7)+aux(165) s(1740) =< aux(159)*(1/3)+aux(161) s(1741) =< aux(159)*(1/3)+aux(161) s(1742) =< aux(159)*(1/3)+aux(161) s(1743) =< aux(159)*(1/3)+aux(161) s(1744) =< aux(159)*(1/3)+aux(161) s(1746) =< aux(159)*(1/8)+aux(162) s(1738) =< aux(159)*(1/8)+aux(162) s(1745) =< aux(159)*(1/4)+aux(160) s(1746) =< aux(159)*(1/4)+aux(160) s(1738) =< aux(159)*(1/4)+aux(160) s(1747) =< aux(159)*(5/16)+aux(163) s(1745) =< aux(159)*(5/16)+aux(163) s(1746) =< aux(159)*(5/16)+aux(163) s(1738) =< aux(159)*(5/16)+aux(163) s(1753) =< s(1744)*s(1748) s(1754) =< s(1744)*s(1748) s(1755) =< s(1744)*s(1749) s(1756) =< s(1743)*s(1749) s(1757) =< s(1742)*s(1750) s(1758) =< s(1742)*s(1751) s(1759) =< s(1740)*s(1752) s(1760) =< s(1746)*s(1752) s(1761) =< s(1745)*s(1752) s(1762) =< s(1747)*s(1748) s(1763) =< s(1754) s(1764) =< s(1755) s(1765) =< s(1756) s(1766) =< s(1758) s(1767) =< s(1766)*s(1751) s(1768) =< s(1760) s(1769) =< s(1761) s(1770) =< s(1762) s(1771) =< s(1770)*aux(158) s(1774) =< aux(149) s(1695) =< aux(148) s(1696) =< aux(148) s(1697) =< aux(148) s(1698) =< aux(148) s(1699) =< aux(148) s(1700) =< aux(148) s(1701) =< aux(148) s(1702) =< aux(151) s(1697) =< aux(152) s(1699) =< aux(152) s(1703) =< aux(153) s(1704) =< aux(154) s(1700) =< aux(155) s(1699) =< aux(156) s(1705) =< aux(149) s(1706) =< aux(149)+2 s(1707) =< aux(149)-2 s(1708) =< aux(149)+1 s(1709) =< aux(149)-1 s(1700) =< aux(150)*(1/5)+aux(155) s(1701) =< aux(150)*(1/5)+aux(155) s(1699) =< aux(150)*(3/7)+aux(156) s(1700) =< aux(150)*(3/7)+aux(156) s(1701) =< aux(150)*(3/7)+aux(156) s(1697) =< aux(150)*(1/3)+aux(152) s(1698) =< aux(150)*(1/3)+aux(152) s(1699) =< aux(150)*(1/3)+aux(152) s(1700) =< aux(150)*(1/3)+aux(152) s(1701) =< aux(150)*(1/3)+aux(152) s(1703) =< aux(150)*(1/8)+aux(153) s(1695) =< aux(150)*(1/8)+aux(153) s(1702) =< aux(150)*(1/4)+aux(151) s(1703) =< aux(150)*(1/4)+aux(151) s(1695) =< aux(150)*(1/4)+aux(151) s(1704) =< aux(150)*(5/16)+aux(154) s(1702) =< aux(150)*(5/16)+aux(154) s(1703) =< aux(150)*(5/16)+aux(154) s(1695) =< aux(150)*(5/16)+aux(154) s(1710) =< s(1701)*s(1705) s(1711) =< s(1701)*s(1705) s(1712) =< s(1701)*s(1706) s(1713) =< s(1700)*s(1706) s(1714) =< s(1699)*s(1707) s(1715) =< s(1699)*s(1708) s(1716) =< s(1697)*s(1709) s(1717) =< s(1703)*s(1709) s(1718) =< s(1702)*s(1709) s(1719) =< s(1704)*s(1705) s(1720) =< s(1711) s(1721) =< s(1712) s(1722) =< s(1713) s(1723) =< s(1715) s(1724) =< s(1723)*s(1708) s(1725) =< s(1717) s(1726) =< s(1718) s(1727) =< s(1719) s(1728) =< s(1727)*aux(149) with precondition: [Out=0,V>=0,V2>=0] * Chain [70]: 3*s(1938)+6*s(1939)+3*s(1940)+3*s(1941)+21*s(1942)+21*s(1943)+9*s(1944)+27*s(1945)+15*s(1946)+27*s(1947)+3*s(1953)+3*s(1957)+3*s(1959)+6*s(1963)+6*s(1964)+42*s(1965)+54*s(1966)+6*s(1967)+18*s(1968)+42*s(1969)+54*s(1970)+6*s(1971)+4*s(1981)+8*s(1982)+4*s(1983)+4*s(1984)+28*s(1985)+28*s(1986)+12*s(1987)+36*s(1988)+20*s(1989)+36*s(1990)+4*s(1996)+4*s(2000)+4*s(2002)+8*s(2006)+8*s(2007)+56*s(2008)+72*s(2009)+8*s(2010)+24*s(2011)+56*s(2012)+72*s(2013)+8*s(2014)+46*s(2017)+2*s(2111)+24*s(2204)+22*s(2205)+2*s(2255)+7 Such that:aux(170) =< 1 aux(171) =< 2 aux(172) =< V aux(173) =< 2*V aux(174) =< 2*V+1 aux(175) =< V/2 aux(176) =< 2/3*V aux(177) =< 3/4*V aux(178) =< 3/8*V aux(179) =< 4/5*V aux(180) =< 4/7*V aux(181) =< V2 aux(182) =< 2*V2 aux(183) =< 2*V2+1 aux(184) =< V2/2 aux(185) =< 2/3*V2 aux(186) =< 3/4*V2 aux(187) =< 3/8*V2 aux(188) =< 4/5*V2 aux(189) =< 4/7*V2 s(2204) =< aux(171) s(2205) =< aux(170) s(1981) =< aux(181) s(1982) =< aux(181) s(1983) =< aux(181) s(1984) =< aux(181) s(1985) =< aux(181) s(1986) =< aux(181) s(1987) =< aux(181) s(1988) =< aux(184) s(1983) =< aux(185) s(1985) =< aux(185) s(1989) =< aux(186) s(1990) =< aux(187) s(1986) =< aux(188) s(1985) =< aux(189) s(1991) =< aux(182) s(1992) =< aux(182)+2 s(1993) =< aux(182)-2 s(1994) =< aux(182)+1 s(1995) =< aux(182)-1 s(1986) =< aux(183)*(1/5)+aux(188) s(1987) =< aux(183)*(1/5)+aux(188) s(1985) =< aux(183)*(3/7)+aux(189) s(1986) =< aux(183)*(3/7)+aux(189) s(1987) =< aux(183)*(3/7)+aux(189) s(1983) =< aux(183)*(1/3)+aux(185) s(1984) =< aux(183)*(1/3)+aux(185) s(1985) =< aux(183)*(1/3)+aux(185) s(1986) =< aux(183)*(1/3)+aux(185) s(1987) =< aux(183)*(1/3)+aux(185) s(1989) =< aux(183)*(1/8)+aux(186) s(1981) =< aux(183)*(1/8)+aux(186) s(1988) =< aux(183)*(1/4)+aux(184) s(1989) =< aux(183)*(1/4)+aux(184) s(1981) =< aux(183)*(1/4)+aux(184) s(1990) =< aux(183)*(5/16)+aux(187) s(1988) =< aux(183)*(5/16)+aux(187) s(1989) =< aux(183)*(5/16)+aux(187) s(1981) =< aux(183)*(5/16)+aux(187) s(1996) =< s(1987)*s(1991) s(1997) =< s(1987)*s(1991) s(1998) =< s(1987)*s(1992) s(1999) =< s(1986)*s(1992) s(2000) =< s(1985)*s(1993) s(2001) =< s(1985)*s(1994) s(2002) =< s(1983)*s(1995) s(2003) =< s(1989)*s(1995) s(2004) =< s(1988)*s(1995) s(2005) =< s(1990)*s(1991) s(2006) =< s(1997) s(2007) =< s(1998) s(2008) =< s(1999) s(2009) =< s(2001) s(2010) =< s(2009)*s(1994) s(2011) =< s(2003) s(2012) =< s(2004) s(2013) =< s(2005) s(2014) =< s(2013)*aux(182) s(2017) =< aux(173) s(1938) =< aux(172) s(1939) =< aux(172) s(1940) =< aux(172) s(1941) =< aux(172) s(1942) =< aux(172) s(1943) =< aux(172) s(1944) =< aux(172) s(1945) =< aux(175) s(1940) =< aux(176) s(1942) =< aux(176) s(1946) =< aux(177) s(1947) =< aux(178) s(1943) =< aux(179) s(1942) =< aux(180) s(1948) =< aux(173) s(1949) =< aux(173)+2 s(1950) =< aux(173)-2 s(1951) =< aux(173)+1 s(1952) =< aux(173)-1 s(1943) =< aux(174)*(1/5)+aux(179) s(1944) =< aux(174)*(1/5)+aux(179) s(1942) =< aux(174)*(3/7)+aux(180) s(1943) =< aux(174)*(3/7)+aux(180) s(1944) =< aux(174)*(3/7)+aux(180) s(1940) =< aux(174)*(1/3)+aux(176) s(1941) =< aux(174)*(1/3)+aux(176) s(1942) =< aux(174)*(1/3)+aux(176) s(1943) =< aux(174)*(1/3)+aux(176) s(1944) =< aux(174)*(1/3)+aux(176) s(1946) =< aux(174)*(1/8)+aux(177) s(1938) =< aux(174)*(1/8)+aux(177) s(1945) =< aux(174)*(1/4)+aux(175) s(1946) =< aux(174)*(1/4)+aux(175) s(1938) =< aux(174)*(1/4)+aux(175) s(1947) =< aux(174)*(5/16)+aux(178) s(1945) =< aux(174)*(5/16)+aux(178) s(1946) =< aux(174)*(5/16)+aux(178) s(1938) =< aux(174)*(5/16)+aux(178) s(1953) =< s(1944)*s(1948) s(1954) =< s(1944)*s(1948) s(1955) =< s(1944)*s(1949) s(1956) =< s(1943)*s(1949) s(1957) =< s(1942)*s(1950) s(1958) =< s(1942)*s(1951) s(1959) =< s(1940)*s(1952) s(1960) =< s(1946)*s(1952) s(1961) =< s(1945)*s(1952) s(1962) =< s(1947)*s(1948) s(1963) =< s(1954) s(1964) =< s(1955) s(1965) =< s(1956) s(1966) =< s(1958) s(1967) =< s(1966)*s(1951) s(1968) =< s(1960) s(1969) =< s(1961) s(1970) =< s(1962) s(1971) =< s(1970)*aux(173) s(2111) =< s(2017)*aux(173) s(2255) =< s(2205)*aux(170) with precondition: [V>=1,V2>=0,Out>=1,2*V>=Out] * Chain [69]: 1*s(2269)+2*s(2270)+1*s(2271)+1*s(2272)+7*s(2273)+7*s(2274)+3*s(2275)+9*s(2276)+5*s(2277)+9*s(2278)+1*s(2284)+1*s(2288)+1*s(2290)+2*s(2294)+2*s(2295)+14*s(2296)+18*s(2297)+2*s(2298)+6*s(2299)+14*s(2300)+18*s(2301)+2*s(2302)+2*s(2305)+4*s(2306)+3 Such that:s(2260) =< V aux(190) =< 2*V s(2262) =< 2*V+1 s(2263) =< V/2 s(2264) =< 2/3*V s(2265) =< 3/4*V s(2266) =< 3/8*V s(2267) =< 4/5*V s(2268) =< 4/7*V aux(191) =< 2 s(2305) =< aux(190) s(2306) =< aux(191) s(2269) =< s(2260) s(2270) =< s(2260) s(2271) =< s(2260) s(2272) =< s(2260) s(2273) =< s(2260) s(2274) =< s(2260) s(2275) =< s(2260) s(2276) =< s(2263) s(2271) =< s(2264) s(2273) =< s(2264) s(2277) =< s(2265) s(2278) =< s(2266) s(2274) =< s(2267) s(2273) =< s(2268) s(2279) =< aux(190) s(2280) =< aux(190)+2 s(2281) =< aux(190)-2 s(2282) =< aux(190)+1 s(2283) =< aux(190)-1 s(2274) =< s(2262)*(1/5)+s(2267) s(2275) =< s(2262)*(1/5)+s(2267) s(2273) =< s(2262)*(3/7)+s(2268) s(2274) =< s(2262)*(3/7)+s(2268) s(2275) =< s(2262)*(3/7)+s(2268) s(2271) =< s(2262)*(1/3)+s(2264) s(2272) =< s(2262)*(1/3)+s(2264) s(2273) =< s(2262)*(1/3)+s(2264) s(2274) =< s(2262)*(1/3)+s(2264) s(2275) =< s(2262)*(1/3)+s(2264) s(2277) =< s(2262)*(1/8)+s(2265) s(2269) =< s(2262)*(1/8)+s(2265) s(2276) =< s(2262)*(1/4)+s(2263) s(2277) =< s(2262)*(1/4)+s(2263) s(2269) =< s(2262)*(1/4)+s(2263) s(2278) =< s(2262)*(5/16)+s(2266) s(2276) =< s(2262)*(5/16)+s(2266) s(2277) =< s(2262)*(5/16)+s(2266) s(2269) =< s(2262)*(5/16)+s(2266) s(2284) =< s(2275)*s(2279) s(2285) =< s(2275)*s(2279) s(2286) =< s(2275)*s(2280) s(2287) =< s(2274)*s(2280) s(2288) =< s(2273)*s(2281) s(2289) =< s(2273)*s(2282) s(2290) =< s(2271)*s(2283) s(2291) =< s(2277)*s(2283) s(2292) =< s(2276)*s(2283) s(2293) =< s(2278)*s(2279) s(2294) =< s(2285) s(2295) =< s(2286) s(2296) =< s(2287) s(2297) =< s(2289) s(2298) =< s(2297)*s(2282) s(2299) =< s(2291) s(2300) =< s(2292) s(2301) =< s(2293) s(2302) =< s(2301)*aux(190) with precondition: [V2=2,Out=0,V>=0] * Chain [68]: 1*s(2320)+2*s(2321)+1*s(2322)+1*s(2323)+7*s(2324)+7*s(2325)+3*s(2326)+9*s(2327)+5*s(2328)+9*s(2329)+1*s(2335)+1*s(2339)+1*s(2341)+2*s(2345)+2*s(2346)+14*s(2347)+18*s(2348)+2*s(2349)+6*s(2350)+14*s(2351)+18*s(2352)+2*s(2353)+10*s(2357)+8*s(2359)+2*s(2360)+7 Such that:s(2355) =< 2 s(2311) =< V s(2313) =< 2*V+1 s(2314) =< V/2 s(2315) =< 2/3*V s(2316) =< 3/4*V s(2317) =< 3/8*V s(2318) =< 4/5*V s(2319) =< 4/7*V aux(192) =< 2*V s(2357) =< aux(192) s(2359) =< s(2355) s(2360) =< s(2357)*s(2355) s(2320) =< s(2311) s(2321) =< s(2311) s(2322) =< s(2311) s(2323) =< s(2311) s(2324) =< s(2311) s(2325) =< s(2311) s(2326) =< s(2311) s(2327) =< s(2314) s(2322) =< s(2315) s(2324) =< s(2315) s(2328) =< s(2316) s(2329) =< s(2317) s(2325) =< s(2318) s(2324) =< s(2319) s(2330) =< aux(192) s(2331) =< aux(192)+2 s(2332) =< aux(192)-2 s(2333) =< aux(192)+1 s(2334) =< aux(192)-1 s(2325) =< s(2313)*(1/5)+s(2318) s(2326) =< s(2313)*(1/5)+s(2318) s(2324) =< s(2313)*(3/7)+s(2319) s(2325) =< s(2313)*(3/7)+s(2319) s(2326) =< s(2313)*(3/7)+s(2319) s(2322) =< s(2313)*(1/3)+s(2315) s(2323) =< s(2313)*(1/3)+s(2315) s(2324) =< s(2313)*(1/3)+s(2315) s(2325) =< s(2313)*(1/3)+s(2315) s(2326) =< s(2313)*(1/3)+s(2315) s(2328) =< s(2313)*(1/8)+s(2316) s(2320) =< s(2313)*(1/8)+s(2316) s(2327) =< s(2313)*(1/4)+s(2314) s(2328) =< s(2313)*(1/4)+s(2314) s(2320) =< s(2313)*(1/4)+s(2314) s(2329) =< s(2313)*(5/16)+s(2317) s(2327) =< s(2313)*(5/16)+s(2317) s(2328) =< s(2313)*(5/16)+s(2317) s(2320) =< s(2313)*(5/16)+s(2317) s(2335) =< s(2326)*s(2330) s(2336) =< s(2326)*s(2330) s(2337) =< s(2326)*s(2331) s(2338) =< s(2325)*s(2331) s(2339) =< s(2324)*s(2332) s(2340) =< s(2324)*s(2333) s(2341) =< s(2322)*s(2334) s(2342) =< s(2328)*s(2334) s(2343) =< s(2327)*s(2334) s(2344) =< s(2329)*s(2330) s(2345) =< s(2336) s(2346) =< s(2337) s(2347) =< s(2338) s(2348) =< s(2340) s(2349) =< s(2348)*s(2333) s(2350) =< s(2342) s(2351) =< s(2343) s(2352) =< s(2344) s(2353) =< s(2352)*aux(192) with precondition: [V2=2,Out>=1,2*V>=Out+2] #### Cost of chains of fun7(V,V2,V11,Out): * Chain [78]: 8*s(2646)+16*s(2647)+8*s(2648)+8*s(2649)+56*s(2650)+56*s(2651)+24*s(2652)+72*s(2653)+40*s(2654)+72*s(2655)+8*s(2661)+8*s(2665)+8*s(2667)+16*s(2671)+16*s(2672)+112*s(2673)+144*s(2674)+16*s(2675)+48*s(2676)+112*s(2677)+144*s(2678)+16*s(2679)+10*s(2689)+20*s(2690)+10*s(2691)+10*s(2692)+70*s(2693)+70*s(2694)+30*s(2695)+90*s(2696)+50*s(2697)+90*s(2698)+10*s(2704)+10*s(2708)+10*s(2710)+20*s(2714)+20*s(2715)+140*s(2716)+180*s(2717)+20*s(2718)+60*s(2719)+140*s(2720)+180*s(2721)+20*s(2722)+12*s(2732)+24*s(2733)+12*s(2734)+12*s(2735)+84*s(2736)+84*s(2737)+36*s(2738)+108*s(2739)+60*s(2740)+108*s(2741)+12*s(2747)+12*s(2751)+12*s(2753)+24*s(2757)+24*s(2758)+168*s(2759)+216*s(2760)+24*s(2761)+72*s(2762)+168*s(2763)+216*s(2764)+24*s(2765)+1 Such that:aux(213) =< V aux(214) =< 2*V aux(215) =< 2*V+1 aux(216) =< V/2 aux(217) =< 2/3*V aux(218) =< 3/4*V aux(219) =< 3/8*V aux(220) =< 4/5*V aux(221) =< 4/7*V aux(222) =< V2 aux(223) =< 2*V2 aux(224) =< 2*V2+1 aux(225) =< V2/2 aux(226) =< 2/3*V2 aux(227) =< 3/4*V2 aux(228) =< 3/8*V2 aux(229) =< 4/5*V2 aux(230) =< 4/7*V2 aux(231) =< V11 aux(232) =< 2*V11 aux(233) =< 2*V11+1 aux(234) =< V11/2 aux(235) =< 2/3*V11 aux(236) =< 3/4*V11 aux(237) =< 3/8*V11 aux(238) =< 4/5*V11 aux(239) =< 4/7*V11 s(2732) =< aux(231) s(2733) =< aux(231) s(2734) =< aux(231) s(2735) =< aux(231) s(2736) =< aux(231) s(2737) =< aux(231) s(2738) =< aux(231) s(2739) =< aux(234) s(2734) =< aux(235) s(2736) =< aux(235) s(2740) =< aux(236) s(2741) =< aux(237) s(2737) =< aux(238) s(2736) =< aux(239) s(2742) =< aux(232) s(2743) =< aux(232)+2 s(2744) =< aux(232)-2 s(2745) =< aux(232)+1 s(2746) =< aux(232)-1 s(2737) =< aux(233)*(1/5)+aux(238) s(2738) =< aux(233)*(1/5)+aux(238) s(2736) =< aux(233)*(3/7)+aux(239) s(2737) =< aux(233)*(3/7)+aux(239) s(2738) =< aux(233)*(3/7)+aux(239) s(2734) =< aux(233)*(1/3)+aux(235) s(2735) =< aux(233)*(1/3)+aux(235) s(2736) =< aux(233)*(1/3)+aux(235) s(2737) =< aux(233)*(1/3)+aux(235) s(2738) =< aux(233)*(1/3)+aux(235) s(2740) =< aux(233)*(1/8)+aux(236) s(2732) =< aux(233)*(1/8)+aux(236) s(2739) =< aux(233)*(1/4)+aux(234) s(2740) =< aux(233)*(1/4)+aux(234) s(2732) =< aux(233)*(1/4)+aux(234) s(2741) =< aux(233)*(5/16)+aux(237) s(2739) =< aux(233)*(5/16)+aux(237) s(2740) =< aux(233)*(5/16)+aux(237) s(2732) =< aux(233)*(5/16)+aux(237) s(2747) =< s(2738)*s(2742) s(2748) =< s(2738)*s(2742) s(2749) =< s(2738)*s(2743) s(2750) =< s(2737)*s(2743) s(2751) =< s(2736)*s(2744) s(2752) =< s(2736)*s(2745) s(2753) =< s(2734)*s(2746) s(2754) =< s(2740)*s(2746) s(2755) =< s(2739)*s(2746) s(2756) =< s(2741)*s(2742) s(2757) =< s(2748) s(2758) =< s(2749) s(2759) =< s(2750) s(2760) =< s(2752) s(2761) =< s(2760)*s(2745) s(2762) =< s(2754) s(2763) =< s(2755) s(2764) =< s(2756) s(2765) =< s(2764)*aux(232) s(2689) =< aux(222) s(2690) =< aux(222) s(2691) =< aux(222) s(2692) =< aux(222) s(2693) =< aux(222) s(2694) =< aux(222) s(2695) =< aux(222) s(2696) =< aux(225) s(2691) =< aux(226) s(2693) =< aux(226) s(2697) =< aux(227) s(2698) =< aux(228) s(2694) =< aux(229) s(2693) =< aux(230) s(2699) =< aux(223) s(2700) =< aux(223)+2 s(2701) =< aux(223)-2 s(2702) =< aux(223)+1 s(2703) =< aux(223)-1 s(2694) =< aux(224)*(1/5)+aux(229) s(2695) =< aux(224)*(1/5)+aux(229) s(2693) =< aux(224)*(3/7)+aux(230) s(2694) =< aux(224)*(3/7)+aux(230) s(2695) =< aux(224)*(3/7)+aux(230) s(2691) =< aux(224)*(1/3)+aux(226) s(2692) =< aux(224)*(1/3)+aux(226) s(2693) =< aux(224)*(1/3)+aux(226) s(2694) =< aux(224)*(1/3)+aux(226) s(2695) =< aux(224)*(1/3)+aux(226) s(2697) =< aux(224)*(1/8)+aux(227) s(2689) =< aux(224)*(1/8)+aux(227) s(2696) =< aux(224)*(1/4)+aux(225) s(2697) =< aux(224)*(1/4)+aux(225) s(2689) =< aux(224)*(1/4)+aux(225) s(2698) =< aux(224)*(5/16)+aux(228) s(2696) =< aux(224)*(5/16)+aux(228) s(2697) =< aux(224)*(5/16)+aux(228) s(2689) =< aux(224)*(5/16)+aux(228) s(2704) =< s(2695)*s(2699) s(2705) =< s(2695)*s(2699) s(2706) =< s(2695)*s(2700) s(2707) =< s(2694)*s(2700) s(2708) =< s(2693)*s(2701) s(2709) =< s(2693)*s(2702) s(2710) =< s(2691)*s(2703) s(2711) =< s(2697)*s(2703) s(2712) =< s(2696)*s(2703) s(2713) =< s(2698)*s(2699) s(2714) =< s(2705) s(2715) =< s(2706) s(2716) =< s(2707) s(2717) =< s(2709) s(2718) =< s(2717)*s(2702) s(2719) =< s(2711) s(2720) =< s(2712) s(2721) =< s(2713) s(2722) =< s(2721)*aux(223) s(2646) =< aux(213) s(2647) =< aux(213) s(2648) =< aux(213) s(2649) =< aux(213) s(2650) =< aux(213) s(2651) =< aux(213) s(2652) =< aux(213) s(2653) =< aux(216) s(2648) =< aux(217) s(2650) =< aux(217) s(2654) =< aux(218) s(2655) =< aux(219) s(2651) =< aux(220) s(2650) =< aux(221) s(2656) =< aux(214) s(2657) =< aux(214)+2 s(2658) =< aux(214)-2 s(2659) =< aux(214)+1 s(2660) =< aux(214)-1 s(2651) =< aux(215)*(1/5)+aux(220) s(2652) =< aux(215)*(1/5)+aux(220) s(2650) =< aux(215)*(3/7)+aux(221) s(2651) =< aux(215)*(3/7)+aux(221) s(2652) =< aux(215)*(3/7)+aux(221) s(2648) =< aux(215)*(1/3)+aux(217) s(2649) =< aux(215)*(1/3)+aux(217) s(2650) =< aux(215)*(1/3)+aux(217) s(2651) =< aux(215)*(1/3)+aux(217) s(2652) =< aux(215)*(1/3)+aux(217) s(2654) =< aux(215)*(1/8)+aux(218) s(2646) =< aux(215)*(1/8)+aux(218) s(2653) =< aux(215)*(1/4)+aux(216) s(2654) =< aux(215)*(1/4)+aux(216) s(2646) =< aux(215)*(1/4)+aux(216) s(2655) =< aux(215)*(5/16)+aux(219) s(2653) =< aux(215)*(5/16)+aux(219) s(2654) =< aux(215)*(5/16)+aux(219) s(2646) =< aux(215)*(5/16)+aux(219) s(2661) =< s(2652)*s(2656) s(2662) =< s(2652)*s(2656) s(2663) =< s(2652)*s(2657) s(2664) =< s(2651)*s(2657) s(2665) =< s(2650)*s(2658) s(2666) =< s(2650)*s(2659) s(2667) =< s(2648)*s(2660) s(2668) =< s(2654)*s(2660) s(2669) =< s(2653)*s(2660) s(2670) =< s(2655)*s(2656) s(2671) =< s(2662) s(2672) =< s(2663) s(2673) =< s(2664) s(2674) =< s(2666) s(2675) =< s(2674)*s(2659) s(2676) =< s(2668) s(2677) =< s(2669) s(2678) =< s(2670) s(2679) =< s(2678)*aux(214) with precondition: [Out=0,V>=0,V2>=0,V11>=0] * Chain [77]: 4*s(3936)+8*s(3937)+4*s(3938)+4*s(3939)+28*s(3940)+28*s(3941)+12*s(3942)+36*s(3943)+20*s(3944)+36*s(3945)+4*s(3951)+4*s(3955)+4*s(3957)+8*s(3961)+8*s(3962)+56*s(3963)+72*s(3964)+8*s(3965)+24*s(3966)+56*s(3967)+72*s(3968)+8*s(3969)+5*s(3979)+10*s(3980)+5*s(3981)+5*s(3982)+35*s(3983)+35*s(3984)+15*s(3985)+45*s(3986)+25*s(3987)+45*s(3988)+5*s(3994)+5*s(3998)+5*s(4000)+10*s(4004)+10*s(4005)+70*s(4006)+90*s(4007)+10*s(4008)+30*s(4009)+70*s(4010)+90*s(4011)+10*s(4012)+1 Such that:aux(240) =< V aux(241) =< 2*V aux(242) =< 2*V+1 aux(243) =< V/2 aux(244) =< 2/3*V aux(245) =< 3/4*V aux(246) =< 3/8*V aux(247) =< 4/5*V aux(248) =< 4/7*V aux(249) =< V2 aux(250) =< 2*V2 aux(251) =< 2*V2+1 aux(252) =< V2/2 aux(253) =< 2/3*V2 aux(254) =< 3/4*V2 aux(255) =< 3/8*V2 aux(256) =< 4/5*V2 aux(257) =< 4/7*V2 s(3979) =< aux(249) s(3980) =< aux(249) s(3981) =< aux(249) s(3982) =< aux(249) s(3983) =< aux(249) s(3984) =< aux(249) s(3985) =< aux(249) s(3986) =< aux(252) s(3981) =< aux(253) s(3983) =< aux(253) s(3987) =< aux(254) s(3988) =< aux(255) s(3984) =< aux(256) s(3983) =< aux(257) s(3989) =< aux(250) s(3990) =< aux(250)+2 s(3991) =< aux(250)-2 s(3992) =< aux(250)+1 s(3993) =< aux(250)-1 s(3984) =< aux(251)*(1/5)+aux(256) s(3985) =< aux(251)*(1/5)+aux(256) s(3983) =< aux(251)*(3/7)+aux(257) s(3984) =< aux(251)*(3/7)+aux(257) s(3985) =< aux(251)*(3/7)+aux(257) s(3981) =< aux(251)*(1/3)+aux(253) s(3982) =< aux(251)*(1/3)+aux(253) s(3983) =< aux(251)*(1/3)+aux(253) s(3984) =< aux(251)*(1/3)+aux(253) s(3985) =< aux(251)*(1/3)+aux(253) s(3987) =< aux(251)*(1/8)+aux(254) s(3979) =< aux(251)*(1/8)+aux(254) s(3986) =< aux(251)*(1/4)+aux(252) s(3987) =< aux(251)*(1/4)+aux(252) s(3979) =< aux(251)*(1/4)+aux(252) s(3988) =< aux(251)*(5/16)+aux(255) s(3986) =< aux(251)*(5/16)+aux(255) s(3987) =< aux(251)*(5/16)+aux(255) s(3979) =< aux(251)*(5/16)+aux(255) s(3994) =< s(3985)*s(3989) s(3995) =< s(3985)*s(3989) s(3996) =< s(3985)*s(3990) s(3997) =< s(3984)*s(3990) s(3998) =< s(3983)*s(3991) s(3999) =< s(3983)*s(3992) s(4000) =< s(3981)*s(3993) s(4001) =< s(3987)*s(3993) s(4002) =< s(3986)*s(3993) s(4003) =< s(3988)*s(3989) s(4004) =< s(3995) s(4005) =< s(3996) s(4006) =< s(3997) s(4007) =< s(3999) s(4008) =< s(4007)*s(3992) s(4009) =< s(4001) s(4010) =< s(4002) s(4011) =< s(4003) s(4012) =< s(4011)*aux(250) s(3936) =< aux(240) s(3937) =< aux(240) s(3938) =< aux(240) s(3939) =< aux(240) s(3940) =< aux(240) s(3941) =< aux(240) s(3942) =< aux(240) s(3943) =< aux(243) s(3938) =< aux(244) s(3940) =< aux(244) s(3944) =< aux(245) s(3945) =< aux(246) s(3941) =< aux(247) s(3940) =< aux(248) s(3946) =< aux(241) s(3947) =< aux(241)+2 s(3948) =< aux(241)-2 s(3949) =< aux(241)+1 s(3950) =< aux(241)-1 s(3941) =< aux(242)*(1/5)+aux(247) s(3942) =< aux(242)*(1/5)+aux(247) s(3940) =< aux(242)*(3/7)+aux(248) s(3941) =< aux(242)*(3/7)+aux(248) s(3942) =< aux(242)*(3/7)+aux(248) s(3938) =< aux(242)*(1/3)+aux(244) s(3939) =< aux(242)*(1/3)+aux(244) s(3940) =< aux(242)*(1/3)+aux(244) s(3941) =< aux(242)*(1/3)+aux(244) s(3942) =< aux(242)*(1/3)+aux(244) s(3944) =< aux(242)*(1/8)+aux(245) s(3936) =< aux(242)*(1/8)+aux(245) s(3943) =< aux(242)*(1/4)+aux(243) s(3944) =< aux(242)*(1/4)+aux(243) s(3936) =< aux(242)*(1/4)+aux(243) s(3945) =< aux(242)*(5/16)+aux(246) s(3943) =< aux(242)*(5/16)+aux(246) s(3944) =< aux(242)*(5/16)+aux(246) s(3936) =< aux(242)*(5/16)+aux(246) s(3951) =< s(3942)*s(3946) s(3952) =< s(3942)*s(3946) s(3953) =< s(3942)*s(3947) s(3954) =< s(3941)*s(3947) s(3955) =< s(3940)*s(3948) s(3956) =< s(3940)*s(3949) s(3957) =< s(3938)*s(3950) s(3958) =< s(3944)*s(3950) s(3959) =< s(3943)*s(3950) s(3960) =< s(3945)*s(3946) s(3961) =< s(3952) s(3962) =< s(3953) s(3963) =< s(3954) s(3964) =< s(3956) s(3965) =< s(3964)*s(3949) s(3966) =< s(3958) s(3967) =< s(3959) s(3968) =< s(3960) s(3969) =< s(3968)*aux(241) with precondition: [V11=2,Out=0,V>=0,V2>=0] * Chain [76]: 6*s(4323)+12*s(4324)+6*s(4325)+6*s(4326)+42*s(4327)+42*s(4328)+18*s(4329)+54*s(4330)+30*s(4331)+54*s(4332)+6*s(4338)+6*s(4342)+6*s(4344)+12*s(4348)+12*s(4349)+84*s(4350)+108*s(4351)+12*s(4352)+36*s(4353)+84*s(4354)+108*s(4355)+12*s(4356)+3*s(4366)+6*s(4367)+3*s(4368)+3*s(4369)+21*s(4370)+21*s(4371)+9*s(4372)+27*s(4373)+15*s(4374)+27*s(4375)+3*s(4381)+3*s(4385)+3*s(4387)+6*s(4391)+6*s(4392)+42*s(4393)+54*s(4394)+6*s(4395)+18*s(4396)+42*s(4397)+54*s(4398)+6*s(4399)+1 Such that:aux(258) =< V aux(259) =< 2*V aux(260) =< 2*V+1 aux(261) =< V/2 aux(262) =< 2/3*V aux(263) =< 3/4*V aux(264) =< 3/8*V aux(265) =< 4/5*V aux(266) =< 4/7*V aux(267) =< V11 aux(268) =< 2*V11 aux(269) =< 2*V11+1 aux(270) =< V11/2 aux(271) =< 2/3*V11 aux(272) =< 3/4*V11 aux(273) =< 3/8*V11 aux(274) =< 4/5*V11 aux(275) =< 4/7*V11 s(4366) =< aux(267) s(4367) =< aux(267) s(4368) =< aux(267) s(4369) =< aux(267) s(4370) =< aux(267) s(4371) =< aux(267) s(4372) =< aux(267) s(4373) =< aux(270) s(4368) =< aux(271) s(4370) =< aux(271) s(4374) =< aux(272) s(4375) =< aux(273) s(4371) =< aux(274) s(4370) =< aux(275) s(4376) =< aux(268) s(4377) =< aux(268)+2 s(4378) =< aux(268)-2 s(4379) =< aux(268)+1 s(4380) =< aux(268)-1 s(4371) =< aux(269)*(1/5)+aux(274) s(4372) =< aux(269)*(1/5)+aux(274) s(4370) =< aux(269)*(3/7)+aux(275) s(4371) =< aux(269)*(3/7)+aux(275) s(4372) =< aux(269)*(3/7)+aux(275) s(4368) =< aux(269)*(1/3)+aux(271) s(4369) =< aux(269)*(1/3)+aux(271) s(4370) =< aux(269)*(1/3)+aux(271) s(4371) =< aux(269)*(1/3)+aux(271) s(4372) =< aux(269)*(1/3)+aux(271) s(4374) =< aux(269)*(1/8)+aux(272) s(4366) =< aux(269)*(1/8)+aux(272) s(4373) =< aux(269)*(1/4)+aux(270) s(4374) =< aux(269)*(1/4)+aux(270) s(4366) =< aux(269)*(1/4)+aux(270) s(4375) =< aux(269)*(5/16)+aux(273) s(4373) =< aux(269)*(5/16)+aux(273) s(4374) =< aux(269)*(5/16)+aux(273) s(4366) =< aux(269)*(5/16)+aux(273) s(4381) =< s(4372)*s(4376) s(4382) =< s(4372)*s(4376) s(4383) =< s(4372)*s(4377) s(4384) =< s(4371)*s(4377) s(4385) =< s(4370)*s(4378) s(4386) =< s(4370)*s(4379) s(4387) =< s(4368)*s(4380) s(4388) =< s(4374)*s(4380) s(4389) =< s(4373)*s(4380) s(4390) =< s(4375)*s(4376) s(4391) =< s(4382) s(4392) =< s(4383) s(4393) =< s(4384) s(4394) =< s(4386) s(4395) =< s(4394)*s(4379) s(4396) =< s(4388) s(4397) =< s(4389) s(4398) =< s(4390) s(4399) =< s(4398)*aux(268) s(4323) =< aux(258) s(4324) =< aux(258) s(4325) =< aux(258) s(4326) =< aux(258) s(4327) =< aux(258) s(4328) =< aux(258) s(4329) =< aux(258) s(4330) =< aux(261) s(4325) =< aux(262) s(4327) =< aux(262) s(4331) =< aux(263) s(4332) =< aux(264) s(4328) =< aux(265) s(4327) =< aux(266) s(4333) =< aux(259) s(4334) =< aux(259)+2 s(4335) =< aux(259)-2 s(4336) =< aux(259)+1 s(4337) =< aux(259)-1 s(4328) =< aux(260)*(1/5)+aux(265) s(4329) =< aux(260)*(1/5)+aux(265) s(4327) =< aux(260)*(3/7)+aux(266) s(4328) =< aux(260)*(3/7)+aux(266) s(4329) =< aux(260)*(3/7)+aux(266) s(4325) =< aux(260)*(1/3)+aux(262) s(4326) =< aux(260)*(1/3)+aux(262) s(4327) =< aux(260)*(1/3)+aux(262) s(4328) =< aux(260)*(1/3)+aux(262) s(4329) =< aux(260)*(1/3)+aux(262) s(4331) =< aux(260)*(1/8)+aux(263) s(4323) =< aux(260)*(1/8)+aux(263) s(4330) =< aux(260)*(1/4)+aux(261) s(4331) =< aux(260)*(1/4)+aux(261) s(4323) =< aux(260)*(1/4)+aux(261) s(4332) =< aux(260)*(5/16)+aux(264) s(4330) =< aux(260)*(5/16)+aux(264) s(4331) =< aux(260)*(5/16)+aux(264) s(4323) =< aux(260)*(5/16)+aux(264) s(4338) =< s(4329)*s(4333) s(4339) =< s(4329)*s(4333) s(4340) =< s(4329)*s(4334) s(4341) =< s(4328)*s(4334) s(4342) =< s(4327)*s(4335) s(4343) =< s(4327)*s(4336) s(4344) =< s(4325)*s(4337) s(4345) =< s(4331)*s(4337) s(4346) =< s(4330)*s(4337) s(4347) =< s(4332)*s(4333) s(4348) =< s(4339) s(4349) =< s(4340) s(4350) =< s(4341) s(4351) =< s(4343) s(4352) =< s(4351)*s(4336) s(4353) =< s(4345) s(4354) =< s(4346) s(4355) =< s(4347) s(4356) =< s(4355)*aux(259) with precondition: [V2=2,Out=0,V>=0,V11>=0] * Chain [75]: 12*s(4710)+24*s(4711)+12*s(4712)+12*s(4713)+84*s(4714)+84*s(4715)+36*s(4716)+108*s(4717)+60*s(4718)+108*s(4719)+12*s(4725)+12*s(4729)+12*s(4731)+24*s(4735)+24*s(4736)+168*s(4737)+216*s(4738)+24*s(4739)+72*s(4740)+168*s(4741)+216*s(4742)+24*s(4743)+4*s(4753)+8*s(4754)+4*s(4755)+4*s(4756)+28*s(4757)+28*s(4758)+12*s(4759)+36*s(4760)+20*s(4761)+36*s(4762)+4*s(4768)+4*s(4772)+4*s(4774)+8*s(4778)+8*s(4779)+56*s(4780)+72*s(4781)+8*s(4782)+24*s(4783)+56*s(4784)+72*s(4785)+8*s(4786)+5*s(4796)+10*s(4797)+5*s(4798)+5*s(4799)+35*s(4800)+35*s(4801)+15*s(4802)+45*s(4803)+25*s(4804)+45*s(4805)+5*s(4811)+5*s(4815)+5*s(4817)+10*s(4821)+10*s(4822)+70*s(4823)+90*s(4824)+10*s(4825)+30*s(4826)+70*s(4827)+90*s(4828)+10*s(4829)+10*s(4833)+4*s(4965)+6*s(5325)+4*s(5373)+5 Such that:aux(286) =< 1 aux(287) =< 2 aux(288) =< V aux(289) =< 2*V aux(290) =< 2*V+1 aux(291) =< V/2 aux(292) =< 2/3*V aux(293) =< 3/4*V aux(294) =< 3/8*V aux(295) =< 4/5*V aux(296) =< 4/7*V aux(297) =< V2 aux(298) =< 2*V2 aux(299) =< 2*V2+1 aux(300) =< V2/2 aux(301) =< 2/3*V2 aux(302) =< 3/4*V2 aux(303) =< 3/8*V2 aux(304) =< 4/5*V2 aux(305) =< 4/7*V2 aux(306) =< V11 aux(307) =< 2*V11 aux(308) =< 2*V11+1 aux(309) =< V11/2 aux(310) =< 2/3*V11 aux(311) =< 3/4*V11 aux(312) =< 3/8*V11 aux(313) =< 4/5*V11 aux(314) =< 4/7*V11 s(5325) =< aux(286) s(4833) =< aux(307) s(4796) =< aux(306) s(4797) =< aux(306) s(4798) =< aux(306) s(4799) =< aux(306) s(4800) =< aux(306) s(4801) =< aux(306) s(4802) =< aux(306) s(4803) =< aux(309) s(4798) =< aux(310) s(4800) =< aux(310) s(4804) =< aux(311) s(4805) =< aux(312) s(4801) =< aux(313) s(4800) =< aux(314) s(4806) =< aux(307) s(4807) =< aux(307)+2 s(4808) =< aux(307)-2 s(4809) =< aux(307)+1 s(4810) =< aux(307)-1 s(4801) =< aux(308)*(1/5)+aux(313) s(4802) =< aux(308)*(1/5)+aux(313) s(4800) =< aux(308)*(3/7)+aux(314) s(4801) =< aux(308)*(3/7)+aux(314) s(4802) =< aux(308)*(3/7)+aux(314) s(4798) =< aux(308)*(1/3)+aux(310) s(4799) =< aux(308)*(1/3)+aux(310) s(4800) =< aux(308)*(1/3)+aux(310) s(4801) =< aux(308)*(1/3)+aux(310) s(4802) =< aux(308)*(1/3)+aux(310) s(4804) =< aux(308)*(1/8)+aux(311) s(4796) =< aux(308)*(1/8)+aux(311) s(4803) =< aux(308)*(1/4)+aux(309) s(4804) =< aux(308)*(1/4)+aux(309) s(4796) =< aux(308)*(1/4)+aux(309) s(4805) =< aux(308)*(5/16)+aux(312) s(4803) =< aux(308)*(5/16)+aux(312) s(4804) =< aux(308)*(5/16)+aux(312) s(4796) =< aux(308)*(5/16)+aux(312) s(4811) =< s(4802)*s(4806) s(4812) =< s(4802)*s(4806) s(4813) =< s(4802)*s(4807) s(4814) =< s(4801)*s(4807) s(4815) =< s(4800)*s(4808) s(4816) =< s(4800)*s(4809) s(4817) =< s(4798)*s(4810) s(4818) =< s(4804)*s(4810) s(4819) =< s(4803)*s(4810) s(4820) =< s(4805)*s(4806) s(4821) =< s(4812) s(4822) =< s(4813) s(4823) =< s(4814) s(4824) =< s(4816) s(4825) =< s(4824)*s(4809) s(4826) =< s(4818) s(4827) =< s(4819) s(4828) =< s(4820) s(4829) =< s(4828)*aux(307) s(4710) =< aux(288) s(4711) =< aux(288) s(4712) =< aux(288) s(4713) =< aux(288) s(4714) =< aux(288) s(4715) =< aux(288) s(4716) =< aux(288) s(4717) =< aux(291) s(4712) =< aux(292) s(4714) =< aux(292) s(4718) =< aux(293) s(4719) =< aux(294) s(4715) =< aux(295) s(4714) =< aux(296) s(4720) =< aux(289) s(4721) =< aux(289)+2 s(4722) =< aux(289)-2 s(4723) =< aux(289)+1 s(4724) =< aux(289)-1 s(4715) =< aux(290)*(1/5)+aux(295) s(4716) =< aux(290)*(1/5)+aux(295) s(4714) =< aux(290)*(3/7)+aux(296) s(4715) =< aux(290)*(3/7)+aux(296) s(4716) =< aux(290)*(3/7)+aux(296) s(4712) =< aux(290)*(1/3)+aux(292) s(4713) =< aux(290)*(1/3)+aux(292) s(4714) =< aux(290)*(1/3)+aux(292) s(4715) =< aux(290)*(1/3)+aux(292) s(4716) =< aux(290)*(1/3)+aux(292) s(4718) =< aux(290)*(1/8)+aux(293) s(4710) =< aux(290)*(1/8)+aux(293) s(4717) =< aux(290)*(1/4)+aux(291) s(4718) =< aux(290)*(1/4)+aux(291) s(4710) =< aux(290)*(1/4)+aux(291) s(4719) =< aux(290)*(5/16)+aux(294) s(4717) =< aux(290)*(5/16)+aux(294) s(4718) =< aux(290)*(5/16)+aux(294) s(4710) =< aux(290)*(5/16)+aux(294) s(4725) =< s(4716)*s(4720) s(4726) =< s(4716)*s(4720) s(4727) =< s(4716)*s(4721) s(4728) =< s(4715)*s(4721) s(4729) =< s(4714)*s(4722) s(4730) =< s(4714)*s(4723) s(4731) =< s(4712)*s(4724) s(4732) =< s(4718)*s(4724) s(4733) =< s(4717)*s(4724) s(4734) =< s(4719)*s(4720) s(4735) =< s(4726) s(4736) =< s(4727) s(4737) =< s(4728) s(4738) =< s(4730) s(4739) =< s(4738)*s(4723) s(4740) =< s(4732) s(4741) =< s(4733) s(4742) =< s(4734) s(4743) =< s(4742)*aux(289) s(5373) =< aux(287) s(4753) =< aux(297) s(4754) =< aux(297) s(4755) =< aux(297) s(4756) =< aux(297) s(4757) =< aux(297) s(4758) =< aux(297) s(4759) =< aux(297) s(4760) =< aux(300) s(4755) =< aux(301) s(4757) =< aux(301) s(4761) =< aux(302) s(4762) =< aux(303) s(4758) =< aux(304) s(4757) =< aux(305) s(4763) =< aux(298) s(4764) =< aux(298)+2 s(4765) =< aux(298)-2 s(4766) =< aux(298)+1 s(4767) =< aux(298)-1 s(4758) =< aux(299)*(1/5)+aux(304) s(4759) =< aux(299)*(1/5)+aux(304) s(4757) =< aux(299)*(3/7)+aux(305) s(4758) =< aux(299)*(3/7)+aux(305) s(4759) =< aux(299)*(3/7)+aux(305) s(4755) =< aux(299)*(1/3)+aux(301) s(4756) =< aux(299)*(1/3)+aux(301) s(4757) =< aux(299)*(1/3)+aux(301) s(4758) =< aux(299)*(1/3)+aux(301) s(4759) =< aux(299)*(1/3)+aux(301) s(4761) =< aux(299)*(1/8)+aux(302) s(4753) =< aux(299)*(1/8)+aux(302) s(4760) =< aux(299)*(1/4)+aux(300) s(4761) =< aux(299)*(1/4)+aux(300) s(4753) =< aux(299)*(1/4)+aux(300) s(4762) =< aux(299)*(5/16)+aux(303) s(4760) =< aux(299)*(5/16)+aux(303) s(4761) =< aux(299)*(5/16)+aux(303) s(4753) =< aux(299)*(5/16)+aux(303) s(4768) =< s(4759)*s(4763) s(4769) =< s(4759)*s(4763) s(4770) =< s(4759)*s(4764) s(4771) =< s(4758)*s(4764) s(4772) =< s(4757)*s(4765) s(4773) =< s(4757)*s(4766) s(4774) =< s(4755)*s(4767) s(4775) =< s(4761)*s(4767) s(4776) =< s(4760)*s(4767) s(4777) =< s(4762)*s(4763) s(4778) =< s(4769) s(4779) =< s(4770) s(4780) =< s(4771) s(4781) =< s(4773) s(4782) =< s(4781)*s(4766) s(4783) =< s(4775) s(4784) =< s(4776) s(4785) =< s(4777) s(4786) =< s(4785)*aux(298) s(4965) =< aux(298) with precondition: [Out=1,V>=1,V2>=0,V11>=0] * Chain [74]: 5*s(5661)+10*s(5662)+5*s(5663)+5*s(5664)+35*s(5665)+35*s(5666)+15*s(5667)+45*s(5668)+25*s(5669)+45*s(5670)+5*s(5676)+5*s(5680)+5*s(5682)+10*s(5686)+10*s(5687)+70*s(5688)+90*s(5689)+10*s(5690)+30*s(5691)+70*s(5692)+90*s(5693)+10*s(5694)+3*s(5704)+6*s(5705)+3*s(5706)+3*s(5707)+21*s(5708)+21*s(5709)+9*s(5710)+27*s(5711)+15*s(5712)+27*s(5713)+3*s(5719)+3*s(5723)+3*s(5725)+6*s(5729)+6*s(5730)+42*s(5731)+54*s(5732)+6*s(5733)+18*s(5734)+42*s(5735)+54*s(5736)+6*s(5737)+3*s(5747)+6*s(5748)+3*s(5749)+3*s(5750)+21*s(5751)+21*s(5752)+9*s(5753)+27*s(5754)+15*s(5755)+27*s(5756)+3*s(5762)+3*s(5766)+3*s(5768)+6*s(5772)+6*s(5773)+42*s(5774)+54*s(5775)+6*s(5776)+18*s(5777)+42*s(5778)+54*s(5779)+6*s(5780)+46*s(5783)+2*s(5920)+24*s(6099)+9 Such that:aux(318) =< 1 aux(319) =< V aux(320) =< 2*V aux(321) =< 2*V+1 aux(322) =< V/2 aux(323) =< 2/3*V aux(324) =< 3/4*V aux(325) =< 3/8*V aux(326) =< 4/5*V aux(327) =< 4/7*V aux(328) =< V2 aux(329) =< 2*V2 aux(330) =< 2*V2+1 aux(331) =< V2/2 aux(332) =< 2/3*V2 aux(333) =< 3/4*V2 aux(334) =< 3/8*V2 aux(335) =< 4/5*V2 aux(336) =< 4/7*V2 aux(337) =< V11 aux(338) =< 2*V11 aux(339) =< 2*V11+1 aux(340) =< V11/2 aux(341) =< 2/3*V11 aux(342) =< 3/4*V11 aux(343) =< 3/8*V11 aux(344) =< 4/5*V11 aux(345) =< 4/7*V11 s(6099) =< aux(318) s(5747) =< aux(337) s(5748) =< aux(337) s(5749) =< aux(337) s(5750) =< aux(337) s(5751) =< aux(337) s(5752) =< aux(337) s(5753) =< aux(337) s(5754) =< aux(340) s(5749) =< aux(341) s(5751) =< aux(341) s(5755) =< aux(342) s(5756) =< aux(343) s(5752) =< aux(344) s(5751) =< aux(345) s(5757) =< aux(338) s(5758) =< aux(338)+2 s(5759) =< aux(338)-2 s(5760) =< aux(338)+1 s(5761) =< aux(338)-1 s(5752) =< aux(339)*(1/5)+aux(344) s(5753) =< aux(339)*(1/5)+aux(344) s(5751) =< aux(339)*(3/7)+aux(345) s(5752) =< aux(339)*(3/7)+aux(345) s(5753) =< aux(339)*(3/7)+aux(345) s(5749) =< aux(339)*(1/3)+aux(341) s(5750) =< aux(339)*(1/3)+aux(341) s(5751) =< aux(339)*(1/3)+aux(341) s(5752) =< aux(339)*(1/3)+aux(341) s(5753) =< aux(339)*(1/3)+aux(341) s(5755) =< aux(339)*(1/8)+aux(342) s(5747) =< aux(339)*(1/8)+aux(342) s(5754) =< aux(339)*(1/4)+aux(340) s(5755) =< aux(339)*(1/4)+aux(340) s(5747) =< aux(339)*(1/4)+aux(340) s(5756) =< aux(339)*(5/16)+aux(343) s(5754) =< aux(339)*(5/16)+aux(343) s(5755) =< aux(339)*(5/16)+aux(343) s(5747) =< aux(339)*(5/16)+aux(343) s(5762) =< s(5753)*s(5757) s(5763) =< s(5753)*s(5757) s(5764) =< s(5753)*s(5758) s(5765) =< s(5752)*s(5758) s(5766) =< s(5751)*s(5759) s(5767) =< s(5751)*s(5760) s(5768) =< s(5749)*s(5761) s(5769) =< s(5755)*s(5761) s(5770) =< s(5754)*s(5761) s(5771) =< s(5756)*s(5757) s(5772) =< s(5763) s(5773) =< s(5764) s(5774) =< s(5765) s(5775) =< s(5767) s(5776) =< s(5775)*s(5760) s(5777) =< s(5769) s(5778) =< s(5770) s(5779) =< s(5771) s(5780) =< s(5779)*aux(338) s(5661) =< aux(319) s(5662) =< aux(319) s(5663) =< aux(319) s(5664) =< aux(319) s(5665) =< aux(319) s(5666) =< aux(319) s(5667) =< aux(319) s(5668) =< aux(322) s(5663) =< aux(323) s(5665) =< aux(323) s(5669) =< aux(324) s(5670) =< aux(325) s(5666) =< aux(326) s(5665) =< aux(327) s(5671) =< aux(320) s(5672) =< aux(320)+2 s(5673) =< aux(320)-2 s(5674) =< aux(320)+1 s(5675) =< aux(320)-1 s(5666) =< aux(321)*(1/5)+aux(326) s(5667) =< aux(321)*(1/5)+aux(326) s(5665) =< aux(321)*(3/7)+aux(327) s(5666) =< aux(321)*(3/7)+aux(327) s(5667) =< aux(321)*(3/7)+aux(327) s(5663) =< aux(321)*(1/3)+aux(323) s(5664) =< aux(321)*(1/3)+aux(323) s(5665) =< aux(321)*(1/3)+aux(323) s(5666) =< aux(321)*(1/3)+aux(323) s(5667) =< aux(321)*(1/3)+aux(323) s(5669) =< aux(321)*(1/8)+aux(324) s(5661) =< aux(321)*(1/8)+aux(324) s(5668) =< aux(321)*(1/4)+aux(322) s(5669) =< aux(321)*(1/4)+aux(322) s(5661) =< aux(321)*(1/4)+aux(322) s(5670) =< aux(321)*(5/16)+aux(325) s(5668) =< aux(321)*(5/16)+aux(325) s(5669) =< aux(321)*(5/16)+aux(325) s(5661) =< aux(321)*(5/16)+aux(325) s(5676) =< s(5667)*s(5671) s(5677) =< s(5667)*s(5671) s(5678) =< s(5667)*s(5672) s(5679) =< s(5666)*s(5672) s(5680) =< s(5665)*s(5673) s(5681) =< s(5665)*s(5674) s(5682) =< s(5663)*s(5675) s(5683) =< s(5669)*s(5675) s(5684) =< s(5668)*s(5675) s(5685) =< s(5670)*s(5671) s(5686) =< s(5677) s(5687) =< s(5678) s(5688) =< s(5679) s(5689) =< s(5681) s(5690) =< s(5689)*s(5674) s(5691) =< s(5683) s(5692) =< s(5684) s(5693) =< s(5685) s(5694) =< s(5693)*aux(320) s(5783) =< aux(329) s(5704) =< aux(328) s(5705) =< aux(328) s(5706) =< aux(328) s(5707) =< aux(328) s(5708) =< aux(328) s(5709) =< aux(328) s(5710) =< aux(328) s(5711) =< aux(331) s(5706) =< aux(332) s(5708) =< aux(332) s(5712) =< aux(333) s(5713) =< aux(334) s(5709) =< aux(335) s(5708) =< aux(336) s(5714) =< aux(329) s(5715) =< aux(329)+2 s(5716) =< aux(329)-2 s(5717) =< aux(329)+1 s(5718) =< aux(329)-1 s(5709) =< aux(330)*(1/5)+aux(335) s(5710) =< aux(330)*(1/5)+aux(335) s(5708) =< aux(330)*(3/7)+aux(336) s(5709) =< aux(330)*(3/7)+aux(336) s(5710) =< aux(330)*(3/7)+aux(336) s(5706) =< aux(330)*(1/3)+aux(332) s(5707) =< aux(330)*(1/3)+aux(332) s(5708) =< aux(330)*(1/3)+aux(332) s(5709) =< aux(330)*(1/3)+aux(332) s(5710) =< aux(330)*(1/3)+aux(332) s(5712) =< aux(330)*(1/8)+aux(333) s(5704) =< aux(330)*(1/8)+aux(333) s(5711) =< aux(330)*(1/4)+aux(331) s(5712) =< aux(330)*(1/4)+aux(331) s(5704) =< aux(330)*(1/4)+aux(331) s(5713) =< aux(330)*(5/16)+aux(334) s(5711) =< aux(330)*(5/16)+aux(334) s(5712) =< aux(330)*(5/16)+aux(334) s(5704) =< aux(330)*(5/16)+aux(334) s(5719) =< s(5710)*s(5714) s(5720) =< s(5710)*s(5714) s(5721) =< s(5710)*s(5715) s(5722) =< s(5709)*s(5715) s(5723) =< s(5708)*s(5716) s(5724) =< s(5708)*s(5717) s(5725) =< s(5706)*s(5718) s(5726) =< s(5712)*s(5718) s(5727) =< s(5711)*s(5718) s(5728) =< s(5713)*s(5714) s(5729) =< s(5720) s(5730) =< s(5721) s(5731) =< s(5722) s(5732) =< s(5724) s(5733) =< s(5732)*s(5717) s(5734) =< s(5726) s(5735) =< s(5727) s(5736) =< s(5728) s(5737) =< s(5736)*aux(329) s(5920) =< s(5783)*aux(329) with precondition: [V>=1,V11>=0,Out>=2,2*V2>=Out] * Chain [73]: 3*s(6157)+6*s(6158)+3*s(6159)+3*s(6160)+21*s(6161)+21*s(6162)+9*s(6163)+27*s(6164)+15*s(6165)+27*s(6166)+3*s(6172)+3*s(6176)+3*s(6178)+6*s(6182)+6*s(6183)+42*s(6184)+54*s(6185)+6*s(6186)+18*s(6187)+42*s(6188)+54*s(6189)+6*s(6190)+2*s(6200)+4*s(6201)+2*s(6202)+2*s(6203)+14*s(6204)+14*s(6205)+6*s(6206)+18*s(6207)+10*s(6208)+18*s(6209)+2*s(6215)+2*s(6219)+2*s(6221)+4*s(6225)+4*s(6226)+28*s(6227)+36*s(6228)+4*s(6229)+12*s(6230)+28*s(6231)+36*s(6232)+4*s(6233)+6*s(6237)+2*s(6326)+5 Such that:aux(347) =< 2 aux(348) =< V aux(349) =< 2*V aux(350) =< 2*V+1 aux(351) =< V/2 aux(352) =< 2/3*V aux(353) =< 3/4*V aux(354) =< 3/8*V aux(355) =< 4/5*V aux(356) =< 4/7*V aux(357) =< V2 aux(358) =< 2*V2 aux(359) =< 2*V2+1 aux(360) =< V2/2 aux(361) =< 2/3*V2 aux(362) =< 3/4*V2 aux(363) =< 3/8*V2 aux(364) =< 4/5*V2 aux(365) =< 4/7*V2 s(6237) =< aux(347) s(6200) =< aux(357) s(6201) =< aux(357) s(6202) =< aux(357) s(6203) =< aux(357) s(6204) =< aux(357) s(6205) =< aux(357) s(6206) =< aux(357) s(6207) =< aux(360) s(6202) =< aux(361) s(6204) =< aux(361) s(6208) =< aux(362) s(6209) =< aux(363) s(6205) =< aux(364) s(6204) =< aux(365) s(6210) =< aux(358) s(6211) =< aux(358)+2 s(6212) =< aux(358)-2 s(6213) =< aux(358)+1 s(6214) =< aux(358)-1 s(6205) =< aux(359)*(1/5)+aux(364) s(6206) =< aux(359)*(1/5)+aux(364) s(6204) =< aux(359)*(3/7)+aux(365) s(6205) =< aux(359)*(3/7)+aux(365) s(6206) =< aux(359)*(3/7)+aux(365) s(6202) =< aux(359)*(1/3)+aux(361) s(6203) =< aux(359)*(1/3)+aux(361) s(6204) =< aux(359)*(1/3)+aux(361) s(6205) =< aux(359)*(1/3)+aux(361) s(6206) =< aux(359)*(1/3)+aux(361) s(6208) =< aux(359)*(1/8)+aux(362) s(6200) =< aux(359)*(1/8)+aux(362) s(6207) =< aux(359)*(1/4)+aux(360) s(6208) =< aux(359)*(1/4)+aux(360) s(6200) =< aux(359)*(1/4)+aux(360) s(6209) =< aux(359)*(5/16)+aux(363) s(6207) =< aux(359)*(5/16)+aux(363) s(6208) =< aux(359)*(5/16)+aux(363) s(6200) =< aux(359)*(5/16)+aux(363) s(6215) =< s(6206)*s(6210) s(6216) =< s(6206)*s(6210) s(6217) =< s(6206)*s(6211) s(6218) =< s(6205)*s(6211) s(6219) =< s(6204)*s(6212) s(6220) =< s(6204)*s(6213) s(6221) =< s(6202)*s(6214) s(6222) =< s(6208)*s(6214) s(6223) =< s(6207)*s(6214) s(6224) =< s(6209)*s(6210) s(6225) =< s(6216) s(6226) =< s(6217) s(6227) =< s(6218) s(6228) =< s(6220) s(6229) =< s(6228)*s(6213) s(6230) =< s(6222) s(6231) =< s(6223) s(6232) =< s(6224) s(6233) =< s(6232)*aux(358) s(6157) =< aux(348) s(6158) =< aux(348) s(6159) =< aux(348) s(6160) =< aux(348) s(6161) =< aux(348) s(6162) =< aux(348) s(6163) =< aux(348) s(6164) =< aux(351) s(6159) =< aux(352) s(6161) =< aux(352) s(6165) =< aux(353) s(6166) =< aux(354) s(6162) =< aux(355) s(6161) =< aux(356) s(6167) =< aux(349) s(6168) =< aux(349)+2 s(6169) =< aux(349)-2 s(6170) =< aux(349)+1 s(6171) =< aux(349)-1 s(6162) =< aux(350)*(1/5)+aux(355) s(6163) =< aux(350)*(1/5)+aux(355) s(6161) =< aux(350)*(3/7)+aux(356) s(6162) =< aux(350)*(3/7)+aux(356) s(6163) =< aux(350)*(3/7)+aux(356) s(6159) =< aux(350)*(1/3)+aux(352) s(6160) =< aux(350)*(1/3)+aux(352) s(6161) =< aux(350)*(1/3)+aux(352) s(6162) =< aux(350)*(1/3)+aux(352) s(6163) =< aux(350)*(1/3)+aux(352) s(6165) =< aux(350)*(1/8)+aux(353) s(6157) =< aux(350)*(1/8)+aux(353) s(6164) =< aux(350)*(1/4)+aux(351) s(6165) =< aux(350)*(1/4)+aux(351) s(6157) =< aux(350)*(1/4)+aux(351) s(6166) =< aux(350)*(5/16)+aux(354) s(6164) =< aux(350)*(5/16)+aux(354) s(6165) =< aux(350)*(5/16)+aux(354) s(6157) =< aux(350)*(5/16)+aux(354) s(6172) =< s(6163)*s(6167) s(6173) =< s(6163)*s(6167) s(6174) =< s(6163)*s(6168) s(6175) =< s(6162)*s(6168) s(6176) =< s(6161)*s(6169) s(6177) =< s(6161)*s(6170) s(6178) =< s(6159)*s(6171) s(6179) =< s(6165)*s(6171) s(6180) =< s(6164)*s(6171) s(6181) =< s(6166)*s(6167) s(6182) =< s(6173) s(6183) =< s(6174) s(6184) =< s(6175) s(6185) =< s(6177) s(6186) =< s(6185)*s(6170) s(6187) =< s(6179) s(6188) =< s(6180) s(6189) =< s(6181) s(6190) =< s(6189)*aux(349) s(6326) =< aux(358) with precondition: [V11=2,Out=1,V>=1,V2>=0] * Chain [72]: 1*s(6384)+2*s(6385)+1*s(6386)+1*s(6387)+7*s(6388)+7*s(6389)+3*s(6390)+9*s(6391)+5*s(6392)+9*s(6393)+1*s(6399)+1*s(6403)+1*s(6405)+2*s(6409)+2*s(6410)+14*s(6411)+18*s(6412)+2*s(6413)+6*s(6414)+14*s(6415)+18*s(6416)+2*s(6417)+1*s(6427)+2*s(6428)+1*s(6429)+1*s(6430)+7*s(6431)+7*s(6432)+3*s(6433)+9*s(6434)+5*s(6435)+9*s(6436)+1*s(6442)+1*s(6446)+1*s(6448)+2*s(6452)+2*s(6453)+14*s(6454)+18*s(6455)+2*s(6456)+6*s(6457)+14*s(6458)+18*s(6459)+2*s(6460)+10*s(6464)+8*s(6466)+2*s(6467)+9 Such that:s(6462) =< 2 s(6375) =< V s(6376) =< 2*V s(6377) =< 2*V+1 s(6378) =< V/2 s(6379) =< 2/3*V s(6380) =< 3/4*V s(6381) =< 3/8*V s(6382) =< 4/5*V s(6383) =< 4/7*V s(6418) =< V2 s(6420) =< 2*V2+1 s(6421) =< V2/2 s(6422) =< 2/3*V2 s(6423) =< 3/4*V2 s(6424) =< 3/8*V2 s(6425) =< 4/5*V2 s(6426) =< 4/7*V2 aux(366) =< 2*V2 s(6464) =< aux(366) s(6466) =< s(6462) s(6467) =< s(6464)*s(6462) s(6427) =< s(6418) s(6428) =< s(6418) s(6429) =< s(6418) s(6430) =< s(6418) s(6431) =< s(6418) s(6432) =< s(6418) s(6433) =< s(6418) s(6434) =< s(6421) s(6429) =< s(6422) s(6431) =< s(6422) s(6435) =< s(6423) s(6436) =< s(6424) s(6432) =< s(6425) s(6431) =< s(6426) s(6437) =< aux(366) s(6438) =< aux(366)+2 s(6439) =< aux(366)-2 s(6440) =< aux(366)+1 s(6441) =< aux(366)-1 s(6432) =< s(6420)*(1/5)+s(6425) s(6433) =< s(6420)*(1/5)+s(6425) s(6431) =< s(6420)*(3/7)+s(6426) s(6432) =< s(6420)*(3/7)+s(6426) s(6433) =< s(6420)*(3/7)+s(6426) s(6429) =< s(6420)*(1/3)+s(6422) s(6430) =< s(6420)*(1/3)+s(6422) s(6431) =< s(6420)*(1/3)+s(6422) s(6432) =< s(6420)*(1/3)+s(6422) s(6433) =< s(6420)*(1/3)+s(6422) s(6435) =< s(6420)*(1/8)+s(6423) s(6427) =< s(6420)*(1/8)+s(6423) s(6434) =< s(6420)*(1/4)+s(6421) s(6435) =< s(6420)*(1/4)+s(6421) s(6427) =< s(6420)*(1/4)+s(6421) s(6436) =< s(6420)*(5/16)+s(6424) s(6434) =< s(6420)*(5/16)+s(6424) s(6435) =< s(6420)*(5/16)+s(6424) s(6427) =< s(6420)*(5/16)+s(6424) s(6442) =< s(6433)*s(6437) s(6443) =< s(6433)*s(6437) s(6444) =< s(6433)*s(6438) s(6445) =< s(6432)*s(6438) s(6446) =< s(6431)*s(6439) s(6447) =< s(6431)*s(6440) s(6448) =< s(6429)*s(6441) s(6449) =< s(6435)*s(6441) s(6450) =< s(6434)*s(6441) s(6451) =< s(6436)*s(6437) s(6452) =< s(6443) s(6453) =< s(6444) s(6454) =< s(6445) s(6455) =< s(6447) s(6456) =< s(6455)*s(6440) s(6457) =< s(6449) s(6458) =< s(6450) s(6459) =< s(6451) s(6460) =< s(6459)*aux(366) s(6384) =< s(6375) s(6385) =< s(6375) s(6386) =< s(6375) s(6387) =< s(6375) s(6388) =< s(6375) s(6389) =< s(6375) s(6390) =< s(6375) s(6391) =< s(6378) s(6386) =< s(6379) s(6388) =< s(6379) s(6392) =< s(6380) s(6393) =< s(6381) s(6389) =< s(6382) s(6388) =< s(6383) s(6394) =< s(6376) s(6395) =< s(6376)+2 s(6396) =< s(6376)-2 s(6397) =< s(6376)+1 s(6398) =< s(6376)-1 s(6389) =< s(6377)*(1/5)+s(6382) s(6390) =< s(6377)*(1/5)+s(6382) s(6388) =< s(6377)*(3/7)+s(6383) s(6389) =< s(6377)*(3/7)+s(6383) s(6390) =< s(6377)*(3/7)+s(6383) s(6386) =< s(6377)*(1/3)+s(6379) s(6387) =< s(6377)*(1/3)+s(6379) s(6388) =< s(6377)*(1/3)+s(6379) s(6389) =< s(6377)*(1/3)+s(6379) s(6390) =< s(6377)*(1/3)+s(6379) s(6392) =< s(6377)*(1/8)+s(6380) s(6384) =< s(6377)*(1/8)+s(6380) s(6391) =< s(6377)*(1/4)+s(6378) s(6392) =< s(6377)*(1/4)+s(6378) s(6384) =< s(6377)*(1/4)+s(6378) s(6393) =< s(6377)*(5/16)+s(6381) s(6391) =< s(6377)*(5/16)+s(6381) s(6392) =< s(6377)*(5/16)+s(6381) s(6384) =< s(6377)*(5/16)+s(6381) s(6399) =< s(6390)*s(6394) s(6400) =< s(6390)*s(6394) s(6401) =< s(6390)*s(6395) s(6402) =< s(6389)*s(6395) s(6403) =< s(6388)*s(6396) s(6404) =< s(6388)*s(6397) s(6405) =< s(6386)*s(6398) s(6406) =< s(6392)*s(6398) s(6407) =< s(6391)*s(6398) s(6408) =< s(6393)*s(6394) s(6409) =< s(6400) s(6410) =< s(6401) s(6411) =< s(6402) s(6412) =< s(6404) s(6413) =< s(6412)*s(6397) s(6414) =< s(6406) s(6415) =< s(6407) s(6416) =< s(6408) s(6417) =< s(6416)*s(6376) with precondition: [V11=2,V>=1,Out>=2,2*V2>=Out+2] #### Cost of chains of start(V,V2,V11): * Chain [79]: 58*s(7133)+124*s(7136)+2*s(7148)+151*s(7151)+2*s(7166)+62*s(7176)+62*s(7178)+62*s(7179)+434*s(7180)+434*s(7181)+186*s(7182)+558*s(7183)+310*s(7184)+558*s(7185)+62*s(7191)+62*s(7195)+62*s(7197)+124*s(7201)+124*s(7202)+868*s(7203)+1116*s(7204)+124*s(7205)+372*s(7206)+868*s(7207)+1116*s(7208)+124*s(7209)+69*s(7358)+72*s(7359)+43*s(7360)+43*s(7362)+43*s(7363)+301*s(7364)+301*s(7365)+129*s(7366)+387*s(7367)+215*s(7368)+387*s(7369)+43*s(7375)+43*s(7379)+43*s(7381)+86*s(7385)+86*s(7386)+602*s(7387)+774*s(7388)+86*s(7389)+258*s(7390)+602*s(7391)+774*s(7392)+86*s(7393)+53*s(7428)+63*s(7516)+2*s(7787)+2*s(7788)+2*s(7789)+23*s(7817)+23*s(7819)+23*s(7820)+161*s(7821)+161*s(7822)+69*s(7823)+207*s(7824)+115*s(7825)+207*s(7826)+23*s(7832)+23*s(7836)+23*s(7838)+46*s(7842)+46*s(7843)+322*s(7844)+414*s(7845)+46*s(7846)+138*s(7847)+322*s(7848)+414*s(7849)+46*s(7850)+10*s(8035)+2*s(8273)+2*s(8275)+9 Such that:aux(426) =< 1 aux(427) =< 2 aux(428) =< V aux(429) =< 2*V aux(430) =< 2*V+1 aux(431) =< V/2 aux(432) =< 2/3*V aux(433) =< 3/4*V aux(434) =< 3/8*V aux(435) =< 4/5*V aux(436) =< 4/7*V aux(437) =< V2 aux(438) =< 2*V2 aux(439) =< 2*V2+1 aux(440) =< V2/2 aux(441) =< 2/3*V2 aux(442) =< 3/4*V2 aux(443) =< 3/8*V2 aux(444) =< 4/5*V2 aux(445) =< 4/7*V2 aux(446) =< V11 aux(447) =< 2*V11 aux(448) =< 2*V11+1 aux(449) =< V11/2 aux(450) =< 2/3*V11 aux(451) =< 3/4*V11 aux(452) =< 3/8*V11 aux(453) =< 4/5*V11 aux(454) =< 4/7*V11 s(7428) =< aux(426) s(7358) =< aux(427) s(7151) =< aux(428) s(7136) =< aux(437) s(7360) =< aux(437) s(7362) =< aux(437) s(7363) =< aux(437) s(7364) =< aux(437) s(7365) =< aux(437) s(7366) =< aux(437) s(7367) =< aux(440) s(7362) =< aux(441) s(7364) =< aux(441) s(7368) =< aux(442) s(7369) =< aux(443) s(7365) =< aux(444) s(7364) =< aux(445) s(7370) =< aux(438) s(7371) =< aux(438)+2 s(7372) =< aux(438)-2 s(7373) =< aux(438)+1 s(7374) =< aux(438)-1 s(7365) =< aux(439)*(1/5)+aux(444) s(7366) =< aux(439)*(1/5)+aux(444) s(7364) =< aux(439)*(3/7)+aux(445) s(7365) =< aux(439)*(3/7)+aux(445) s(7366) =< aux(439)*(3/7)+aux(445) s(7362) =< aux(439)*(1/3)+aux(441) s(7363) =< aux(439)*(1/3)+aux(441) s(7364) =< aux(439)*(1/3)+aux(441) s(7365) =< aux(439)*(1/3)+aux(441) s(7366) =< aux(439)*(1/3)+aux(441) s(7368) =< aux(439)*(1/8)+aux(442) s(7360) =< aux(439)*(1/8)+aux(442) s(7367) =< aux(439)*(1/4)+aux(440) s(7368) =< aux(439)*(1/4)+aux(440) s(7360) =< aux(439)*(1/4)+aux(440) s(7369) =< aux(439)*(5/16)+aux(443) s(7367) =< aux(439)*(5/16)+aux(443) s(7368) =< aux(439)*(5/16)+aux(443) s(7360) =< aux(439)*(5/16)+aux(443) s(7375) =< s(7366)*s(7370) s(7376) =< s(7366)*s(7370) s(7377) =< s(7366)*s(7371) s(7378) =< s(7365)*s(7371) s(7379) =< s(7364)*s(7372) s(7380) =< s(7364)*s(7373) s(7381) =< s(7362)*s(7374) s(7382) =< s(7368)*s(7374) s(7383) =< s(7367)*s(7374) s(7384) =< s(7369)*s(7370) s(7385) =< s(7376) s(7386) =< s(7377) s(7387) =< s(7378) s(7388) =< s(7380) s(7389) =< s(7388)*s(7373) s(7390) =< s(7382) s(7391) =< s(7383) s(7392) =< s(7384) s(7393) =< s(7392)*aux(438) s(7176) =< aux(428) s(7178) =< aux(428) s(7179) =< aux(428) s(7180) =< aux(428) s(7181) =< aux(428) s(7182) =< aux(428) s(7183) =< aux(431) s(7178) =< aux(432) s(7180) =< aux(432) s(7184) =< aux(433) s(7185) =< aux(434) s(7181) =< aux(435) s(7180) =< aux(436) s(7186) =< aux(429) s(7187) =< aux(429)+2 s(7188) =< aux(429)-2 s(7189) =< aux(429)+1 s(7190) =< aux(429)-1 s(7181) =< aux(430)*(1/5)+aux(435) s(7182) =< aux(430)*(1/5)+aux(435) s(7180) =< aux(430)*(3/7)+aux(436) s(7181) =< aux(430)*(3/7)+aux(436) s(7182) =< aux(430)*(3/7)+aux(436) s(7178) =< aux(430)*(1/3)+aux(432) s(7179) =< aux(430)*(1/3)+aux(432) s(7180) =< aux(430)*(1/3)+aux(432) s(7181) =< aux(430)*(1/3)+aux(432) s(7182) =< aux(430)*(1/3)+aux(432) s(7184) =< aux(430)*(1/8)+aux(433) s(7176) =< aux(430)*(1/8)+aux(433) s(7183) =< aux(430)*(1/4)+aux(431) s(7184) =< aux(430)*(1/4)+aux(431) s(7176) =< aux(430)*(1/4)+aux(431) s(7185) =< aux(430)*(5/16)+aux(434) s(7183) =< aux(430)*(5/16)+aux(434) s(7184) =< aux(430)*(5/16)+aux(434) s(7176) =< aux(430)*(5/16)+aux(434) s(7191) =< s(7182)*s(7186) s(7192) =< s(7182)*s(7186) s(7193) =< s(7182)*s(7187) s(7194) =< s(7181)*s(7187) s(7195) =< s(7180)*s(7188) s(7196) =< s(7180)*s(7189) s(7197) =< s(7178)*s(7190) s(7198) =< s(7184)*s(7190) s(7199) =< s(7183)*s(7190) s(7200) =< s(7185)*s(7186) s(7201) =< s(7192) s(7202) =< s(7193) s(7203) =< s(7194) s(7204) =< s(7196) s(7205) =< s(7204)*s(7189) s(7206) =< s(7198) s(7207) =< s(7199) s(7208) =< s(7200) s(7209) =< s(7208)*aux(429) s(7516) =< aux(429) s(7787) =< s(7516)*aux(429) s(7788) =< s(7428)*aux(426) s(7789) =< s(7516)*aux(427) s(8035) =< aux(447) s(7817) =< aux(446) s(7133) =< aux(446) s(7819) =< aux(446) s(7820) =< aux(446) s(7821) =< aux(446) s(7822) =< aux(446) s(7823) =< aux(446) s(7824) =< aux(449) s(7819) =< aux(450) s(7821) =< aux(450) s(7825) =< aux(451) s(7826) =< aux(452) s(7822) =< aux(453) s(7821) =< aux(454) s(7827) =< aux(447) s(7828) =< aux(447)+2 s(7829) =< aux(447)-2 s(7830) =< aux(447)+1 s(7831) =< aux(447)-1 s(7822) =< aux(448)*(1/5)+aux(453) s(7823) =< aux(448)*(1/5)+aux(453) s(7821) =< aux(448)*(3/7)+aux(454) s(7822) =< aux(448)*(3/7)+aux(454) s(7823) =< aux(448)*(3/7)+aux(454) s(7819) =< aux(448)*(1/3)+aux(450) s(7820) =< aux(448)*(1/3)+aux(450) s(7821) =< aux(448)*(1/3)+aux(450) s(7822) =< aux(448)*(1/3)+aux(450) s(7823) =< aux(448)*(1/3)+aux(450) s(7825) =< aux(448)*(1/8)+aux(451) s(7817) =< aux(448)*(1/8)+aux(451) s(7824) =< aux(448)*(1/4)+aux(449) s(7825) =< aux(448)*(1/4)+aux(449) s(7817) =< aux(448)*(1/4)+aux(449) s(7826) =< aux(448)*(5/16)+aux(452) s(7824) =< aux(448)*(5/16)+aux(452) s(7825) =< aux(448)*(5/16)+aux(452) s(7817) =< aux(448)*(5/16)+aux(452) s(7832) =< s(7823)*s(7827) s(7833) =< s(7823)*s(7827) s(7834) =< s(7823)*s(7828) s(7835) =< s(7822)*s(7828) s(7836) =< s(7821)*s(7829) s(7837) =< s(7821)*s(7830) s(7838) =< s(7819)*s(7831) s(7839) =< s(7825)*s(7831) s(7840) =< s(7824)*s(7831) s(7841) =< s(7826)*s(7827) s(7842) =< s(7833) s(7843) =< s(7834) s(7844) =< s(7835) s(7845) =< s(7837) s(7846) =< s(7845)*s(7830) s(7847) =< s(7839) s(7848) =< s(7840) s(7849) =< s(7841) s(7850) =< s(7849)*aux(447) s(7359) =< aux(438) s(8273) =< s(7359)*aux(438) s(8275) =< s(7359)*aux(427) s(7166) =< s(7151)*aux(437) s(7148) =< s(7136)*aux(446) with precondition: [] Closed-form bounds of start(V,V2,V11): ------------------------------------- * Chain [79] with precondition: [] - Upper bound: nat(V)*4615+202+nat(V)*2*nat(V2)+nat(V)*62*nat(nat(2*V)+ -2)+nat(V)*62*nat(nat(2*V)+ -1)+nat(V)*2542*nat(2*V)+nat(V)*124*nat(2*V)*nat(2*V)+nat(V2)*3220+nat(V2)*2*nat(V11)+nat(V2)*43*nat(nat(2*V2)+ -2)+nat(V2)*43*nat(nat(2*V2)+ -1)+nat(V2)*1763*nat(2*V2)+nat(V2)*86*nat(2*V2)*nat(2*V2)+nat(V11)*1714+nat(V11)*23*nat(nat(2*V11)+ -2)+nat(V11)*23*nat(nat(2*V11)+ -1)+nat(V11)*943*nat(2*V11)+nat(V11)*46*nat(2*V11)*nat(2*V11)+nat(nat(2*V)+ -1)*372*nat(3/4*V)+nat(nat(2*V)+ -1)*868*nat(V/2)+nat(nat(2*V2)+ -1)*258*nat(3/4*V2)+nat(nat(2*V2)+ -1)*602*nat(V2/2)+nat(nat(2*V11)+ -1)*138*nat(3/4*V11)+nat(nat(2*V11)+ -1)*322*nat(V11/2)+nat(2*V)*67+nat(2*V)*2*nat(2*V)+nat(2*V)*124*nat(2*V)*nat(3/8*V)+nat(2*V)*1116*nat(3/8*V)+nat(2*V2)*76+nat(2*V2)*2*nat(2*V2)+nat(2*V2)*86*nat(2*V2)*nat(3/8*V2)+nat(2*V2)*774*nat(3/8*V2)+nat(2*V11)*10+nat(2*V11)*46*nat(2*V11)*nat(3/8*V11)+nat(2*V11)*414*nat(3/8*V11)+nat(3/4*V)*310+nat(3/4*V2)*215+nat(3/4*V11)*115+nat(3/8*V)*558+nat(3/8*V2)*387+nat(3/8*V11)*207+nat(V/2)*558+nat(V2/2)*387+nat(V11/2)*207 - Complexity: n^3 ### Maximum cost of start(V,V2,V11): nat(V)*4615+202+nat(V)*2*nat(V2)+nat(V)*62*nat(nat(2*V)+ -2)+nat(V)*62*nat(nat(2*V)+ -1)+nat(V)*2542*nat(2*V)+nat(V)*124*nat(2*V)*nat(2*V)+nat(V2)*3220+nat(V2)*2*nat(V11)+nat(V2)*43*nat(nat(2*V2)+ -2)+nat(V2)*43*nat(nat(2*V2)+ -1)+nat(V2)*1763*nat(2*V2)+nat(V2)*86*nat(2*V2)*nat(2*V2)+nat(V11)*1714+nat(V11)*23*nat(nat(2*V11)+ -2)+nat(V11)*23*nat(nat(2*V11)+ -1)+nat(V11)*943*nat(2*V11)+nat(V11)*46*nat(2*V11)*nat(2*V11)+nat(nat(2*V)+ -1)*372*nat(3/4*V)+nat(nat(2*V)+ -1)*868*nat(V/2)+nat(nat(2*V2)+ -1)*258*nat(3/4*V2)+nat(nat(2*V2)+ -1)*602*nat(V2/2)+nat(nat(2*V11)+ -1)*138*nat(3/4*V11)+nat(nat(2*V11)+ -1)*322*nat(V11/2)+nat(2*V)*67+nat(2*V)*2*nat(2*V)+nat(2*V)*124*nat(2*V)*nat(3/8*V)+nat(2*V)*1116*nat(3/8*V)+nat(2*V2)*76+nat(2*V2)*2*nat(2*V2)+nat(2*V2)*86*nat(2*V2)*nat(3/8*V2)+nat(2*V2)*774*nat(3/8*V2)+nat(2*V11)*10+nat(2*V11)*46*nat(2*V11)*nat(3/8*V11)+nat(2*V11)*414*nat(3/8*V11)+nat(3/4*V)*310+nat(3/4*V2)*215+nat(3/4*V11)*115+nat(3/8*V)*558+nat(3/8*V2)*387+nat(3/8*V11)*207+nat(V/2)*558+nat(V2/2)*387+nat(V11/2)*207 Asymptotic class: n^3 * Total analysis performed in 30018 ms. ---------------------------------------- (14) BOUNDS(1, n^3) ---------------------------------------- (15) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (16) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: p(0') -> 0' p(s(x)) -> x le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) minus(x, y) -> if(le(x, y), x, y) if(true, x, y) -> 0' if(false, x, y) -> s(minus(p(x), y)) The (relative) TRS S consists of the following rules: encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) Rewrite Strategy: INNERMOST ---------------------------------------- (17) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (18) Obligation: Innermost TRS: Rules: p(0') -> 0' p(s(x)) -> x le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) minus(x, y) -> if(le(x, y), x, y) if(true, x, y) -> 0' if(false, x, y) -> s(minus(p(x), y)) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) Types: p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if 0' :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encArg :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_0 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if hole_0':s:true:false:cons_p:cons_le:cons_minus:cons_if1_4 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4 :: Nat -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if ---------------------------------------- (19) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: le, minus, if, encArg They will be analysed ascendingly in the following order: le < minus le < encArg minus = if minus < encArg if < encArg ---------------------------------------- (20) Obligation: Innermost TRS: Rules: p(0') -> 0' p(s(x)) -> x le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) minus(x, y) -> if(le(x, y), x, y) if(true, x, y) -> 0' if(false, x, y) -> s(minus(p(x), y)) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) Types: p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if 0' :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encArg :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_0 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if hole_0':s:true:false:cons_p:cons_le:cons_minus:cons_if1_4 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4 :: Nat -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if Generator Equations: gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(0) <=> 0' gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(+(x, 1)) <=> s(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(x)) The following defined symbols remain to be analysed: le, minus, if, encArg They will be analysed ascendingly in the following order: le < minus le < encArg minus = if minus < encArg if < encArg ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: le(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n4_4), gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n4_4)) -> true, rt in Omega(1 + n4_4) Induction Base: le(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(0), gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(0)) ->_R^Omega(1) true Induction Step: le(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(+(n4_4, 1)), gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(+(n4_4, 1))) ->_R^Omega(1) le(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n4_4), gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n4_4)) ->_IH true We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (22) Complex Obligation (BEST) ---------------------------------------- (23) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: p(0') -> 0' p(s(x)) -> x le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) minus(x, y) -> if(le(x, y), x, y) if(true, x, y) -> 0' if(false, x, y) -> s(minus(p(x), y)) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) Types: p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if 0' :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encArg :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_0 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if hole_0':s:true:false:cons_p:cons_le:cons_minus:cons_if1_4 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4 :: Nat -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if Generator Equations: gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(0) <=> 0' gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(+(x, 1)) <=> s(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(x)) The following defined symbols remain to be analysed: le, minus, if, encArg They will be analysed ascendingly in the following order: le < minus le < encArg minus = if minus < encArg if < encArg ---------------------------------------- (24) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (25) BOUNDS(n^1, INF) ---------------------------------------- (26) Obligation: Innermost TRS: Rules: p(0') -> 0' p(s(x)) -> x le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) minus(x, y) -> if(le(x, y), x, y) if(true, x, y) -> 0' if(false, x, y) -> s(minus(p(x), y)) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) Types: p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if 0' :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encArg :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_0 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if hole_0':s:true:false:cons_p:cons_le:cons_minus:cons_if1_4 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4 :: Nat -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if Lemmas: le(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n4_4), gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n4_4)) -> true, rt in Omega(1 + n4_4) Generator Equations: gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(0) <=> 0' gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(+(x, 1)) <=> s(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(x)) The following defined symbols remain to be analysed: if, minus, encArg They will be analysed ascendingly in the following order: minus = if minus < encArg if < encArg ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n536_4)) -> gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n536_4), rt in Omega(0) Induction Base: encArg(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(0)) ->_R^Omega(0) 0' Induction Step: encArg(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(+(n536_4, 1))) ->_R^Omega(0) s(encArg(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n536_4))) ->_IH s(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(c537_4)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (28) BOUNDS(1, INF)