/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3).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), 197 ms] (4) CpxRelTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxWeightedTrs (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxTypedWeightedTrs (11) CompletionProof [UPPER BOUND(ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) CompleteCoflocoProof [FINISHED, 34.3 s] (16) BOUNDS(1, n^3) (17) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRelTRS (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (20) typed CpxTrs (21) OrderProof [LOWER BOUND(ID), 0 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 247 ms] (24) BEST (25) proven lower bound (26) LowerBoundPropagationProof [FINISHED, 0 ms] (27) BOUNDS(n^1, INF) (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 48 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 130 ms] (32) 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: leq(0, y) -> true leq(s(x), 0) -> false leq(s(x), s(y)) -> leq(x, y) if(true, x, y) -> x if(false, x, y) -> y -(x, 0) -> x -(s(x), s(y)) -> -(x, y) mod(0, y) -> 0 mod(s(x), 0) -> 0 mod(s(x), s(y)) -> if(leq(y, x), mod(-(s(x), s(y)), s(y)), s(x)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_leq(x_1, x_2)) -> leq(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)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_mod(x_1, x_2)) -> mod(encArg(x_1), encArg(x_2)) encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_mod(x_1, x_2) -> mod(encArg(x_1), encArg(x_2)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: leq(0, y) -> true leq(s(x), 0) -> false leq(s(x), s(y)) -> leq(x, y) if(true, x, y) -> x if(false, x, y) -> y -(x, 0) -> x -(s(x), s(y)) -> -(x, y) mod(0, y) -> 0 mod(s(x), 0) -> 0 mod(s(x), s(y)) -> if(leq(y, x), mod(-(s(x), s(y)), s(y)), s(x)) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_leq(x_1, x_2)) -> leq(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)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_mod(x_1, x_2)) -> mod(encArg(x_1), encArg(x_2)) encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_mod(x_1, x_2) -> mod(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: leq(0, y) -> true leq(s(x), 0) -> false leq(s(x), s(y)) -> leq(x, y) if(true, x, y) -> x if(false, x, y) -> y -(x, 0) -> x -(s(x), s(y)) -> -(x, y) mod(0, y) -> 0 mod(s(x), 0) -> 0 mod(s(x), s(y)) -> if(leq(y, x), mod(-(s(x), s(y)), s(y)), s(x)) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_leq(x_1, x_2)) -> leq(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)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_mod(x_1, x_2)) -> mod(encArg(x_1), encArg(x_2)) encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_mod(x_1, x_2) -> mod(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). The TRS R consists of the following rules: leq(0, y) -> true [1] leq(s(x), 0) -> false [1] leq(s(x), s(y)) -> leq(x, y) [1] if(true, x, y) -> x [1] if(false, x, y) -> y [1] -(x, 0) -> x [1] -(s(x), s(y)) -> -(x, y) [1] mod(0, y) -> 0 [1] mod(s(x), 0) -> 0 [1] mod(s(x), s(y)) -> if(leq(y, x), mod(-(s(x), s(y)), s(y)), s(x)) [1] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(false) -> false [0] encArg(cons_leq(x_1, x_2)) -> leq(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] encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) [0] encArg(cons_mod(x_1, x_2)) -> mod(encArg(x_1), encArg(x_2)) [0] encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_false -> false [0] encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) [0] encode_mod(x_1, x_2) -> mod(encArg(x_1), encArg(x_2)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (7) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) Renamed defined symbols to avoid conflicts with arithmetic symbols: - => minus ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). The TRS R consists of the following rules: leq(0, y) -> true [1] leq(s(x), 0) -> false [1] leq(s(x), s(y)) -> leq(x, y) [1] if(true, x, y) -> x [1] if(false, x, y) -> y [1] minus(x, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] mod(0, y) -> 0 [1] mod(s(x), 0) -> 0 [1] mod(s(x), s(y)) -> if(leq(y, x), mod(minus(s(x), s(y)), s(y)), s(x)) [1] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(false) -> false [0] encArg(cons_leq(x_1, x_2)) -> leq(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] encArg(cons_-(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_mod(x_1, x_2)) -> mod(encArg(x_1), encArg(x_2)) [0] encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_false -> false [0] encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_-(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_mod(x_1, x_2) -> mod(encArg(x_1), encArg(x_2)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: leq(0, y) -> true [1] leq(s(x), 0) -> false [1] leq(s(x), s(y)) -> leq(x, y) [1] if(true, x, y) -> x [1] if(false, x, y) -> y [1] minus(x, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] mod(0, y) -> 0 [1] mod(s(x), 0) -> 0 [1] mod(s(x), s(y)) -> if(leq(y, x), mod(minus(s(x), s(y)), s(y)), s(x)) [1] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(false) -> false [0] encArg(cons_leq(x_1, x_2)) -> leq(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] encArg(cons_-(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_mod(x_1, x_2)) -> mod(encArg(x_1), encArg(x_2)) [0] encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_false -> false [0] encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_-(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_mod(x_1, x_2) -> mod(encArg(x_1), encArg(x_2)) [0] The TRS has the following type information: leq :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod 0 :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod true :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod s :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod false :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod if :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod minus :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod mod :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod encArg :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_leq :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_if :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_- :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_mod :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_leq :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_0 :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_true :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_s :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_false :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_if :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_- :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_mod :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod Rewrite Strategy: INNERMOST ---------------------------------------- (11) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: encArg(v0) -> null_encArg [0] encode_leq(v0, v1) -> null_encode_leq [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s(v0) -> null_encode_s [0] encode_false -> null_encode_false [0] encode_if(v0, v1, v2) -> null_encode_if [0] encode_-(v0, v1) -> null_encode_- [0] encode_mod(v0, v1) -> null_encode_mod [0] leq(v0, v1) -> null_leq [0] if(v0, v1, v2) -> null_if [0] minus(v0, v1) -> null_minus [0] mod(v0, v1) -> null_mod [0] And the following fresh constants: null_encArg, null_encode_leq, null_encode_0, null_encode_true, null_encode_s, null_encode_false, null_encode_if, null_encode_-, null_encode_mod, null_leq, null_if, null_minus, null_mod ---------------------------------------- (12) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: leq(0, y) -> true [1] leq(s(x), 0) -> false [1] leq(s(x), s(y)) -> leq(x, y) [1] if(true, x, y) -> x [1] if(false, x, y) -> y [1] minus(x, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] mod(0, y) -> 0 [1] mod(s(x), 0) -> 0 [1] mod(s(x), s(y)) -> if(leq(y, x), mod(minus(s(x), s(y)), s(y)), s(x)) [1] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(false) -> false [0] encArg(cons_leq(x_1, x_2)) -> leq(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] encArg(cons_-(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_mod(x_1, x_2)) -> mod(encArg(x_1), encArg(x_2)) [0] encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_false -> false [0] encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_-(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_mod(x_1, x_2) -> mod(encArg(x_1), encArg(x_2)) [0] encArg(v0) -> null_encArg [0] encode_leq(v0, v1) -> null_encode_leq [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s(v0) -> null_encode_s [0] encode_false -> null_encode_false [0] encode_if(v0, v1, v2) -> null_encode_if [0] encode_-(v0, v1) -> null_encode_- [0] encode_mod(v0, v1) -> null_encode_mod [0] leq(v0, v1) -> null_leq [0] if(v0, v1, v2) -> null_if [0] minus(v0, v1) -> null_minus [0] mod(v0, v1) -> null_mod [0] The TRS has the following type information: leq :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod 0 :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod true :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod s :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod false :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod if :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod minus :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod mod :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod encArg :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod cons_leq :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod cons_if :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod cons_- :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod cons_mod :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod encode_leq :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod encode_0 :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod encode_true :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod encode_s :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod encode_false :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod encode_if :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod encode_- :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod encode_mod :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod -> 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod null_encArg :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod null_encode_leq :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod null_encode_0 :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod null_encode_true :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod null_encode_s :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod null_encode_false :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod null_encode_if :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod null_encode_- :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod null_encode_mod :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod null_leq :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod null_if :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod null_minus :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod null_mod :: 0:true:s:false:cons_leq:cons_if:cons_-:cons_mod:null_encArg:null_encode_leq:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_if:null_encode_-:null_encode_mod:null_leq:null_if:null_minus:null_mod Rewrite Strategy: INNERMOST ---------------------------------------- (13) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 true => 2 false => 1 null_encArg => 0 null_encode_leq => 0 null_encode_0 => 0 null_encode_true => 0 null_encode_s => 0 null_encode_false => 0 null_encode_if => 0 null_encode_- => 0 null_encode_mod => 0 null_leq => 0 null_if => 0 null_minus => 0 null_mod => 0 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: encArg(z) -{ 0 }-> mod(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 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 }-> leq(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_-(z, z') -{ 0 }-> minus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_-(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_0 -{ 0 }-> 0 :|: encode_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_leq(z, z') -{ 0 }-> leq(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_leq(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_mod(z, z') -{ 0 }-> mod(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_mod(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_s(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 encode_true -{ 0 }-> 2 :|: encode_true -{ 0 }-> 0 :|: if(z, z', z'') -{ 1 }-> x :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0 if(z, z', z'') -{ 1 }-> y :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0 if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 leq(z, z') -{ 1 }-> leq(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x leq(z, z') -{ 1 }-> 2 :|: y >= 0, z = 0, z' = y leq(z, z') -{ 1 }-> 1 :|: x >= 0, z = 1 + x, z' = 0 leq(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 minus(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0 minus(z, z') -{ 1 }-> minus(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 mod(z, z') -{ 1 }-> if(leq(y, x), mod(minus(1 + x, 1 + y), 1 + y), 1 + x) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x mod(z, z') -{ 1 }-> 0 :|: y >= 0, z = 0, z' = y mod(z, z') -{ 1 }-> 0 :|: x >= 0, z = 1 + x, z' = 0 mod(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (15) CompleteCoflocoProof (FINISHED) Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: eq(start(V1, V, V8),0,[leq(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V8),0,[if(V1, V, V8, Out)],[V1 >= 0,V >= 0,V8 >= 0]). eq(start(V1, V, V8),0,[minus(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V8),0,[mod(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V8),0,[encArg(V1, Out)],[V1 >= 0]). eq(start(V1, V, V8),0,[fun(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V8),0,[fun1(Out)],[]). eq(start(V1, V, V8),0,[fun2(Out)],[]). eq(start(V1, V, V8),0,[fun3(V1, Out)],[V1 >= 0]). eq(start(V1, V, V8),0,[fun4(Out)],[]). eq(start(V1, V, V8),0,[fun5(V1, V, V8, Out)],[V1 >= 0,V >= 0,V8 >= 0]). eq(start(V1, V, V8),0,[fun6(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V8),0,[fun7(V1, V, Out)],[V1 >= 0,V >= 0]). eq(leq(V1, V, Out),1,[],[Out = 2,V2 >= 0,V1 = 0,V = V2]). eq(leq(V1, V, Out),1,[],[Out = 1,V3 >= 0,V1 = 1 + V3,V = 0]). eq(leq(V1, V, Out),1,[leq(V4, V5, Ret)],[Out = Ret,V = 1 + V5,V4 >= 0,V5 >= 0,V1 = 1 + V4]). eq(if(V1, V, V8, Out),1,[],[Out = V7,V1 = 2,V = V7,V8 = V6,V7 >= 0,V6 >= 0]). eq(if(V1, V, V8, Out),1,[],[Out = V10,V = V9,V8 = V10,V1 = 1,V9 >= 0,V10 >= 0]). eq(minus(V1, V, Out),1,[],[Out = V11,V11 >= 0,V1 = V11,V = 0]). eq(minus(V1, V, Out),1,[minus(V13, V12, Ret1)],[Out = Ret1,V = 1 + V12,V13 >= 0,V12 >= 0,V1 = 1 + V13]). eq(mod(V1, V, Out),1,[],[Out = 0,V14 >= 0,V1 = 0,V = V14]). eq(mod(V1, V, Out),1,[],[Out = 0,V15 >= 0,V1 = 1 + V15,V = 0]). eq(mod(V1, V, Out),1,[leq(V17, V16, Ret0),minus(1 + V16, 1 + V17, Ret10),mod(Ret10, 1 + V17, Ret11),if(Ret0, Ret11, 1 + V16, Ret2)],[Out = Ret2,V = 1 + V17,V16 >= 0,V17 >= 0,V1 = 1 + V16]). eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]). eq(encArg(V1, Out),0,[],[Out = 2,V1 = 2]). eq(encArg(V1, Out),0,[encArg(V18, Ret12)],[Out = 1 + Ret12,V1 = 1 + V18,V18 >= 0]). eq(encArg(V1, Out),0,[],[Out = 1,V1 = 1]). eq(encArg(V1, Out),0,[encArg(V19, Ret01),encArg(V20, Ret13),leq(Ret01, Ret13, Ret3)],[Out = Ret3,V19 >= 0,V1 = 1 + V19 + V20,V20 >= 0]). eq(encArg(V1, Out),0,[encArg(V22, Ret02),encArg(V23, Ret14),encArg(V21, Ret21),if(Ret02, Ret14, Ret21, Ret4)],[Out = Ret4,V22 >= 0,V1 = 1 + V21 + V22 + V23,V21 >= 0,V23 >= 0]). eq(encArg(V1, Out),0,[encArg(V25, Ret03),encArg(V24, Ret15),minus(Ret03, Ret15, Ret5)],[Out = Ret5,V25 >= 0,V1 = 1 + V24 + V25,V24 >= 0]). eq(encArg(V1, Out),0,[encArg(V27, Ret04),encArg(V26, Ret16),mod(Ret04, Ret16, Ret6)],[Out = Ret6,V27 >= 0,V1 = 1 + V26 + V27,V26 >= 0]). eq(fun(V1, V, Out),0,[encArg(V28, Ret05),encArg(V29, Ret17),leq(Ret05, Ret17, Ret7)],[Out = Ret7,V28 >= 0,V29 >= 0,V1 = V28,V = V29]). eq(fun1(Out),0,[],[Out = 0]). eq(fun2(Out),0,[],[Out = 2]). eq(fun3(V1, Out),0,[encArg(V30, Ret18)],[Out = 1 + Ret18,V30 >= 0,V1 = V30]). eq(fun4(Out),0,[],[Out = 1]). eq(fun5(V1, V, V8, Out),0,[encArg(V33, Ret06),encArg(V32, Ret19),encArg(V31, Ret22),if(Ret06, Ret19, Ret22, Ret8)],[Out = Ret8,V33 >= 0,V31 >= 0,V32 >= 0,V1 = V33,V = V32,V8 = V31]). eq(fun6(V1, V, Out),0,[encArg(V35, Ret07),encArg(V34, Ret110),minus(Ret07, Ret110, Ret9)],[Out = Ret9,V35 >= 0,V34 >= 0,V1 = V35,V = V34]). eq(fun7(V1, V, Out),0,[encArg(V36, Ret08),encArg(V37, Ret111),mod(Ret08, Ret111, Ret20)],[Out = Ret20,V36 >= 0,V37 >= 0,V1 = V36,V = V37]). eq(encArg(V1, Out),0,[],[Out = 0,V38 >= 0,V1 = V38]). eq(fun(V1, V, Out),0,[],[Out = 0,V40 >= 0,V39 >= 0,V1 = V40,V = V39]). eq(fun2(Out),0,[],[Out = 0]). eq(fun3(V1, Out),0,[],[Out = 0,V41 >= 0,V1 = V41]). eq(fun4(Out),0,[],[Out = 0]). eq(fun5(V1, V, V8, Out),0,[],[Out = 0,V42 >= 0,V8 = V44,V43 >= 0,V1 = V42,V = V43,V44 >= 0]). eq(fun6(V1, V, Out),0,[],[Out = 0,V45 >= 0,V46 >= 0,V1 = V45,V = V46]). eq(fun7(V1, V, Out),0,[],[Out = 0,V47 >= 0,V48 >= 0,V1 = V47,V = V48]). eq(leq(V1, V, Out),0,[],[Out = 0,V50 >= 0,V49 >= 0,V1 = V50,V = V49]). eq(if(V1, V, V8, Out),0,[],[Out = 0,V51 >= 0,V8 = V53,V52 >= 0,V1 = V51,V = V52,V53 >= 0]). eq(minus(V1, V, Out),0,[],[Out = 0,V54 >= 0,V55 >= 0,V1 = V54,V = V55]). eq(mod(V1, V, Out),0,[],[Out = 0,V56 >= 0,V57 >= 0,V1 = V56,V = V57]). input_output_vars(leq(V1,V,Out),[V1,V],[Out]). input_output_vars(if(V1,V,V8,Out),[V1,V,V8],[Out]). input_output_vars(minus(V1,V,Out),[V1,V],[Out]). input_output_vars(mod(V1,V,Out),[V1,V],[Out]). input_output_vars(encArg(V1,Out),[V1],[Out]). input_output_vars(fun(V1,V,Out),[V1,V],[Out]). input_output_vars(fun1(Out),[],[Out]). input_output_vars(fun2(Out),[],[Out]). input_output_vars(fun3(V1,Out),[V1],[Out]). input_output_vars(fun4(Out),[],[Out]). input_output_vars(fun5(V1,V,V8,Out),[V1,V,V8],[Out]). input_output_vars(fun6(V1,V,Out),[V1,V],[Out]). input_output_vars(fun7(V1,V,Out),[V1,V],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. non_recursive : [if/4] 1. recursive : [leq/3] 2. recursive : [minus/3] 3. recursive [non_tail] : [(mod)/3] 4. recursive [non_tail,multiple] : [encArg/2] 5. non_recursive : [fun/3] 6. non_recursive : [fun1/1] 7. non_recursive : [fun2/1] 8. non_recursive : [fun3/2] 9. non_recursive : [fun4/1] 10. non_recursive : [fun5/4] 11. non_recursive : [fun6/3] 12. non_recursive : [fun7/3] 13. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into if/4 1. SCC is partially evaluated into leq/3 2. SCC is partially evaluated into minus/3 3. SCC is partially evaluated into (mod)/3 4. SCC is partially evaluated into encArg/2 5. SCC is partially evaluated into fun/3 6. SCC is completely evaluated into other SCCs 7. SCC is partially evaluated into fun2/1 8. SCC is partially evaluated into fun3/2 9. SCC is partially evaluated into fun4/1 10. SCC is partially evaluated into fun5/4 11. SCC is partially evaluated into fun6/3 12. SCC is partially evaluated into fun7/3 13. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations if/4 * CE 20 is refined into CE [50] * CE 18 is refined into CE [51] * CE 19 is refined into CE [52] ### Cost equations --> "Loop" of if/4 * CEs [50] --> Loop 30 * CEs [51] --> Loop 31 * CEs [52] --> Loop 32 ### Ranking functions of CR if(V1,V,V8,Out) #### Partial ranking functions of CR if(V1,V,V8,Out) ### Specialization of cost equations leq/3 * CE 17 is refined into CE [53] * CE 15 is refined into CE [54] * CE 14 is refined into CE [55] * CE 16 is refined into CE [56] ### Cost equations --> "Loop" of leq/3 * CEs [56] --> Loop 33 * CEs [53] --> Loop 34 * CEs [54] --> Loop 35 * CEs [55] --> Loop 36 ### Ranking functions of CR leq(V1,V,Out) * RF of phase [33]: [V,V1] #### Partial ranking functions of CR leq(V1,V,Out) * Partial RF of phase [33]: - RF of loop [33:1]: V V1 ### Specialization of cost equations minus/3 * CE 23 is refined into CE [57] * CE 21 is refined into CE [58] * CE 22 is refined into CE [59] ### Cost equations --> "Loop" of minus/3 * CEs [59] --> Loop 37 * CEs [57] --> Loop 38 * CEs [58] --> Loop 39 ### Ranking functions of CR minus(V1,V,Out) * RF of phase [37]: [V,V1] #### Partial ranking functions of CR minus(V1,V,Out) * Partial RF of phase [37]: - RF of loop [37:1]: V V1 ### Specialization of cost equations (mod)/3 * CE 25 is refined into CE [60] * CE 24 is refined into CE [61] * CE 27 is refined into CE [62] * CE 26 is refined into CE [63,64,65,66,67,68,69,70,71,72,73,74,75,76] ### Cost equations --> "Loop" of (mod)/3 * CEs [75] --> Loop 40 * CEs [73] --> Loop 41 * CEs [71] --> Loop 42 * CEs [65] --> Loop 43 * CEs [63] --> Loop 44 * CEs [66,70,76] --> Loop 45 * CEs [64] --> Loop 46 * CEs [67] --> Loop 47 * CEs [68,69,72,74] --> Loop 48 * CEs [60] --> Loop 49 * CEs [61,62] --> Loop 50 ### Ranking functions of CR mod(V1,V,Out) * RF of phase [40,43,45]: [V1,V1-V+1] #### Partial ranking functions of CR mod(V1,V,Out) * Partial RF of phase [40,43,45]: - RF of loop [40:1]: V1-1 - RF of loop [40:1,45:1]: V1-V+1 - RF of loop [43:1,45:1]: V1 ### Specialization of cost equations encArg/2 * CE 28 is refined into CE [77] * CE 29 is refined into CE [78] * CE 31 is refined into CE [79] * CE 32 is refined into CE [80,81,82,83,84] * CE 34 is refined into CE [85,86,87] * CE 35 is refined into CE [88,89,90,91,92,93] * CE 33 is refined into CE [94,95,96] * CE 30 is refined into CE [97] ### Cost equations --> "Loop" of encArg/2 * CEs [97] --> Loop 51 * CEs [95] --> Loop 52 * CEs [94] --> Loop 53 * CEs [96] --> Loop 54 * CEs [93] --> Loop 55 * CEs [92] --> Loop 56 * CEs [87] --> Loop 57 * CEs [91] --> Loop 58 * CEs [85] --> Loop 59 * CEs [84] --> Loop 60 * CEs [80] --> Loop 61 * CEs [83] --> Loop 62 * CEs [81] --> Loop 63 * CEs [88] --> Loop 64 * CEs [82,86,89,90] --> Loop 65 * CEs [77] --> Loop 66 * CEs [78] --> Loop 67 * CEs [79] --> Loop 68 ### Ranking functions of CR encArg(V1,Out) * RF of phase [51,52,53,54,55,56,57,58,59,60,61,62,63,64,65]: [V1] #### Partial ranking functions of CR encArg(V1,Out) * Partial RF of phase [51,52,53,54,55,56,57,58,59,60,61,62,63,64,65]: - RF of loop [51:1,52:1,52:2,52:3,53:1,53:2,53:3,54:1,54:2,54:3,55:1,55:2,56:1,56:2,57:1,57:2,58:1,58:2,59:1,59:2,60:1,60:2,61:1,61:2,62:1,62:2,63:1,63:2,64:1,64:2,65:1,65:2]: V1 ### Specialization of cost equations fun/3 * CE 36 is refined into CE [98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123] * CE 37 is refined into CE [124] ### Cost equations --> "Loop" of fun/3 * CEs [103,106,120] --> Loop 69 * CEs [105] --> Loop 70 * CEs [104,121] --> Loop 71 * CEs [99,101,108,110,112,116] --> Loop 72 * CEs [98,102,107,113,115,118,122] --> Loop 73 * CEs [100,109,111,114,117,119,123,124] --> Loop 74 ### Ranking functions of CR fun(V1,V,Out) #### Partial ranking functions of CR fun(V1,V,Out) ### Specialization of cost equations fun2/1 * CE 38 is refined into CE [125] * CE 39 is refined into CE [126] ### Cost equations --> "Loop" of fun2/1 * CEs [125] --> Loop 75 * CEs [126] --> Loop 76 ### Ranking functions of CR fun2(Out) #### Partial ranking functions of CR fun2(Out) ### Specialization of cost equations fun3/2 * CE 40 is refined into CE [127,128,129] * CE 41 is refined into CE [130] ### Cost equations --> "Loop" of fun3/2 * CEs [129] --> Loop 77 * CEs [130] --> Loop 78 * CEs [127,128] --> Loop 79 ### Ranking functions of CR fun3(V1,Out) #### Partial ranking functions of CR fun3(V1,Out) ### Specialization of cost equations fun4/1 * CE 42 is refined into CE [131] * CE 43 is refined into CE [132] ### Cost equations --> "Loop" of fun4/1 * CEs [131] --> Loop 80 * CEs [132] --> Loop 81 ### Ranking functions of CR fun4(Out) #### Partial ranking functions of CR fun4(Out) ### Specialization of cost equations fun5/4 * CE 44 is refined into CE [133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186] * CE 45 is refined into CE [187] ### Cost equations --> "Loop" of fun5/4 * CEs [136,154] --> Loop 82 * CEs [133,142,151] --> Loop 83 * CEs [143,145,146,149] --> Loop 84 * CEs [144,147,148,150,181,182,183] --> Loop 85 * CEs [137,162] --> Loop 86 * CEs [138,155,156,163,174,175,179,185] --> Loop 87 * CEs [134,140,160,164,166,168,170] --> Loop 88 * CEs [135,139,141,152,153,157,158,159,161,165,167,169,171,172,173,176,177,178,180,184,186,187] --> Loop 89 ### Ranking functions of CR fun5(V1,V,V8,Out) #### Partial ranking functions of CR fun5(V1,V,V8,Out) ### Specialization of cost equations fun6/3 * CE 46 is refined into CE [188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206] * CE 47 is refined into CE [207] ### Cost equations --> "Loop" of fun6/3 * CEs [192] --> Loop 90 * CEs [191,204] --> Loop 91 * CEs [197] --> Loop 92 * CEs [188,190,193,195,200] --> Loop 93 * CEs [189,194,196,198,199,201,202,203,205,206,207] --> Loop 94 ### Ranking functions of CR fun6(V1,V,Out) #### Partial ranking functions of CR fun6(V1,V,Out) ### Specialization of cost equations fun7/3 * CE 48 is refined into CE [208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225] * CE 49 is refined into CE [226] ### Cost equations --> "Loop" of fun7/3 * CEs [213] --> Loop 95 * CEs [212,216] --> Loop 96 * CEs [208,214] --> Loop 97 * CEs [215,224] --> Loop 98 * CEs [211,220] --> Loop 99 * CEs [209,210,217,218,219,221,222,223,225,226] --> Loop 100 ### Ranking functions of CR fun7(V1,V,Out) #### Partial ranking functions of CR fun7(V1,V,Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [227,228,229,230,231] * CE 2 is refined into CE [232,233,234] * CE 3 is refined into CE [235,236,237] * CE 4 is refined into CE [238,239,240,241,242,243] * CE 5 is refined into CE [244,245,246] * CE 6 is refined into CE [247,248,249] * CE 7 is refined into CE [250] * CE 8 is refined into CE [251,252] * CE 9 is refined into CE [253,254,255] * CE 10 is refined into CE [256,257] * CE 11 is refined into CE [258,259,260,261,262] * CE 12 is refined into CE [263,264,265] * CE 13 is refined into CE [266,267,268,269,270] ### Cost equations --> "Loop" of start/3 * CEs [227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270] --> Loop 101 ### Ranking functions of CR start(V1,V,V8) #### Partial ranking functions of CR start(V1,V,V8) Computing Bounds ===================================== #### Cost of chains of if(V1,V,V8,Out): * Chain [32]: 1 with precondition: [V1=1,V8=Out,V>=0,V8>=0] * Chain [31]: 1 with precondition: [V1=2,V=Out,V>=0,V8>=0] * Chain [30]: 0 with precondition: [Out=0,V1>=0,V>=0,V8>=0] #### Cost of chains of leq(V1,V,Out): * Chain [[33],36]: 1*it(33)+1 Such that:it(33) =< V1 with precondition: [Out=2,V1>=1,V>=V1] * Chain [[33],35]: 1*it(33)+1 Such that:it(33) =< V with precondition: [Out=1,V>=1,V1>=V+1] * Chain [[33],34]: 1*it(33)+0 Such that:it(33) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [36]: 1 with precondition: [V1=0,Out=2,V>=0] * Chain [35]: 1 with precondition: [V=0,Out=1,V1>=1] * Chain [34]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of minus(V1,V,Out): * Chain [[37],39]: 1*it(37)+1 Such that:it(37) =< V with precondition: [V1=Out+V,V>=1,V1>=V] * Chain [[37],38]: 1*it(37)+0 Such that:it(37) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [39]: 1 with precondition: [V=0,V1=Out,V1>=0] * Chain [38]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of mod(V1,V,Out): * Chain [[40,43,45],50]: 11*it(40)+5*s(19)+2*s(21)+1*s(23)+1 Such that:aux(7) =< V1-V+1 aux(10) =< V1 aux(3) =< aux(10) it(40) =< aux(10) s(19) =< aux(10) aux(3) =< aux(7) it(40) =< aux(7) s(23) =< it(40)*aux(10) s(21) =< aux(3) with precondition: [Out=0,V>=1,V1>=V] * Chain [[40,43,45],48,50]: 11*it(40)+7*s(19)+2*s(21)+1*s(23)+5*s(27)+3 Such that:aux(7) =< V1-V+1 aux(13) =< V aux(14) =< V1 s(19) =< aux(14) s(27) =< aux(13) aux(3) =< aux(14) it(40) =< aux(14) aux(3) =< aux(7) it(40) =< aux(7) s(23) =< it(40)*aux(14) s(21) =< aux(3) with precondition: [Out=0,V>=1,V1>=V+1] * Chain [[40,43,45],47,50]: 11*it(40)+5*s(19)+2*s(21)+1*s(23)+1*s(34)+4 Such that:aux(7) =< V1-V+1 s(34) =< V aux(15) =< V1 aux(3) =< aux(15) it(40) =< aux(15) s(19) =< aux(15) aux(3) =< aux(7) it(40) =< aux(7) s(23) =< it(40)*aux(15) s(21) =< aux(3) with precondition: [1>=Out,V>=2,Out>=0,V1>=V+1] * Chain [[40,43,45],46,50]: 18*it(40)+1*s(23)+1*s(35)+3 Such that:s(35) =< 1 aux(16) =< V1 it(40) =< aux(16) s(23) =< it(40)*aux(16) with precondition: [V=1,Out=0,V1>=2] * Chain [[40,43,45],44,50]: 18*it(40)+1*s(23)+1*s(36)+4 Such that:s(36) =< 1 aux(17) =< V1 it(40) =< aux(17) s(23) =< it(40)*aux(17) with precondition: [V=1,Out=0,V1>=2] * Chain [[40,43,45],42,50]: 11*it(40)+6*s(19)+2*s(21)+1*s(23)+1*s(38)+4 Such that:aux(7) =< V1-V+1 s(38) =< V aux(18) =< V1 s(19) =< aux(18) aux(3) =< aux(18) it(40) =< aux(18) aux(3) =< aux(7) it(40) =< aux(7) s(23) =< it(40)*aux(18) s(21) =< aux(3) with precondition: [V>=3,Out>=0,V1>=V+2,V>=Out+1,V1>=Out+V] * Chain [[40,43,45],41,50]: 11*it(40)+4*s(19)+2*s(21)+1*s(23)+1*s(24)+2*s(39)+4 Such that:aux(6) =< V1 aux(7) =< V1-V+1 aux(19) =< V aux(20) =< V1-V s(39) =< aux(19) aux(3) =< aux(6) it(40) =< aux(6) s(20) =< aux(6) s(24) =< aux(6) aux(3) =< aux(7) it(40) =< aux(7) aux(3) =< aux(20) it(40) =< aux(20) s(20) =< aux(20) s(24) =< aux(20) s(23) =< it(40)*aux(6) s(21) =< aux(3) s(19) =< s(20) with precondition: [Out=0,V>=2,V1>=2*V] * Chain [50]: 1 with precondition: [Out=0,V1>=0,V>=0] * Chain [49]: 1 with precondition: [V=0,Out=0,V1>=1] * Chain [48,50]: 5*s(27)+2*s(28)+3 Such that:aux(12) =< V1 aux(13) =< V s(28) =< aux(12) s(27) =< aux(13) with precondition: [Out=0,V1>=1,V>=1] * Chain [47,50]: 1*s(34)+4 Such that:s(34) =< V with precondition: [V1=1,Out=1,V>=2] * Chain [46,50]: 1*s(35)+3 Such that:s(35) =< 1 with precondition: [V=1,Out=0,V1>=1] * Chain [44,50]: 1*s(36)+4 Such that:s(36) =< 1 with precondition: [V=1,Out=0,V1>=1] * Chain [42,50]: 1*s(37)+1*s(38)+4 Such that:s(38) =< V s(37) =< Out with precondition: [V1=Out,V1>=2,V>=V1+1] * Chain [41,50]: 2*s(39)+4 Such that:aux(19) =< V s(39) =< aux(19) with precondition: [Out=0,V>=2,V1>=V] #### Cost of chains of encArg(V1,Out): * Chain [68]: 0 with precondition: [V1=1,Out=1] * Chain [67]: 0 with precondition: [V1=2,Out=2] * Chain [66]: 0 with precondition: [Out=0,V1>=0] * Chain [multiple([51,52,53,54,55,56,57,58,59,60,61,62,63,64,65],[[68],[67],[66]])]: 1*it(52)+1*it(53)+4*it(55)+4*it(56)+2*it(57)+4*it(58)+10*it(59)+1*it(62)+1*it(63)+4*it(64)+20*s(155)+1*s(156)+19*s(158)+1*s(159)+2*s(161)+1*s(162)+1*s(163)+1*s(165)+1*s(166)+16*s(167)+55*s(168)+33*s(169)+3*s(170)+6*s(171)+2*s(173)+0 Such that:s(93) =< 2*V1 aux(60) =< V1 aux(61) =< 2/3*V1 aux(62) =< 2/5*V1 aux(63) =< 3/4*V1 aux(64) =< 3/5*V1 aux(65) =< 4/5*V1 aux(66) =< 4/7*V1 aux(67) =< 4/9*V1 it(52) =< aux(60) it(53) =< aux(60) it(55) =< aux(60) it(56) =< aux(60) it(57) =< aux(60) it(58) =< aux(60) it(59) =< aux(60) it(62) =< aux(60) it(63) =< aux(60) it(64) =< aux(60) it(57) =< aux(61) it(58) =< aux(61) it(62) =< aux(61) it(64) =< aux(61) it(55) =< aux(62) it(53) =< aux(63) it(52) =< aux(64) it(63) =< aux(65) it(64) =< aux(65) it(62) =< aux(66) it(64) =< aux(66) it(56) =< aux(67) it(58) =< aux(67) aux(36) =< s(93)+1 aux(51) =< s(93)+2 aux(50) =< s(93)+3 aux(34) =< s(93) aux(41) =< s(93)-1 s(178) =< it(59)*aux(36) s(175) =< it(59)*aux(51) s(176) =< it(59)*aux(50) s(166) =< it(64)*aux(34) s(165) =< it(62)*aux(41) s(161) =< it(57)*aux(34) s(162) =< it(58)*aux(41) s(163) =< it(58)*aux(34) s(160) =< it(56)*aux(36) s(157) =< it(55)*aux(34) s(167) =< s(178) s(168) =< s(176) s(173) =< s(168)*aux(50) s(174) =< s(176) s(169) =< s(176) s(174) =< s(175) s(169) =< s(175) s(170) =< s(169)*aux(50) s(171) =< s(174) s(158) =< s(160) s(159) =< s(158)*aux(36) s(155) =< s(157) s(156) =< s(155)*s(93) with precondition: [V1>=1,Out>=0,2*V1>=Out] #### Cost of chains of fun(V1,V,Out): * Chain [74]: 2*s(233)+2*s(234)+8*s(235)+8*s(236)+4*s(237)+8*s(238)+20*s(239)+2*s(240)+2*s(241)+8*s(242)+2*s(251)+2*s(252)+4*s(253)+2*s(254)+2*s(255)+32*s(258)+110*s(259)+4*s(260)+66*s(262)+6*s(263)+12*s(264)+38*s(265)+2*s(266)+40*s(267)+2*s(268)+3*s(278)+3*s(279)+12*s(280)+12*s(281)+6*s(282)+12*s(283)+30*s(284)+3*s(285)+3*s(286)+12*s(287)+3*s(296)+3*s(297)+6*s(298)+3*s(299)+3*s(300)+48*s(303)+165*s(304)+6*s(305)+99*s(307)+9*s(308)+18*s(309)+57*s(310)+3*s(311)+60*s(312)+3*s(313)+3*s(314)+1*s(407)+0 Such that:s(407) =< 2 aux(71) =< V1 aux(72) =< 2*V1 aux(73) =< 2/3*V1 aux(74) =< 2/5*V1 aux(75) =< 3/4*V1 aux(76) =< 3/5*V1 aux(77) =< 4/5*V1 aux(78) =< 4/7*V1 aux(79) =< 4/9*V1 aux(80) =< V aux(81) =< 2*V aux(82) =< 2/3*V aux(83) =< 2/5*V aux(84) =< 3/4*V aux(85) =< 3/5*V aux(86) =< 4/5*V aux(87) =< 4/7*V aux(88) =< 4/9*V s(314) =< aux(81) s(278) =< aux(80) s(279) =< aux(80) s(280) =< aux(80) s(281) =< aux(80) s(282) =< aux(80) s(283) =< aux(80) s(284) =< aux(80) s(285) =< aux(80) s(286) =< aux(80) s(287) =< aux(80) s(282) =< aux(82) s(283) =< aux(82) s(285) =< aux(82) s(287) =< aux(82) s(280) =< aux(83) s(279) =< aux(84) s(278) =< aux(85) s(286) =< aux(86) s(287) =< aux(86) s(285) =< aux(87) s(287) =< aux(87) s(281) =< aux(88) s(283) =< aux(88) s(288) =< aux(81)+1 s(289) =< aux(81)+2 s(290) =< aux(81)+3 s(291) =< aux(81) s(292) =< aux(81)-1 s(293) =< s(284)*s(288) s(294) =< s(284)*s(289) s(295) =< s(284)*s(290) s(296) =< s(287)*s(291) s(297) =< s(285)*s(292) s(298) =< s(282)*s(291) s(299) =< s(283)*s(292) s(300) =< s(283)*s(291) s(301) =< s(281)*s(288) s(302) =< s(280)*s(291) s(303) =< s(293) s(304) =< s(295) s(305) =< s(304)*s(290) s(306) =< s(295) s(307) =< s(295) s(306) =< s(294) s(307) =< s(294) s(308) =< s(307)*s(290) s(309) =< s(306) s(310) =< s(301) s(311) =< s(310)*s(288) s(312) =< s(302) s(313) =< s(312)*aux(81) s(233) =< aux(71) s(234) =< aux(71) s(235) =< aux(71) s(236) =< aux(71) s(237) =< aux(71) s(238) =< aux(71) s(239) =< aux(71) s(240) =< aux(71) s(241) =< aux(71) s(242) =< aux(71) s(237) =< aux(73) s(238) =< aux(73) s(240) =< aux(73) s(242) =< aux(73) s(235) =< aux(74) s(234) =< aux(75) s(233) =< aux(76) s(241) =< aux(77) s(242) =< aux(77) s(240) =< aux(78) s(242) =< aux(78) s(236) =< aux(79) s(238) =< aux(79) s(243) =< aux(72)+1 s(244) =< aux(72)+2 s(245) =< aux(72)+3 s(246) =< aux(72) s(247) =< aux(72)-1 s(248) =< s(239)*s(243) s(249) =< s(239)*s(244) s(250) =< s(239)*s(245) s(251) =< s(242)*s(246) s(252) =< s(240)*s(247) s(253) =< s(237)*s(246) s(254) =< s(238)*s(247) s(255) =< s(238)*s(246) s(256) =< s(236)*s(243) s(257) =< s(235)*s(246) s(258) =< s(248) s(259) =< s(250) s(260) =< s(259)*s(245) s(261) =< s(250) s(262) =< s(250) s(261) =< s(249) s(262) =< s(249) s(263) =< s(262)*s(245) s(264) =< s(261) s(265) =< s(256) s(266) =< s(265)*s(243) s(267) =< s(257) s(268) =< s(267)*aux(72) with precondition: [Out=0,V1>=0,V>=0] * Chain [73]: 3*s(465)+3*s(466)+12*s(467)+12*s(468)+6*s(469)+12*s(470)+30*s(471)+3*s(472)+3*s(473)+12*s(474)+3*s(483)+3*s(484)+6*s(485)+3*s(486)+3*s(487)+48*s(490)+165*s(491)+6*s(492)+99*s(494)+9*s(495)+18*s(496)+57*s(497)+3*s(498)+60*s(499)+3*s(500)+4*s(510)+4*s(511)+16*s(512)+16*s(513)+8*s(514)+16*s(515)+40*s(516)+4*s(517)+4*s(518)+16*s(519)+4*s(528)+4*s(529)+8*s(530)+4*s(531)+4*s(532)+64*s(535)+220*s(536)+8*s(537)+132*s(539)+12*s(540)+24*s(541)+76*s(542)+4*s(543)+80*s(544)+4*s(545)+1*s(636)+2*s(727)+1 Such that:aux(90) =< 2 aux(91) =< V1 aux(92) =< 2*V1 aux(93) =< 2/3*V1 aux(94) =< 2/5*V1 aux(95) =< 3/4*V1 aux(96) =< 3/5*V1 aux(97) =< 4/5*V1 aux(98) =< 4/7*V1 aux(99) =< 4/9*V1 aux(100) =< V aux(101) =< 2*V aux(102) =< 2/3*V aux(103) =< 2/5*V aux(104) =< 3/4*V aux(105) =< 3/5*V aux(106) =< 4/5*V aux(107) =< 4/7*V aux(108) =< 4/9*V s(727) =< aux(90) s(510) =< aux(100) s(511) =< aux(100) s(512) =< aux(100) s(513) =< aux(100) s(514) =< aux(100) s(515) =< aux(100) s(516) =< aux(100) s(517) =< aux(100) s(518) =< aux(100) s(519) =< aux(100) s(514) =< aux(102) s(515) =< aux(102) s(517) =< aux(102) s(519) =< aux(102) s(512) =< aux(103) s(511) =< aux(104) s(510) =< aux(105) s(518) =< aux(106) s(519) =< aux(106) s(517) =< aux(107) s(519) =< aux(107) s(513) =< aux(108) s(515) =< aux(108) s(520) =< aux(101)+1 s(521) =< aux(101)+2 s(522) =< aux(101)+3 s(523) =< aux(101) s(524) =< aux(101)-1 s(525) =< s(516)*s(520) s(526) =< s(516)*s(521) s(527) =< s(516)*s(522) s(528) =< s(519)*s(523) s(529) =< s(517)*s(524) s(530) =< s(514)*s(523) s(531) =< s(515)*s(524) s(532) =< s(515)*s(523) s(533) =< s(513)*s(520) s(534) =< s(512)*s(523) s(535) =< s(525) s(536) =< s(527) s(537) =< s(536)*s(522) s(538) =< s(527) s(539) =< s(527) s(538) =< s(526) s(539) =< s(526) s(540) =< s(539)*s(522) s(541) =< s(538) s(542) =< s(533) s(543) =< s(542)*s(520) s(544) =< s(534) s(545) =< s(544)*aux(101) s(465) =< aux(91) s(466) =< aux(91) s(467) =< aux(91) s(468) =< aux(91) s(469) =< aux(91) s(470) =< aux(91) s(471) =< aux(91) s(472) =< aux(91) s(473) =< aux(91) s(474) =< aux(91) s(469) =< aux(93) s(470) =< aux(93) s(472) =< aux(93) s(474) =< aux(93) s(467) =< aux(94) s(466) =< aux(95) s(465) =< aux(96) s(473) =< aux(97) s(474) =< aux(97) s(472) =< aux(98) s(474) =< aux(98) s(468) =< aux(99) s(470) =< aux(99) s(475) =< aux(92)+1 s(476) =< aux(92)+2 s(477) =< aux(92)+3 s(478) =< aux(92) s(479) =< aux(92)-1 s(480) =< s(471)*s(475) s(481) =< s(471)*s(476) s(482) =< s(471)*s(477) s(483) =< s(474)*s(478) s(484) =< s(472)*s(479) s(485) =< s(469)*s(478) s(486) =< s(470)*s(479) s(487) =< s(470)*s(478) s(488) =< s(468)*s(475) s(489) =< s(467)*s(478) s(490) =< s(480) s(491) =< s(482) s(492) =< s(491)*s(477) s(493) =< s(482) s(494) =< s(482) s(493) =< s(481) s(494) =< s(481) s(495) =< s(494)*s(477) s(496) =< s(493) s(497) =< s(488) s(498) =< s(497)*s(475) s(499) =< s(489) s(500) =< s(499)*aux(92) s(636) =< aux(101) with precondition: [Out=2,V1>=0,V>=0] * Chain [72]: 3*s(783)+3*s(784)+12*s(785)+12*s(786)+6*s(787)+12*s(788)+30*s(789)+3*s(790)+3*s(791)+12*s(792)+3*s(801)+3*s(802)+6*s(803)+3*s(804)+3*s(805)+48*s(808)+165*s(809)+6*s(810)+99*s(812)+9*s(813)+18*s(814)+57*s(815)+3*s(816)+60*s(817)+3*s(818)+4*s(828)+4*s(829)+16*s(830)+16*s(831)+8*s(832)+16*s(833)+40*s(834)+4*s(835)+4*s(836)+16*s(837)+4*s(846)+4*s(847)+8*s(848)+4*s(849)+4*s(850)+64*s(853)+220*s(854)+8*s(855)+132*s(857)+12*s(858)+24*s(859)+76*s(860)+4*s(861)+80*s(862)+4*s(863)+1*s(954)+1*s(1090)+1 Such that:s(1090) =< 1 aux(110) =< V1 aux(111) =< 2*V1 aux(112) =< 2/3*V1 aux(113) =< 2/5*V1 aux(114) =< 3/4*V1 aux(115) =< 3/5*V1 aux(116) =< 4/5*V1 aux(117) =< 4/7*V1 aux(118) =< 4/9*V1 aux(119) =< V aux(120) =< 2*V aux(121) =< 2/3*V aux(122) =< 2/5*V aux(123) =< 3/4*V aux(124) =< 3/5*V aux(125) =< 4/5*V aux(126) =< 4/7*V aux(127) =< 4/9*V s(828) =< aux(119) s(829) =< aux(119) s(830) =< aux(119) s(831) =< aux(119) s(832) =< aux(119) s(833) =< aux(119) s(834) =< aux(119) s(835) =< aux(119) s(836) =< aux(119) s(837) =< aux(119) s(832) =< aux(121) s(833) =< aux(121) s(835) =< aux(121) s(837) =< aux(121) s(830) =< aux(122) s(829) =< aux(123) s(828) =< aux(124) s(836) =< aux(125) s(837) =< aux(125) s(835) =< aux(126) s(837) =< aux(126) s(831) =< aux(127) s(833) =< aux(127) s(838) =< aux(120)+1 s(839) =< aux(120)+2 s(840) =< aux(120)+3 s(841) =< aux(120) s(842) =< aux(120)-1 s(843) =< s(834)*s(838) s(844) =< s(834)*s(839) s(845) =< s(834)*s(840) s(846) =< s(837)*s(841) s(847) =< s(835)*s(842) s(848) =< s(832)*s(841) s(849) =< s(833)*s(842) s(850) =< s(833)*s(841) s(851) =< s(831)*s(838) s(852) =< s(830)*s(841) s(853) =< s(843) s(854) =< s(845) s(855) =< s(854)*s(840) s(856) =< s(845) s(857) =< s(845) s(856) =< s(844) s(857) =< s(844) s(858) =< s(857)*s(840) s(859) =< s(856) s(860) =< s(851) s(861) =< s(860)*s(838) s(862) =< s(852) s(863) =< s(862)*aux(120) s(783) =< aux(110) s(784) =< aux(110) s(785) =< aux(110) s(786) =< aux(110) s(787) =< aux(110) s(788) =< aux(110) s(789) =< aux(110) s(790) =< aux(110) s(791) =< aux(110) s(792) =< aux(110) s(787) =< aux(112) s(788) =< aux(112) s(790) =< aux(112) s(792) =< aux(112) s(785) =< aux(113) s(784) =< aux(114) s(783) =< aux(115) s(791) =< aux(116) s(792) =< aux(116) s(790) =< aux(117) s(792) =< aux(117) s(786) =< aux(118) s(788) =< aux(118) s(793) =< aux(111)+1 s(794) =< aux(111)+2 s(795) =< aux(111)+3 s(796) =< aux(111) s(797) =< aux(111)-1 s(798) =< s(789)*s(793) s(799) =< s(789)*s(794) s(800) =< s(789)*s(795) s(801) =< s(792)*s(796) s(802) =< s(790)*s(797) s(803) =< s(787)*s(796) s(804) =< s(788)*s(797) s(805) =< s(788)*s(796) s(806) =< s(786)*s(793) s(807) =< s(785)*s(796) s(808) =< s(798) s(809) =< s(800) s(810) =< s(809)*s(795) s(811) =< s(800) s(812) =< s(800) s(811) =< s(799) s(812) =< s(799) s(813) =< s(812)*s(795) s(814) =< s(811) s(815) =< s(806) s(816) =< s(815)*s(793) s(817) =< s(807) s(818) =< s(817)*aux(111) s(954) =< aux(111) with precondition: [Out=1,V1>=1,V>=0] * Chain [71]: 1*s(1100)+1*s(1101)+4*s(1102)+4*s(1103)+2*s(1104)+4*s(1105)+10*s(1106)+1*s(1107)+1*s(1108)+4*s(1109)+1*s(1118)+1*s(1119)+2*s(1120)+1*s(1121)+1*s(1122)+16*s(1125)+55*s(1126)+2*s(1127)+33*s(1129)+3*s(1130)+6*s(1131)+19*s(1132)+1*s(1133)+20*s(1134)+1*s(1135)+2*s(1136)+0 Such that:s(1091) =< V1 s(1092) =< 2*V1 s(1093) =< 2/3*V1 s(1094) =< 2/5*V1 s(1095) =< 3/4*V1 s(1096) =< 3/5*V1 s(1097) =< 4/5*V1 s(1098) =< 4/7*V1 s(1099) =< 4/9*V1 aux(128) =< 2 s(1136) =< aux(128) s(1100) =< s(1091) s(1101) =< s(1091) s(1102) =< s(1091) s(1103) =< s(1091) s(1104) =< s(1091) s(1105) =< s(1091) s(1106) =< s(1091) s(1107) =< s(1091) s(1108) =< s(1091) s(1109) =< s(1091) s(1104) =< s(1093) s(1105) =< s(1093) s(1107) =< s(1093) s(1109) =< s(1093) s(1102) =< s(1094) s(1101) =< s(1095) s(1100) =< s(1096) s(1108) =< s(1097) s(1109) =< s(1097) s(1107) =< s(1098) s(1109) =< s(1098) s(1103) =< s(1099) s(1105) =< s(1099) s(1110) =< s(1092)+1 s(1111) =< s(1092)+2 s(1112) =< s(1092)+3 s(1113) =< s(1092) s(1114) =< s(1092)-1 s(1115) =< s(1106)*s(1110) s(1116) =< s(1106)*s(1111) s(1117) =< s(1106)*s(1112) s(1118) =< s(1109)*s(1113) s(1119) =< s(1107)*s(1114) s(1120) =< s(1104)*s(1113) s(1121) =< s(1105)*s(1114) s(1122) =< s(1105)*s(1113) s(1123) =< s(1103)*s(1110) s(1124) =< s(1102)*s(1113) s(1125) =< s(1115) s(1126) =< s(1117) s(1127) =< s(1126)*s(1112) s(1128) =< s(1117) s(1129) =< s(1117) s(1128) =< s(1116) s(1129) =< s(1116) s(1130) =< s(1129)*s(1112) s(1131) =< s(1128) s(1132) =< s(1123) s(1133) =< s(1132)*s(1110) s(1134) =< s(1124) s(1135) =< s(1134)*s(1092) with precondition: [V=2,Out=0,V1>=0] * Chain [70]: 1*s(1147)+1*s(1148)+4*s(1149)+4*s(1150)+2*s(1151)+4*s(1152)+10*s(1153)+1*s(1154)+1*s(1155)+4*s(1156)+1*s(1165)+1*s(1166)+2*s(1167)+1*s(1168)+1*s(1169)+16*s(1172)+55*s(1173)+2*s(1174)+33*s(1176)+3*s(1177)+6*s(1178)+19*s(1179)+1*s(1180)+20*s(1181)+1*s(1182)+1*s(1183)+1 Such that:s(1183) =< 2 s(1138) =< V1 s(1139) =< 2*V1 s(1140) =< 2/3*V1 s(1141) =< 2/5*V1 s(1142) =< 3/4*V1 s(1143) =< 3/5*V1 s(1144) =< 4/5*V1 s(1145) =< 4/7*V1 s(1146) =< 4/9*V1 s(1147) =< s(1138) s(1148) =< s(1138) s(1149) =< s(1138) s(1150) =< s(1138) s(1151) =< s(1138) s(1152) =< s(1138) s(1153) =< s(1138) s(1154) =< s(1138) s(1155) =< s(1138) s(1156) =< s(1138) s(1151) =< s(1140) s(1152) =< s(1140) s(1154) =< s(1140) s(1156) =< s(1140) s(1149) =< s(1141) s(1148) =< s(1142) s(1147) =< s(1143) s(1155) =< s(1144) s(1156) =< s(1144) s(1154) =< s(1145) s(1156) =< s(1145) s(1150) =< s(1146) s(1152) =< s(1146) s(1157) =< s(1139)+1 s(1158) =< s(1139)+2 s(1159) =< s(1139)+3 s(1160) =< s(1139) s(1161) =< s(1139)-1 s(1162) =< s(1153)*s(1157) s(1163) =< s(1153)*s(1158) s(1164) =< s(1153)*s(1159) s(1165) =< s(1156)*s(1160) s(1166) =< s(1154)*s(1161) s(1167) =< s(1151)*s(1160) s(1168) =< s(1152)*s(1161) s(1169) =< s(1152)*s(1160) s(1170) =< s(1150)*s(1157) s(1171) =< s(1149)*s(1160) s(1172) =< s(1162) s(1173) =< s(1164) s(1174) =< s(1173)*s(1159) s(1175) =< s(1164) s(1176) =< s(1164) s(1175) =< s(1163) s(1176) =< s(1163) s(1177) =< s(1176)*s(1159) s(1178) =< s(1175) s(1179) =< s(1170) s(1180) =< s(1179)*s(1157) s(1181) =< s(1171) s(1182) =< s(1181)*s(1139) with precondition: [V=2,Out=1,2*V1>=3] * Chain [69]: 2*s(1193)+2*s(1194)+8*s(1195)+8*s(1196)+4*s(1197)+8*s(1198)+20*s(1199)+2*s(1200)+2*s(1201)+8*s(1202)+2*s(1211)+2*s(1212)+4*s(1213)+2*s(1214)+2*s(1215)+32*s(1218)+110*s(1219)+4*s(1220)+66*s(1222)+6*s(1223)+12*s(1224)+38*s(1225)+2*s(1226)+40*s(1227)+2*s(1228)+1*s(1274)+1 Such that:s(1274) =< 2 aux(129) =< V1 aux(130) =< 2*V1 aux(131) =< 2/3*V1 aux(132) =< 2/5*V1 aux(133) =< 3/4*V1 aux(134) =< 3/5*V1 aux(135) =< 4/5*V1 aux(136) =< 4/7*V1 aux(137) =< 4/9*V1 s(1193) =< aux(129) s(1194) =< aux(129) s(1195) =< aux(129) s(1196) =< aux(129) s(1197) =< aux(129) s(1198) =< aux(129) s(1199) =< aux(129) s(1200) =< aux(129) s(1201) =< aux(129) s(1202) =< aux(129) s(1197) =< aux(131) s(1198) =< aux(131) s(1200) =< aux(131) s(1202) =< aux(131) s(1195) =< aux(132) s(1194) =< aux(133) s(1193) =< aux(134) s(1201) =< aux(135) s(1202) =< aux(135) s(1200) =< aux(136) s(1202) =< aux(136) s(1196) =< aux(137) s(1198) =< aux(137) s(1203) =< aux(130)+1 s(1204) =< aux(130)+2 s(1205) =< aux(130)+3 s(1206) =< aux(130) s(1207) =< aux(130)-1 s(1208) =< s(1199)*s(1203) s(1209) =< s(1199)*s(1204) s(1210) =< s(1199)*s(1205) s(1211) =< s(1202)*s(1206) s(1212) =< s(1200)*s(1207) s(1213) =< s(1197)*s(1206) s(1214) =< s(1198)*s(1207) s(1215) =< s(1198)*s(1206) s(1216) =< s(1196)*s(1203) s(1217) =< s(1195)*s(1206) s(1218) =< s(1208) s(1219) =< s(1210) s(1220) =< s(1219)*s(1205) s(1221) =< s(1210) s(1222) =< s(1210) s(1221) =< s(1209) s(1222) =< s(1209) s(1223) =< s(1222)*s(1205) s(1224) =< s(1221) s(1225) =< s(1216) s(1226) =< s(1225)*s(1203) s(1227) =< s(1217) s(1228) =< s(1227)*aux(130) with precondition: [V=2,Out=2,V1>=0] #### Cost of chains of fun2(Out): * Chain [76]: 0 with precondition: [Out=0] * Chain [75]: 0 with precondition: [Out=2] #### Cost of chains of fun3(V1,Out): * Chain [79]: 1*s(1700)+1*s(1701)+4*s(1702)+4*s(1703)+2*s(1704)+4*s(1705)+10*s(1706)+1*s(1707)+1*s(1708)+4*s(1709)+1*s(1718)+1*s(1719)+2*s(1720)+1*s(1721)+1*s(1722)+16*s(1725)+55*s(1726)+2*s(1727)+33*s(1729)+3*s(1730)+6*s(1731)+19*s(1732)+1*s(1733)+20*s(1734)+1*s(1735)+0 Such that:s(1691) =< V1 s(1692) =< 2*V1 s(1693) =< 2/3*V1 s(1694) =< 2/5*V1 s(1695) =< 3/4*V1 s(1696) =< 3/5*V1 s(1697) =< 4/5*V1 s(1698) =< 4/7*V1 s(1699) =< 4/9*V1 s(1700) =< s(1691) s(1701) =< s(1691) s(1702) =< s(1691) s(1703) =< s(1691) s(1704) =< s(1691) s(1705) =< s(1691) s(1706) =< s(1691) s(1707) =< s(1691) s(1708) =< s(1691) s(1709) =< s(1691) s(1704) =< s(1693) s(1705) =< s(1693) s(1707) =< s(1693) s(1709) =< s(1693) s(1702) =< s(1694) s(1701) =< s(1695) s(1700) =< s(1696) s(1708) =< s(1697) s(1709) =< s(1697) s(1707) =< s(1698) s(1709) =< s(1698) s(1703) =< s(1699) s(1705) =< s(1699) s(1710) =< s(1692)+1 s(1711) =< s(1692)+2 s(1712) =< s(1692)+3 s(1713) =< s(1692) s(1714) =< s(1692)-1 s(1715) =< s(1706)*s(1710) s(1716) =< s(1706)*s(1711) s(1717) =< s(1706)*s(1712) s(1718) =< s(1709)*s(1713) s(1719) =< s(1707)*s(1714) s(1720) =< s(1704)*s(1713) s(1721) =< s(1705)*s(1714) s(1722) =< s(1705)*s(1713) s(1723) =< s(1703)*s(1710) s(1724) =< s(1702)*s(1713) s(1725) =< s(1715) s(1726) =< s(1717) s(1727) =< s(1726)*s(1712) s(1728) =< s(1717) s(1729) =< s(1717) s(1728) =< s(1716) s(1729) =< s(1716) s(1730) =< s(1729)*s(1712) s(1731) =< s(1728) s(1732) =< s(1723) s(1733) =< s(1732)*s(1710) s(1734) =< s(1724) s(1735) =< s(1734)*s(1692) with precondition: [V1>=1,Out>=1,2*V1+1>=Out] * Chain [78]: 0 with precondition: [Out=0,V1>=0] * Chain [77]: 0 with precondition: [Out=1,V1>=0] #### Cost of chains of fun4(Out): * Chain [81]: 0 with precondition: [Out=0] * Chain [80]: 0 with precondition: [Out=1] #### Cost of chains of fun5(V1,V,V8,Out): * Chain [89]: 8*s(1745)+8*s(1746)+32*s(1747)+32*s(1748)+16*s(1749)+32*s(1750)+80*s(1751)+8*s(1752)+8*s(1753)+32*s(1754)+8*s(1763)+8*s(1764)+16*s(1765)+8*s(1766)+8*s(1767)+128*s(1770)+440*s(1771)+16*s(1772)+264*s(1774)+24*s(1775)+48*s(1776)+152*s(1777)+8*s(1778)+160*s(1779)+8*s(1780)+7*s(1790)+7*s(1791)+28*s(1792)+28*s(1793)+14*s(1794)+28*s(1795)+70*s(1796)+7*s(1797)+7*s(1798)+28*s(1799)+7*s(1808)+7*s(1809)+14*s(1810)+7*s(1811)+7*s(1812)+112*s(1815)+385*s(1816)+14*s(1817)+231*s(1819)+21*s(1820)+42*s(1821)+133*s(1822)+7*s(1823)+140*s(1824)+7*s(1825)+9*s(1835)+9*s(1836)+36*s(1837)+36*s(1838)+18*s(1839)+36*s(1840)+90*s(1841)+9*s(1842)+9*s(1843)+36*s(1844)+9*s(1853)+9*s(1854)+18*s(1855)+9*s(1856)+9*s(1857)+144*s(1860)+495*s(1861)+18*s(1862)+297*s(1864)+27*s(1865)+54*s(1866)+171*s(1867)+9*s(1868)+180*s(1869)+9*s(1870)+1 Such that:aux(167) =< V1 aux(168) =< 2*V1 aux(169) =< 2/3*V1 aux(170) =< 2/5*V1 aux(171) =< 3/4*V1 aux(172) =< 3/5*V1 aux(173) =< 4/5*V1 aux(174) =< 4/7*V1 aux(175) =< 4/9*V1 aux(176) =< V aux(177) =< 2*V aux(178) =< 2/3*V aux(179) =< 2/5*V aux(180) =< 3/4*V aux(181) =< 3/5*V aux(182) =< 4/5*V aux(183) =< 4/7*V aux(184) =< 4/9*V aux(185) =< V8 aux(186) =< 2*V8 aux(187) =< 2/3*V8 aux(188) =< 2/5*V8 aux(189) =< 3/4*V8 aux(190) =< 3/5*V8 aux(191) =< 4/5*V8 aux(192) =< 4/7*V8 aux(193) =< 4/9*V8 s(1835) =< aux(185) s(1836) =< aux(185) s(1837) =< aux(185) s(1838) =< aux(185) s(1839) =< aux(185) s(1840) =< aux(185) s(1841) =< aux(185) s(1842) =< aux(185) s(1843) =< aux(185) s(1844) =< aux(185) s(1839) =< aux(187) s(1840) =< aux(187) s(1842) =< aux(187) s(1844) =< aux(187) s(1837) =< aux(188) s(1836) =< aux(189) s(1835) =< aux(190) s(1843) =< aux(191) s(1844) =< aux(191) s(1842) =< aux(192) s(1844) =< aux(192) s(1838) =< aux(193) s(1840) =< aux(193) s(1845) =< aux(186)+1 s(1846) =< aux(186)+2 s(1847) =< aux(186)+3 s(1848) =< aux(186) s(1849) =< aux(186)-1 s(1850) =< s(1841)*s(1845) s(1851) =< s(1841)*s(1846) s(1852) =< s(1841)*s(1847) s(1853) =< s(1844)*s(1848) s(1854) =< s(1842)*s(1849) s(1855) =< s(1839)*s(1848) s(1856) =< s(1840)*s(1849) s(1857) =< s(1840)*s(1848) s(1858) =< s(1838)*s(1845) s(1859) =< s(1837)*s(1848) s(1860) =< s(1850) s(1861) =< s(1852) s(1862) =< s(1861)*s(1847) s(1863) =< s(1852) s(1864) =< s(1852) s(1863) =< s(1851) s(1864) =< s(1851) s(1865) =< s(1864)*s(1847) s(1866) =< s(1863) s(1867) =< s(1858) s(1868) =< s(1867)*s(1845) s(1869) =< s(1859) s(1870) =< s(1869)*aux(186) s(1790) =< aux(176) s(1791) =< aux(176) s(1792) =< aux(176) s(1793) =< aux(176) s(1794) =< aux(176) s(1795) =< aux(176) s(1796) =< aux(176) s(1797) =< aux(176) s(1798) =< aux(176) s(1799) =< aux(176) s(1794) =< aux(178) s(1795) =< aux(178) s(1797) =< aux(178) s(1799) =< aux(178) s(1792) =< aux(179) s(1791) =< aux(180) s(1790) =< aux(181) s(1798) =< aux(182) s(1799) =< aux(182) s(1797) =< aux(183) s(1799) =< aux(183) s(1793) =< aux(184) s(1795) =< aux(184) s(1800) =< aux(177)+1 s(1801) =< aux(177)+2 s(1802) =< aux(177)+3 s(1803) =< aux(177) s(1804) =< aux(177)-1 s(1805) =< s(1796)*s(1800) s(1806) =< s(1796)*s(1801) s(1807) =< s(1796)*s(1802) s(1808) =< s(1799)*s(1803) s(1809) =< s(1797)*s(1804) s(1810) =< s(1794)*s(1803) s(1811) =< s(1795)*s(1804) s(1812) =< s(1795)*s(1803) s(1813) =< s(1793)*s(1800) s(1814) =< s(1792)*s(1803) s(1815) =< s(1805) s(1816) =< s(1807) s(1817) =< s(1816)*s(1802) s(1818) =< s(1807) s(1819) =< s(1807) s(1818) =< s(1806) s(1819) =< s(1806) s(1820) =< s(1819)*s(1802) s(1821) =< s(1818) s(1822) =< s(1813) s(1823) =< s(1822)*s(1800) s(1824) =< s(1814) s(1825) =< s(1824)*aux(177) s(1745) =< aux(167) s(1746) =< aux(167) s(1747) =< aux(167) s(1748) =< aux(167) s(1749) =< aux(167) s(1750) =< aux(167) s(1751) =< aux(167) s(1752) =< aux(167) s(1753) =< aux(167) s(1754) =< aux(167) s(1749) =< aux(169) s(1750) =< aux(169) s(1752) =< aux(169) s(1754) =< aux(169) s(1747) =< aux(170) s(1746) =< aux(171) s(1745) =< aux(172) s(1753) =< aux(173) s(1754) =< aux(173) s(1752) =< aux(174) s(1754) =< aux(174) s(1748) =< aux(175) s(1750) =< aux(175) s(1755) =< aux(168)+1 s(1756) =< aux(168)+2 s(1757) =< aux(168)+3 s(1758) =< aux(168) s(1759) =< aux(168)-1 s(1760) =< s(1751)*s(1755) s(1761) =< s(1751)*s(1756) s(1762) =< s(1751)*s(1757) s(1763) =< s(1754)*s(1758) s(1764) =< s(1752)*s(1759) s(1765) =< s(1749)*s(1758) s(1766) =< s(1750)*s(1759) s(1767) =< s(1750)*s(1758) s(1768) =< s(1748)*s(1755) s(1769) =< s(1747)*s(1758) s(1770) =< s(1760) s(1771) =< s(1762) s(1772) =< s(1771)*s(1757) s(1773) =< s(1762) s(1774) =< s(1762) s(1773) =< s(1761) s(1774) =< s(1761) s(1775) =< s(1774)*s(1757) s(1776) =< s(1773) s(1777) =< s(1768) s(1778) =< s(1777)*s(1755) s(1779) =< s(1769) s(1780) =< s(1779)*aux(168) with precondition: [Out=0,V1>=0,V>=0,V8>=0] * Chain [88]: 2*s(2825)+2*s(2826)+8*s(2827)+8*s(2828)+4*s(2829)+8*s(2830)+20*s(2831)+2*s(2832)+2*s(2833)+8*s(2834)+2*s(2843)+2*s(2844)+4*s(2845)+2*s(2846)+2*s(2847)+32*s(2850)+110*s(2851)+4*s(2852)+66*s(2854)+6*s(2855)+12*s(2856)+38*s(2857)+2*s(2858)+40*s(2859)+2*s(2860)+4*s(2870)+4*s(2871)+16*s(2872)+16*s(2873)+8*s(2874)+16*s(2875)+40*s(2876)+4*s(2877)+4*s(2878)+16*s(2879)+4*s(2888)+4*s(2889)+8*s(2890)+4*s(2891)+4*s(2892)+64*s(2895)+220*s(2896)+8*s(2897)+132*s(2899)+12*s(2900)+24*s(2901)+76*s(2902)+4*s(2903)+80*s(2904)+4*s(2905)+3*s(2915)+3*s(2916)+12*s(2917)+12*s(2918)+6*s(2919)+12*s(2920)+30*s(2921)+3*s(2922)+3*s(2923)+12*s(2924)+3*s(2933)+3*s(2934)+6*s(2935)+3*s(2936)+3*s(2937)+48*s(2940)+165*s(2941)+6*s(2942)+99*s(2944)+9*s(2945)+18*s(2946)+57*s(2947)+3*s(2948)+60*s(2949)+3*s(2950)+1 Such that:aux(194) =< V1 aux(195) =< 2*V1 aux(196) =< 2/3*V1 aux(197) =< 2/5*V1 aux(198) =< 3/4*V1 aux(199) =< 3/5*V1 aux(200) =< 4/5*V1 aux(201) =< 4/7*V1 aux(202) =< 4/9*V1 aux(203) =< V aux(204) =< 2*V aux(205) =< 2/3*V aux(206) =< 2/5*V aux(207) =< 3/4*V aux(208) =< 3/5*V aux(209) =< 4/5*V aux(210) =< 4/7*V aux(211) =< 4/9*V aux(212) =< V8 aux(213) =< 2*V8 aux(214) =< 2/3*V8 aux(215) =< 2/5*V8 aux(216) =< 3/4*V8 aux(217) =< 3/5*V8 aux(218) =< 4/5*V8 aux(219) =< 4/7*V8 aux(220) =< 4/9*V8 s(2915) =< aux(212) s(2916) =< aux(212) s(2917) =< aux(212) s(2918) =< aux(212) s(2919) =< aux(212) s(2920) =< aux(212) s(2921) =< aux(212) s(2922) =< aux(212) s(2923) =< aux(212) s(2924) =< aux(212) s(2919) =< aux(214) s(2920) =< aux(214) s(2922) =< aux(214) s(2924) =< aux(214) s(2917) =< aux(215) s(2916) =< aux(216) s(2915) =< aux(217) s(2923) =< aux(218) s(2924) =< aux(218) s(2922) =< aux(219) s(2924) =< aux(219) s(2918) =< aux(220) s(2920) =< aux(220) s(2925) =< aux(213)+1 s(2926) =< aux(213)+2 s(2927) =< aux(213)+3 s(2928) =< aux(213) s(2929) =< aux(213)-1 s(2930) =< s(2921)*s(2925) s(2931) =< s(2921)*s(2926) s(2932) =< s(2921)*s(2927) s(2933) =< s(2924)*s(2928) s(2934) =< s(2922)*s(2929) s(2935) =< s(2919)*s(2928) s(2936) =< s(2920)*s(2929) s(2937) =< s(2920)*s(2928) s(2938) =< s(2918)*s(2925) s(2939) =< s(2917)*s(2928) s(2940) =< s(2930) s(2941) =< s(2932) s(2942) =< s(2941)*s(2927) s(2943) =< s(2932) s(2944) =< s(2932) s(2943) =< s(2931) s(2944) =< s(2931) s(2945) =< s(2944)*s(2927) s(2946) =< s(2943) s(2947) =< s(2938) s(2948) =< s(2947)*s(2925) s(2949) =< s(2939) s(2950) =< s(2949)*aux(213) s(2870) =< aux(203) s(2871) =< aux(203) s(2872) =< aux(203) s(2873) =< aux(203) s(2874) =< aux(203) s(2875) =< aux(203) s(2876) =< aux(203) s(2877) =< aux(203) s(2878) =< aux(203) s(2879) =< aux(203) s(2874) =< aux(205) s(2875) =< aux(205) s(2877) =< aux(205) s(2879) =< aux(205) s(2872) =< aux(206) s(2871) =< aux(207) s(2870) =< aux(208) s(2878) =< aux(209) s(2879) =< aux(209) s(2877) =< aux(210) s(2879) =< aux(210) s(2873) =< aux(211) s(2875) =< aux(211) s(2880) =< aux(204)+1 s(2881) =< aux(204)+2 s(2882) =< aux(204)+3 s(2883) =< aux(204) s(2884) =< aux(204)-1 s(2885) =< s(2876)*s(2880) s(2886) =< s(2876)*s(2881) s(2887) =< s(2876)*s(2882) s(2888) =< s(2879)*s(2883) s(2889) =< s(2877)*s(2884) s(2890) =< s(2874)*s(2883) s(2891) =< s(2875)*s(2884) s(2892) =< s(2875)*s(2883) s(2893) =< s(2873)*s(2880) s(2894) =< s(2872)*s(2883) s(2895) =< s(2885) s(2896) =< s(2887) s(2897) =< s(2896)*s(2882) s(2898) =< s(2887) s(2899) =< s(2887) s(2898) =< s(2886) s(2899) =< s(2886) s(2900) =< s(2899)*s(2882) s(2901) =< s(2898) s(2902) =< s(2893) s(2903) =< s(2902)*s(2880) s(2904) =< s(2894) s(2905) =< s(2904)*aux(204) s(2825) =< aux(194) s(2826) =< aux(194) s(2827) =< aux(194) s(2828) =< aux(194) s(2829) =< aux(194) s(2830) =< aux(194) s(2831) =< aux(194) s(2832) =< aux(194) s(2833) =< aux(194) s(2834) =< aux(194) s(2829) =< aux(196) s(2830) =< aux(196) s(2832) =< aux(196) s(2834) =< aux(196) s(2827) =< aux(197) s(2826) =< aux(198) s(2825) =< aux(199) s(2833) =< aux(200) s(2834) =< aux(200) s(2832) =< aux(201) s(2834) =< aux(201) s(2828) =< aux(202) s(2830) =< aux(202) s(2835) =< aux(195)+1 s(2836) =< aux(195)+2 s(2837) =< aux(195)+3 s(2838) =< aux(195) s(2839) =< aux(195)-1 s(2840) =< s(2831)*s(2835) s(2841) =< s(2831)*s(2836) s(2842) =< s(2831)*s(2837) s(2843) =< s(2834)*s(2838) s(2844) =< s(2832)*s(2839) s(2845) =< s(2829)*s(2838) s(2846) =< s(2830)*s(2839) s(2847) =< s(2830)*s(2838) s(2848) =< s(2828)*s(2835) s(2849) =< s(2827)*s(2838) s(2850) =< s(2840) s(2851) =< s(2842) s(2852) =< s(2851)*s(2837) s(2853) =< s(2842) s(2854) =< s(2842) s(2853) =< s(2841) s(2854) =< s(2841) s(2855) =< s(2854)*s(2837) s(2856) =< s(2853) s(2857) =< s(2848) s(2858) =< s(2857)*s(2835) s(2859) =< s(2849) s(2860) =< s(2859)*aux(195) with precondition: [V1>=1,V>=1,V8>=0,Out>=0,2*V>=Out] * Chain [87]: 3*s(3230)+3*s(3231)+12*s(3232)+12*s(3233)+6*s(3234)+12*s(3235)+30*s(3236)+3*s(3237)+3*s(3238)+12*s(3239)+3*s(3248)+3*s(3249)+6*s(3250)+3*s(3251)+3*s(3252)+48*s(3255)+165*s(3256)+6*s(3257)+99*s(3259)+9*s(3260)+18*s(3261)+57*s(3262)+3*s(3263)+60*s(3264)+3*s(3265)+3*s(3275)+3*s(3276)+12*s(3277)+12*s(3278)+6*s(3279)+12*s(3280)+30*s(3281)+3*s(3282)+3*s(3283)+12*s(3284)+3*s(3293)+3*s(3294)+6*s(3295)+3*s(3296)+3*s(3297)+48*s(3300)+165*s(3301)+6*s(3302)+99*s(3304)+9*s(3305)+18*s(3306)+57*s(3307)+3*s(3308)+60*s(3309)+3*s(3310)+1 Such that:aux(221) =< V1 aux(222) =< 2*V1 aux(223) =< 2/3*V1 aux(224) =< 2/5*V1 aux(225) =< 3/4*V1 aux(226) =< 3/5*V1 aux(227) =< 4/5*V1 aux(228) =< 4/7*V1 aux(229) =< 4/9*V1 aux(230) =< V aux(231) =< 2*V aux(232) =< 2/3*V aux(233) =< 2/5*V aux(234) =< 3/4*V aux(235) =< 3/5*V aux(236) =< 4/5*V aux(237) =< 4/7*V aux(238) =< 4/9*V s(3275) =< aux(230) s(3276) =< aux(230) s(3277) =< aux(230) s(3278) =< aux(230) s(3279) =< aux(230) s(3280) =< aux(230) s(3281) =< aux(230) s(3282) =< aux(230) s(3283) =< aux(230) s(3284) =< aux(230) s(3279) =< aux(232) s(3280) =< aux(232) s(3282) =< aux(232) s(3284) =< aux(232) s(3277) =< aux(233) s(3276) =< aux(234) s(3275) =< aux(235) s(3283) =< aux(236) s(3284) =< aux(236) s(3282) =< aux(237) s(3284) =< aux(237) s(3278) =< aux(238) s(3280) =< aux(238) s(3285) =< aux(231)+1 s(3286) =< aux(231)+2 s(3287) =< aux(231)+3 s(3288) =< aux(231) s(3289) =< aux(231)-1 s(3290) =< s(3281)*s(3285) s(3291) =< s(3281)*s(3286) s(3292) =< s(3281)*s(3287) s(3293) =< s(3284)*s(3288) s(3294) =< s(3282)*s(3289) s(3295) =< s(3279)*s(3288) s(3296) =< s(3280)*s(3289) s(3297) =< s(3280)*s(3288) s(3298) =< s(3278)*s(3285) s(3299) =< s(3277)*s(3288) s(3300) =< s(3290) s(3301) =< s(3292) s(3302) =< s(3301)*s(3287) s(3303) =< s(3292) s(3304) =< s(3292) s(3303) =< s(3291) s(3304) =< s(3291) s(3305) =< s(3304)*s(3287) s(3306) =< s(3303) s(3307) =< s(3298) s(3308) =< s(3307)*s(3285) s(3309) =< s(3299) s(3310) =< s(3309)*aux(231) s(3230) =< aux(221) s(3231) =< aux(221) s(3232) =< aux(221) s(3233) =< aux(221) s(3234) =< aux(221) s(3235) =< aux(221) s(3236) =< aux(221) s(3237) =< aux(221) s(3238) =< aux(221) s(3239) =< aux(221) s(3234) =< aux(223) s(3235) =< aux(223) s(3237) =< aux(223) s(3239) =< aux(223) s(3232) =< aux(224) s(3231) =< aux(225) s(3230) =< aux(226) s(3238) =< aux(227) s(3239) =< aux(227) s(3237) =< aux(228) s(3239) =< aux(228) s(3233) =< aux(229) s(3235) =< aux(229) s(3240) =< aux(222)+1 s(3241) =< aux(222)+2 s(3242) =< aux(222)+3 s(3243) =< aux(222) s(3244) =< aux(222)-1 s(3245) =< s(3236)*s(3240) s(3246) =< s(3236)*s(3241) s(3247) =< s(3236)*s(3242) s(3248) =< s(3239)*s(3243) s(3249) =< s(3237)*s(3244) s(3250) =< s(3234)*s(3243) s(3251) =< s(3235)*s(3244) s(3252) =< s(3235)*s(3243) s(3253) =< s(3233)*s(3240) s(3254) =< s(3232)*s(3243) s(3255) =< s(3245) s(3256) =< s(3247) s(3257) =< s(3256)*s(3242) s(3258) =< s(3247) s(3259) =< s(3247) s(3258) =< s(3246) s(3259) =< s(3246) s(3260) =< s(3259)*s(3242) s(3261) =< s(3258) s(3262) =< s(3253) s(3263) =< s(3262)*s(3240) s(3264) =< s(3254) s(3265) =< s(3264)*aux(222) with precondition: [V8=2,Out=0,V1>=0,V>=0] * Chain [86]: 1*s(3500)+1*s(3501)+4*s(3502)+4*s(3503)+2*s(3504)+4*s(3505)+10*s(3506)+1*s(3507)+1*s(3508)+4*s(3509)+1*s(3518)+1*s(3519)+2*s(3520)+1*s(3521)+1*s(3522)+16*s(3525)+55*s(3526)+2*s(3527)+33*s(3529)+3*s(3530)+6*s(3531)+19*s(3532)+1*s(3533)+20*s(3534)+1*s(3535)+2*s(3545)+2*s(3546)+8*s(3547)+8*s(3548)+4*s(3549)+8*s(3550)+20*s(3551)+2*s(3552)+2*s(3553)+8*s(3554)+2*s(3563)+2*s(3564)+4*s(3565)+2*s(3566)+2*s(3567)+32*s(3570)+110*s(3571)+4*s(3572)+66*s(3574)+6*s(3575)+12*s(3576)+38*s(3577)+2*s(3578)+40*s(3579)+2*s(3580)+1 Such that:s(3491) =< V1 s(3492) =< 2*V1 s(3493) =< 2/3*V1 s(3494) =< 2/5*V1 s(3495) =< 3/4*V1 s(3496) =< 3/5*V1 s(3497) =< 4/5*V1 s(3498) =< 4/7*V1 s(3499) =< 4/9*V1 aux(239) =< V aux(240) =< 2*V aux(241) =< 2/3*V aux(242) =< 2/5*V aux(243) =< 3/4*V aux(244) =< 3/5*V aux(245) =< 4/5*V aux(246) =< 4/7*V aux(247) =< 4/9*V s(3545) =< aux(239) s(3546) =< aux(239) s(3547) =< aux(239) s(3548) =< aux(239) s(3549) =< aux(239) s(3550) =< aux(239) s(3551) =< aux(239) s(3552) =< aux(239) s(3553) =< aux(239) s(3554) =< aux(239) s(3549) =< aux(241) s(3550) =< aux(241) s(3552) =< aux(241) s(3554) =< aux(241) s(3547) =< aux(242) s(3546) =< aux(243) s(3545) =< aux(244) s(3553) =< aux(245) s(3554) =< aux(245) s(3552) =< aux(246) s(3554) =< aux(246) s(3548) =< aux(247) s(3550) =< aux(247) s(3555) =< aux(240)+1 s(3556) =< aux(240)+2 s(3557) =< aux(240)+3 s(3558) =< aux(240) s(3559) =< aux(240)-1 s(3560) =< s(3551)*s(3555) s(3561) =< s(3551)*s(3556) s(3562) =< s(3551)*s(3557) s(3563) =< s(3554)*s(3558) s(3564) =< s(3552)*s(3559) s(3565) =< s(3549)*s(3558) s(3566) =< s(3550)*s(3559) s(3567) =< s(3550)*s(3558) s(3568) =< s(3548)*s(3555) s(3569) =< s(3547)*s(3558) s(3570) =< s(3560) s(3571) =< s(3562) s(3572) =< s(3571)*s(3557) s(3573) =< s(3562) s(3574) =< s(3562) s(3573) =< s(3561) s(3574) =< s(3561) s(3575) =< s(3574)*s(3557) s(3576) =< s(3573) s(3577) =< s(3568) s(3578) =< s(3577)*s(3555) s(3579) =< s(3569) s(3580) =< s(3579)*aux(240) s(3500) =< s(3491) s(3501) =< s(3491) s(3502) =< s(3491) s(3503) =< s(3491) s(3504) =< s(3491) s(3505) =< s(3491) s(3506) =< s(3491) s(3507) =< s(3491) s(3508) =< s(3491) s(3509) =< s(3491) s(3504) =< s(3493) s(3505) =< s(3493) s(3507) =< s(3493) s(3509) =< s(3493) s(3502) =< s(3494) s(3501) =< s(3495) s(3500) =< s(3496) s(3508) =< s(3497) s(3509) =< s(3497) s(3507) =< s(3498) s(3509) =< s(3498) s(3503) =< s(3499) s(3505) =< s(3499) s(3510) =< s(3492)+1 s(3511) =< s(3492)+2 s(3512) =< s(3492)+3 s(3513) =< s(3492) s(3514) =< s(3492)-1 s(3515) =< s(3506)*s(3510) s(3516) =< s(3506)*s(3511) s(3517) =< s(3506)*s(3512) s(3518) =< s(3509)*s(3513) s(3519) =< s(3507)*s(3514) s(3520) =< s(3504)*s(3513) s(3521) =< s(3505)*s(3514) s(3522) =< s(3505)*s(3513) s(3523) =< s(3503)*s(3510) s(3524) =< s(3502)*s(3513) s(3525) =< s(3515) s(3526) =< s(3517) s(3527) =< s(3526)*s(3512) s(3528) =< s(3517) s(3529) =< s(3517) s(3528) =< s(3516) s(3529) =< s(3516) s(3530) =< s(3529)*s(3512) s(3531) =< s(3528) s(3532) =< s(3523) s(3533) =< s(3532)*s(3510) s(3534) =< s(3524) s(3535) =< s(3534)*s(3492) with precondition: [V8=2,V1>=1,V>=1,Out>=0,2*V>=Out] * Chain [85]: 4*s(3635)+4*s(3636)+16*s(3637)+16*s(3638)+8*s(3639)+16*s(3640)+40*s(3641)+4*s(3642)+4*s(3643)+16*s(3644)+4*s(3653)+4*s(3654)+8*s(3655)+4*s(3656)+4*s(3657)+64*s(3660)+220*s(3661)+8*s(3662)+132*s(3664)+12*s(3665)+24*s(3666)+76*s(3667)+4*s(3668)+80*s(3669)+4*s(3670)+2*s(3680)+2*s(3681)+8*s(3682)+8*s(3683)+4*s(3684)+8*s(3685)+20*s(3686)+2*s(3687)+2*s(3688)+8*s(3689)+2*s(3698)+2*s(3699)+4*s(3700)+2*s(3701)+2*s(3702)+32*s(3705)+110*s(3706)+4*s(3707)+66*s(3709)+6*s(3710)+12*s(3711)+38*s(3712)+2*s(3713)+40*s(3714)+2*s(3715)+1 Such that:aux(248) =< V1 aux(249) =< 2*V1 aux(250) =< 2/3*V1 aux(251) =< 2/5*V1 aux(252) =< 3/4*V1 aux(253) =< 3/5*V1 aux(254) =< 4/5*V1 aux(255) =< 4/7*V1 aux(256) =< 4/9*V1 aux(257) =< V8 aux(258) =< 2*V8 aux(259) =< 2/3*V8 aux(260) =< 2/5*V8 aux(261) =< 3/4*V8 aux(262) =< 3/5*V8 aux(263) =< 4/5*V8 aux(264) =< 4/7*V8 aux(265) =< 4/9*V8 s(3680) =< aux(257) s(3681) =< aux(257) s(3682) =< aux(257) s(3683) =< aux(257) s(3684) =< aux(257) s(3685) =< aux(257) s(3686) =< aux(257) s(3687) =< aux(257) s(3688) =< aux(257) s(3689) =< aux(257) s(3684) =< aux(259) s(3685) =< aux(259) s(3687) =< aux(259) s(3689) =< aux(259) s(3682) =< aux(260) s(3681) =< aux(261) s(3680) =< aux(262) s(3688) =< aux(263) s(3689) =< aux(263) s(3687) =< aux(264) s(3689) =< aux(264) s(3683) =< aux(265) s(3685) =< aux(265) s(3690) =< aux(258)+1 s(3691) =< aux(258)+2 s(3692) =< aux(258)+3 s(3693) =< aux(258) s(3694) =< aux(258)-1 s(3695) =< s(3686)*s(3690) s(3696) =< s(3686)*s(3691) s(3697) =< s(3686)*s(3692) s(3698) =< s(3689)*s(3693) s(3699) =< s(3687)*s(3694) s(3700) =< s(3684)*s(3693) s(3701) =< s(3685)*s(3694) s(3702) =< s(3685)*s(3693) s(3703) =< s(3683)*s(3690) s(3704) =< s(3682)*s(3693) s(3705) =< s(3695) s(3706) =< s(3697) s(3707) =< s(3706)*s(3692) s(3708) =< s(3697) s(3709) =< s(3697) s(3708) =< s(3696) s(3709) =< s(3696) s(3710) =< s(3709)*s(3692) s(3711) =< s(3708) s(3712) =< s(3703) s(3713) =< s(3712)*s(3690) s(3714) =< s(3704) s(3715) =< s(3714)*aux(258) s(3635) =< aux(248) s(3636) =< aux(248) s(3637) =< aux(248) s(3638) =< aux(248) s(3639) =< aux(248) s(3640) =< aux(248) s(3641) =< aux(248) s(3642) =< aux(248) s(3643) =< aux(248) s(3644) =< aux(248) s(3639) =< aux(250) s(3640) =< aux(250) s(3642) =< aux(250) s(3644) =< aux(250) s(3637) =< aux(251) s(3636) =< aux(252) s(3635) =< aux(253) s(3643) =< aux(254) s(3644) =< aux(254) s(3642) =< aux(255) s(3644) =< aux(255) s(3638) =< aux(256) s(3640) =< aux(256) s(3645) =< aux(249)+1 s(3646) =< aux(249)+2 s(3647) =< aux(249)+3 s(3648) =< aux(249) s(3649) =< aux(249)-1 s(3650) =< s(3641)*s(3645) s(3651) =< s(3641)*s(3646) s(3652) =< s(3641)*s(3647) s(3653) =< s(3644)*s(3648) s(3654) =< s(3642)*s(3649) s(3655) =< s(3639)*s(3648) s(3656) =< s(3640)*s(3649) s(3657) =< s(3640)*s(3648) s(3658) =< s(3638)*s(3645) s(3659) =< s(3637)*s(3648) s(3660) =< s(3650) s(3661) =< s(3652) s(3662) =< s(3661)*s(3647) s(3663) =< s(3652) s(3664) =< s(3652) s(3663) =< s(3651) s(3664) =< s(3651) s(3665) =< s(3664)*s(3647) s(3666) =< s(3663) s(3667) =< s(3658) s(3668) =< s(3667)*s(3645) s(3669) =< s(3659) s(3670) =< s(3669)*aux(249) with precondition: [V=2,Out=0,V1>=0,V8>=0] * Chain [84]: 4*s(3905)+4*s(3906)+16*s(3907)+16*s(3908)+8*s(3909)+16*s(3910)+40*s(3911)+4*s(3912)+4*s(3913)+16*s(3914)+4*s(3923)+4*s(3924)+8*s(3925)+4*s(3926)+4*s(3927)+64*s(3930)+220*s(3931)+8*s(3932)+132*s(3934)+12*s(3935)+24*s(3936)+76*s(3937)+4*s(3938)+80*s(3939)+4*s(3940)+1*s(3950)+1*s(3951)+4*s(3952)+4*s(3953)+2*s(3954)+4*s(3955)+10*s(3956)+1*s(3957)+1*s(3958)+4*s(3959)+1*s(3968)+1*s(3969)+2*s(3970)+1*s(3971)+1*s(3972)+16*s(3975)+55*s(3976)+2*s(3977)+33*s(3979)+3*s(3980)+6*s(3981)+19*s(3982)+1*s(3983)+20*s(3984)+1*s(3985)+1 Such that:s(3941) =< V8 s(3942) =< 2*V8 s(3943) =< 2/3*V8 s(3944) =< 2/5*V8 s(3945) =< 3/4*V8 s(3946) =< 3/5*V8 s(3947) =< 4/5*V8 s(3948) =< 4/7*V8 s(3949) =< 4/9*V8 aux(266) =< V1 aux(267) =< 2*V1 aux(268) =< 2/3*V1 aux(269) =< 2/5*V1 aux(270) =< 3/4*V1 aux(271) =< 3/5*V1 aux(272) =< 4/5*V1 aux(273) =< 4/7*V1 aux(274) =< 4/9*V1 s(3950) =< s(3941) s(3951) =< s(3941) s(3952) =< s(3941) s(3953) =< s(3941) s(3954) =< s(3941) s(3955) =< s(3941) s(3956) =< s(3941) s(3957) =< s(3941) s(3958) =< s(3941) s(3959) =< s(3941) s(3954) =< s(3943) s(3955) =< s(3943) s(3957) =< s(3943) s(3959) =< s(3943) s(3952) =< s(3944) s(3951) =< s(3945) s(3950) =< s(3946) s(3958) =< s(3947) s(3959) =< s(3947) s(3957) =< s(3948) s(3959) =< s(3948) s(3953) =< s(3949) s(3955) =< s(3949) s(3960) =< s(3942)+1 s(3961) =< s(3942)+2 s(3962) =< s(3942)+3 s(3963) =< s(3942) s(3964) =< s(3942)-1 s(3965) =< s(3956)*s(3960) s(3966) =< s(3956)*s(3961) s(3967) =< s(3956)*s(3962) s(3968) =< s(3959)*s(3963) s(3969) =< s(3957)*s(3964) s(3970) =< s(3954)*s(3963) s(3971) =< s(3955)*s(3964) s(3972) =< s(3955)*s(3963) s(3973) =< s(3953)*s(3960) s(3974) =< s(3952)*s(3963) s(3975) =< s(3965) s(3976) =< s(3967) s(3977) =< s(3976)*s(3962) s(3978) =< s(3967) s(3979) =< s(3967) s(3978) =< s(3966) s(3979) =< s(3966) s(3980) =< s(3979)*s(3962) s(3981) =< s(3978) s(3982) =< s(3973) s(3983) =< s(3982)*s(3960) s(3984) =< s(3974) s(3985) =< s(3984)*s(3942) s(3905) =< aux(266) s(3906) =< aux(266) s(3907) =< aux(266) s(3908) =< aux(266) s(3909) =< aux(266) s(3910) =< aux(266) s(3911) =< aux(266) s(3912) =< aux(266) s(3913) =< aux(266) s(3914) =< aux(266) s(3909) =< aux(268) s(3910) =< aux(268) s(3912) =< aux(268) s(3914) =< aux(268) s(3907) =< aux(269) s(3906) =< aux(270) s(3905) =< aux(271) s(3913) =< aux(272) s(3914) =< aux(272) s(3912) =< aux(273) s(3914) =< aux(273) s(3908) =< aux(274) s(3910) =< aux(274) s(3915) =< aux(267)+1 s(3916) =< aux(267)+2 s(3917) =< aux(267)+3 s(3918) =< aux(267) s(3919) =< aux(267)-1 s(3920) =< s(3911)*s(3915) s(3921) =< s(3911)*s(3916) s(3922) =< s(3911)*s(3917) s(3923) =< s(3914)*s(3918) s(3924) =< s(3912)*s(3919) s(3925) =< s(3909)*s(3918) s(3926) =< s(3910)*s(3919) s(3927) =< s(3910)*s(3918) s(3928) =< s(3908)*s(3915) s(3929) =< s(3907)*s(3918) s(3930) =< s(3920) s(3931) =< s(3922) s(3932) =< s(3931)*s(3917) s(3933) =< s(3922) s(3934) =< s(3922) s(3933) =< s(3921) s(3934) =< s(3921) s(3935) =< s(3934)*s(3917) s(3936) =< s(3933) s(3937) =< s(3928) s(3938) =< s(3937)*s(3915) s(3939) =< s(3929) s(3940) =< s(3939)*aux(267) with precondition: [V=2,Out=2,V1>=1,V8>=0] * Chain [83]: 3*s(4130)+3*s(4131)+12*s(4132)+12*s(4133)+6*s(4134)+12*s(4135)+30*s(4136)+3*s(4137)+3*s(4138)+12*s(4139)+3*s(4148)+3*s(4149)+6*s(4150)+3*s(4151)+3*s(4152)+48*s(4155)+165*s(4156)+6*s(4157)+99*s(4159)+9*s(4160)+18*s(4161)+57*s(4162)+3*s(4163)+60*s(4164)+3*s(4165)+1*s(4175)+1*s(4176)+4*s(4177)+4*s(4178)+2*s(4179)+4*s(4180)+10*s(4181)+1*s(4182)+1*s(4183)+4*s(4184)+1*s(4193)+1*s(4194)+2*s(4195)+1*s(4196)+1*s(4197)+16*s(4200)+55*s(4201)+2*s(4202)+33*s(4204)+3*s(4205)+6*s(4206)+19*s(4207)+1*s(4208)+20*s(4209)+1*s(4210)+3*s(4220)+3*s(4221)+12*s(4222)+12*s(4223)+6*s(4224)+12*s(4225)+30*s(4226)+3*s(4227)+3*s(4228)+12*s(4229)+3*s(4238)+3*s(4239)+6*s(4240)+3*s(4241)+3*s(4242)+48*s(4245)+165*s(4246)+6*s(4247)+99*s(4249)+9*s(4250)+18*s(4251)+57*s(4252)+3*s(4253)+60*s(4254)+3*s(4255)+1 Such that:s(4166) =< V s(4167) =< 2*V s(4168) =< 2/3*V s(4169) =< 2/5*V s(4170) =< 3/4*V s(4171) =< 3/5*V s(4172) =< 4/5*V s(4173) =< 4/7*V s(4174) =< 4/9*V aux(275) =< V1 aux(276) =< 2*V1 aux(277) =< 2/3*V1 aux(278) =< 2/5*V1 aux(279) =< 3/4*V1 aux(280) =< 3/5*V1 aux(281) =< 4/5*V1 aux(282) =< 4/7*V1 aux(283) =< 4/9*V1 aux(284) =< V8 aux(285) =< 2*V8 aux(286) =< 2/3*V8 aux(287) =< 2/5*V8 aux(288) =< 3/4*V8 aux(289) =< 3/5*V8 aux(290) =< 4/5*V8 aux(291) =< 4/7*V8 aux(292) =< 4/9*V8 s(4220) =< aux(284) s(4221) =< aux(284) s(4222) =< aux(284) s(4223) =< aux(284) s(4224) =< aux(284) s(4225) =< aux(284) s(4226) =< aux(284) s(4227) =< aux(284) s(4228) =< aux(284) s(4229) =< aux(284) s(4224) =< aux(286) s(4225) =< aux(286) s(4227) =< aux(286) s(4229) =< aux(286) s(4222) =< aux(287) s(4221) =< aux(288) s(4220) =< aux(289) s(4228) =< aux(290) s(4229) =< aux(290) s(4227) =< aux(291) s(4229) =< aux(291) s(4223) =< aux(292) s(4225) =< aux(292) s(4230) =< aux(285)+1 s(4231) =< aux(285)+2 s(4232) =< aux(285)+3 s(4233) =< aux(285) s(4234) =< aux(285)-1 s(4235) =< s(4226)*s(4230) s(4236) =< s(4226)*s(4231) s(4237) =< s(4226)*s(4232) s(4238) =< s(4229)*s(4233) s(4239) =< s(4227)*s(4234) s(4240) =< s(4224)*s(4233) s(4241) =< s(4225)*s(4234) s(4242) =< s(4225)*s(4233) s(4243) =< s(4223)*s(4230) s(4244) =< s(4222)*s(4233) s(4245) =< s(4235) s(4246) =< s(4237) s(4247) =< s(4246)*s(4232) s(4248) =< s(4237) s(4249) =< s(4237) s(4248) =< s(4236) s(4249) =< s(4236) s(4250) =< s(4249)*s(4232) s(4251) =< s(4248) s(4252) =< s(4243) s(4253) =< s(4252)*s(4230) s(4254) =< s(4244) s(4255) =< s(4254)*aux(285) s(4175) =< s(4166) s(4176) =< s(4166) s(4177) =< s(4166) s(4178) =< s(4166) s(4179) =< s(4166) s(4180) =< s(4166) s(4181) =< s(4166) s(4182) =< s(4166) s(4183) =< s(4166) s(4184) =< s(4166) s(4179) =< s(4168) s(4180) =< s(4168) s(4182) =< s(4168) s(4184) =< s(4168) s(4177) =< s(4169) s(4176) =< s(4170) s(4175) =< s(4171) s(4183) =< s(4172) s(4184) =< s(4172) s(4182) =< s(4173) s(4184) =< s(4173) s(4178) =< s(4174) s(4180) =< s(4174) s(4185) =< s(4167)+1 s(4186) =< s(4167)+2 s(4187) =< s(4167)+3 s(4188) =< s(4167) s(4189) =< s(4167)-1 s(4190) =< s(4181)*s(4185) s(4191) =< s(4181)*s(4186) s(4192) =< s(4181)*s(4187) s(4193) =< s(4184)*s(4188) s(4194) =< s(4182)*s(4189) s(4195) =< s(4179)*s(4188) s(4196) =< s(4180)*s(4189) s(4197) =< s(4180)*s(4188) s(4198) =< s(4178)*s(4185) s(4199) =< s(4177)*s(4188) s(4200) =< s(4190) s(4201) =< s(4192) s(4202) =< s(4201)*s(4187) s(4203) =< s(4192) s(4204) =< s(4192) s(4203) =< s(4191) s(4204) =< s(4191) s(4205) =< s(4204)*s(4187) s(4206) =< s(4203) s(4207) =< s(4198) s(4208) =< s(4207)*s(4185) s(4209) =< s(4199) s(4210) =< s(4209)*s(4167) s(4130) =< aux(275) s(4131) =< aux(275) s(4132) =< aux(275) s(4133) =< aux(275) s(4134) =< aux(275) s(4135) =< aux(275) s(4136) =< aux(275) s(4137) =< aux(275) s(4138) =< aux(275) s(4139) =< aux(275) s(4134) =< aux(277) s(4135) =< aux(277) s(4137) =< aux(277) s(4139) =< aux(277) s(4132) =< aux(278) s(4131) =< aux(279) s(4130) =< aux(280) s(4138) =< aux(281) s(4139) =< aux(281) s(4137) =< aux(282) s(4139) =< aux(282) s(4133) =< aux(283) s(4135) =< aux(283) s(4140) =< aux(276)+1 s(4141) =< aux(276)+2 s(4142) =< aux(276)+3 s(4143) =< aux(276) s(4144) =< aux(276)-1 s(4145) =< s(4136)*s(4140) s(4146) =< s(4136)*s(4141) s(4147) =< s(4136)*s(4142) s(4148) =< s(4139)*s(4143) s(4149) =< s(4137)*s(4144) s(4150) =< s(4134)*s(4143) s(4151) =< s(4135)*s(4144) s(4152) =< s(4135)*s(4143) s(4153) =< s(4133)*s(4140) s(4154) =< s(4132)*s(4143) s(4155) =< s(4145) s(4156) =< s(4147) s(4157) =< s(4156)*s(4142) s(4158) =< s(4147) s(4159) =< s(4147) s(4158) =< s(4146) s(4159) =< s(4146) s(4160) =< s(4159)*s(4142) s(4161) =< s(4158) s(4162) =< s(4153) s(4163) =< s(4162)*s(4140) s(4164) =< s(4154) s(4165) =< s(4164)*aux(276) with precondition: [V1>=1,V>=0,V8>=1,Out>=0,2*V8>=Out] * Chain [82]: 2*s(4445)+2*s(4446)+8*s(4447)+8*s(4448)+4*s(4449)+8*s(4450)+20*s(4451)+2*s(4452)+2*s(4453)+8*s(4454)+2*s(4463)+2*s(4464)+4*s(4465)+2*s(4466)+2*s(4467)+32*s(4470)+110*s(4471)+4*s(4472)+66*s(4474)+6*s(4475)+12*s(4476)+38*s(4477)+2*s(4478)+40*s(4479)+2*s(4480)+1*s(4490)+1*s(4491)+4*s(4492)+4*s(4493)+2*s(4494)+4*s(4495)+10*s(4496)+1*s(4497)+1*s(4498)+4*s(4499)+1*s(4508)+1*s(4509)+2*s(4510)+1*s(4511)+1*s(4512)+16*s(4515)+55*s(4516)+2*s(4517)+33*s(4519)+3*s(4520)+6*s(4521)+19*s(4522)+1*s(4523)+20*s(4524)+1*s(4525)+1 Such that:s(4481) =< V s(4482) =< 2*V s(4483) =< 2/3*V s(4484) =< 2/5*V s(4485) =< 3/4*V s(4486) =< 3/5*V s(4487) =< 4/5*V s(4488) =< 4/7*V s(4489) =< 4/9*V aux(293) =< V1 aux(294) =< 2*V1 aux(295) =< 2/3*V1 aux(296) =< 2/5*V1 aux(297) =< 3/4*V1 aux(298) =< 3/5*V1 aux(299) =< 4/5*V1 aux(300) =< 4/7*V1 aux(301) =< 4/9*V1 s(4490) =< s(4481) s(4491) =< s(4481) s(4492) =< s(4481) s(4493) =< s(4481) s(4494) =< s(4481) s(4495) =< s(4481) s(4496) =< s(4481) s(4497) =< s(4481) s(4498) =< s(4481) s(4499) =< s(4481) s(4494) =< s(4483) s(4495) =< s(4483) s(4497) =< s(4483) s(4499) =< s(4483) s(4492) =< s(4484) s(4491) =< s(4485) s(4490) =< s(4486) s(4498) =< s(4487) s(4499) =< s(4487) s(4497) =< s(4488) s(4499) =< s(4488) s(4493) =< s(4489) s(4495) =< s(4489) s(4500) =< s(4482)+1 s(4501) =< s(4482)+2 s(4502) =< s(4482)+3 s(4503) =< s(4482) s(4504) =< s(4482)-1 s(4505) =< s(4496)*s(4500) s(4506) =< s(4496)*s(4501) s(4507) =< s(4496)*s(4502) s(4508) =< s(4499)*s(4503) s(4509) =< s(4497)*s(4504) s(4510) =< s(4494)*s(4503) s(4511) =< s(4495)*s(4504) s(4512) =< s(4495)*s(4503) s(4513) =< s(4493)*s(4500) s(4514) =< s(4492)*s(4503) s(4515) =< s(4505) s(4516) =< s(4507) s(4517) =< s(4516)*s(4502) s(4518) =< s(4507) s(4519) =< s(4507) s(4518) =< s(4506) s(4519) =< s(4506) s(4520) =< s(4519)*s(4502) s(4521) =< s(4518) s(4522) =< s(4513) s(4523) =< s(4522)*s(4500) s(4524) =< s(4514) s(4525) =< s(4524)*s(4482) s(4445) =< aux(293) s(4446) =< aux(293) s(4447) =< aux(293) s(4448) =< aux(293) s(4449) =< aux(293) s(4450) =< aux(293) s(4451) =< aux(293) s(4452) =< aux(293) s(4453) =< aux(293) s(4454) =< aux(293) s(4449) =< aux(295) s(4450) =< aux(295) s(4452) =< aux(295) s(4454) =< aux(295) s(4447) =< aux(296) s(4446) =< aux(297) s(4445) =< aux(298) s(4453) =< aux(299) s(4454) =< aux(299) s(4452) =< aux(300) s(4454) =< aux(300) s(4448) =< aux(301) s(4450) =< aux(301) s(4455) =< aux(294)+1 s(4456) =< aux(294)+2 s(4457) =< aux(294)+3 s(4458) =< aux(294) s(4459) =< aux(294)-1 s(4460) =< s(4451)*s(4455) s(4461) =< s(4451)*s(4456) s(4462) =< s(4451)*s(4457) s(4463) =< s(4454)*s(4458) s(4464) =< s(4452)*s(4459) s(4465) =< s(4449)*s(4458) s(4466) =< s(4450)*s(4459) s(4467) =< s(4450)*s(4458) s(4468) =< s(4448)*s(4455) s(4469) =< s(4447)*s(4458) s(4470) =< s(4460) s(4471) =< s(4462) s(4472) =< s(4471)*s(4457) s(4473) =< s(4462) s(4474) =< s(4462) s(4473) =< s(4461) s(4474) =< s(4461) s(4475) =< s(4474)*s(4457) s(4476) =< s(4473) s(4477) =< s(4468) s(4478) =< s(4477)*s(4455) s(4479) =< s(4469) s(4480) =< s(4479)*aux(294) with precondition: [V8=2,Out=2,V1>=1,V>=0] #### Cost of chains of fun6(V1,V,Out): * Chain [94]: 2*s(5255)+2*s(5256)+8*s(5257)+8*s(5258)+4*s(5259)+8*s(5260)+20*s(5261)+2*s(5262)+2*s(5263)+8*s(5264)+2*s(5273)+2*s(5274)+4*s(5275)+2*s(5276)+2*s(5277)+32*s(5280)+110*s(5281)+4*s(5282)+66*s(5284)+6*s(5285)+12*s(5286)+38*s(5287)+2*s(5288)+40*s(5289)+2*s(5290)+4*s(5300)+4*s(5301)+16*s(5302)+16*s(5303)+8*s(5304)+16*s(5305)+40*s(5306)+4*s(5307)+4*s(5308)+16*s(5309)+4*s(5318)+4*s(5319)+8*s(5320)+4*s(5321)+4*s(5322)+64*s(5325)+220*s(5326)+8*s(5327)+132*s(5329)+12*s(5330)+24*s(5331)+76*s(5332)+4*s(5333)+80*s(5334)+4*s(5335)+3*s(5336)+2*s(5429)+1 Such that:aux(359) =< 2 aux(360) =< V1 aux(361) =< 2*V1 aux(362) =< 2/3*V1 aux(363) =< 2/5*V1 aux(364) =< 3/4*V1 aux(365) =< 3/5*V1 aux(366) =< 4/5*V1 aux(367) =< 4/7*V1 aux(368) =< 4/9*V1 aux(369) =< V aux(370) =< 2*V aux(371) =< 2/3*V aux(372) =< 2/5*V aux(373) =< 3/4*V aux(374) =< 3/5*V aux(375) =< 4/5*V aux(376) =< 4/7*V aux(377) =< 4/9*V s(5429) =< aux(359) s(5336) =< aux(370) s(5300) =< aux(369) s(5301) =< aux(369) s(5302) =< aux(369) s(5303) =< aux(369) s(5304) =< aux(369) s(5305) =< aux(369) s(5306) =< aux(369) s(5307) =< aux(369) s(5308) =< aux(369) s(5309) =< aux(369) s(5304) =< aux(371) s(5305) =< aux(371) s(5307) =< aux(371) s(5309) =< aux(371) s(5302) =< aux(372) s(5301) =< aux(373) s(5300) =< aux(374) s(5308) =< aux(375) s(5309) =< aux(375) s(5307) =< aux(376) s(5309) =< aux(376) s(5303) =< aux(377) s(5305) =< aux(377) s(5310) =< aux(370)+1 s(5311) =< aux(370)+2 s(5312) =< aux(370)+3 s(5313) =< aux(370) s(5314) =< aux(370)-1 s(5315) =< s(5306)*s(5310) s(5316) =< s(5306)*s(5311) s(5317) =< s(5306)*s(5312) s(5318) =< s(5309)*s(5313) s(5319) =< s(5307)*s(5314) s(5320) =< s(5304)*s(5313) s(5321) =< s(5305)*s(5314) s(5322) =< s(5305)*s(5313) s(5323) =< s(5303)*s(5310) s(5324) =< s(5302)*s(5313) s(5325) =< s(5315) s(5326) =< s(5317) s(5327) =< s(5326)*s(5312) s(5328) =< s(5317) s(5329) =< s(5317) s(5328) =< s(5316) s(5329) =< s(5316) s(5330) =< s(5329)*s(5312) s(5331) =< s(5328) s(5332) =< s(5323) s(5333) =< s(5332)*s(5310) s(5334) =< s(5324) s(5335) =< s(5334)*aux(370) s(5255) =< aux(360) s(5256) =< aux(360) s(5257) =< aux(360) s(5258) =< aux(360) s(5259) =< aux(360) s(5260) =< aux(360) s(5261) =< aux(360) s(5262) =< aux(360) s(5263) =< aux(360) s(5264) =< aux(360) s(5259) =< aux(362) s(5260) =< aux(362) s(5262) =< aux(362) s(5264) =< aux(362) s(5257) =< aux(363) s(5256) =< aux(364) s(5255) =< aux(365) s(5263) =< aux(366) s(5264) =< aux(366) s(5262) =< aux(367) s(5264) =< aux(367) s(5258) =< aux(368) s(5260) =< aux(368) s(5265) =< aux(361)+1 s(5266) =< aux(361)+2 s(5267) =< aux(361)+3 s(5268) =< aux(361) s(5269) =< aux(361)-1 s(5270) =< s(5261)*s(5265) s(5271) =< s(5261)*s(5266) s(5272) =< s(5261)*s(5267) s(5273) =< s(5264)*s(5268) s(5274) =< s(5262)*s(5269) s(5275) =< s(5259)*s(5268) s(5276) =< s(5260)*s(5269) s(5277) =< s(5260)*s(5268) s(5278) =< s(5258)*s(5265) s(5279) =< s(5257)*s(5268) s(5280) =< s(5270) s(5281) =< s(5272) s(5282) =< s(5281)*s(5267) s(5283) =< s(5272) s(5284) =< s(5272) s(5283) =< s(5271) s(5284) =< s(5271) s(5285) =< s(5284)*s(5267) s(5286) =< s(5283) s(5287) =< s(5278) s(5288) =< s(5287)*s(5265) s(5289) =< s(5279) s(5290) =< s(5289)*aux(361) with precondition: [Out=0,V1>=0,V>=0] * Chain [93]: 3*s(5533)+3*s(5534)+12*s(5535)+12*s(5536)+6*s(5537)+12*s(5538)+30*s(5539)+3*s(5540)+3*s(5541)+12*s(5542)+3*s(5551)+3*s(5552)+6*s(5553)+3*s(5554)+3*s(5555)+48*s(5558)+165*s(5559)+6*s(5560)+99*s(5562)+9*s(5563)+18*s(5564)+57*s(5565)+3*s(5566)+60*s(5567)+3*s(5568)+3*s(5578)+3*s(5579)+12*s(5580)+12*s(5581)+6*s(5582)+12*s(5583)+30*s(5584)+3*s(5585)+3*s(5586)+12*s(5587)+3*s(5596)+3*s(5597)+6*s(5598)+3*s(5599)+3*s(5600)+48*s(5603)+165*s(5604)+6*s(5605)+99*s(5607)+9*s(5608)+18*s(5609)+57*s(5610)+3*s(5611)+60*s(5612)+3*s(5613)+1*s(5704)+1 Such that:aux(379) =< V1 aux(380) =< 2*V1 aux(381) =< 2/3*V1 aux(382) =< 2/5*V1 aux(383) =< 3/4*V1 aux(384) =< 3/5*V1 aux(385) =< 4/5*V1 aux(386) =< 4/7*V1 aux(387) =< 4/9*V1 aux(388) =< V aux(389) =< 2*V aux(390) =< 2/3*V aux(391) =< 2/5*V aux(392) =< 3/4*V aux(393) =< 3/5*V aux(394) =< 4/5*V aux(395) =< 4/7*V aux(396) =< 4/9*V s(5578) =< aux(388) s(5579) =< aux(388) s(5580) =< aux(388) s(5581) =< aux(388) s(5582) =< aux(388) s(5583) =< aux(388) s(5584) =< aux(388) s(5585) =< aux(388) s(5586) =< aux(388) s(5587) =< aux(388) s(5582) =< aux(390) s(5583) =< aux(390) s(5585) =< aux(390) s(5587) =< aux(390) s(5580) =< aux(391) s(5579) =< aux(392) s(5578) =< aux(393) s(5586) =< aux(394) s(5587) =< aux(394) s(5585) =< aux(395) s(5587) =< aux(395) s(5581) =< aux(396) s(5583) =< aux(396) s(5588) =< aux(389)+1 s(5589) =< aux(389)+2 s(5590) =< aux(389)+3 s(5591) =< aux(389) s(5592) =< aux(389)-1 s(5593) =< s(5584)*s(5588) s(5594) =< s(5584)*s(5589) s(5595) =< s(5584)*s(5590) s(5596) =< s(5587)*s(5591) s(5597) =< s(5585)*s(5592) s(5598) =< s(5582)*s(5591) s(5599) =< s(5583)*s(5592) s(5600) =< s(5583)*s(5591) s(5601) =< s(5581)*s(5588) s(5602) =< s(5580)*s(5591) s(5603) =< s(5593) s(5604) =< s(5595) s(5605) =< s(5604)*s(5590) s(5606) =< s(5595) s(5607) =< s(5595) s(5606) =< s(5594) s(5607) =< s(5594) s(5608) =< s(5607)*s(5590) s(5609) =< s(5606) s(5610) =< s(5601) s(5611) =< s(5610)*s(5588) s(5612) =< s(5602) s(5613) =< s(5612)*aux(389) s(5533) =< aux(379) s(5534) =< aux(379) s(5535) =< aux(379) s(5536) =< aux(379) s(5537) =< aux(379) s(5538) =< aux(379) s(5539) =< aux(379) s(5540) =< aux(379) s(5541) =< aux(379) s(5542) =< aux(379) s(5537) =< aux(381) s(5538) =< aux(381) s(5540) =< aux(381) s(5542) =< aux(381) s(5535) =< aux(382) s(5534) =< aux(383) s(5533) =< aux(384) s(5541) =< aux(385) s(5542) =< aux(385) s(5540) =< aux(386) s(5542) =< aux(386) s(5536) =< aux(387) s(5538) =< aux(387) s(5543) =< aux(380)+1 s(5544) =< aux(380)+2 s(5545) =< aux(380)+3 s(5546) =< aux(380) s(5547) =< aux(380)-1 s(5548) =< s(5539)*s(5543) s(5549) =< s(5539)*s(5544) s(5550) =< s(5539)*s(5545) s(5551) =< s(5542)*s(5546) s(5552) =< s(5540)*s(5547) s(5553) =< s(5537)*s(5546) s(5554) =< s(5538)*s(5547) s(5555) =< s(5538)*s(5546) s(5556) =< s(5536)*s(5543) s(5557) =< s(5535)*s(5546) s(5558) =< s(5548) s(5559) =< s(5550) s(5560) =< s(5559)*s(5545) s(5561) =< s(5550) s(5562) =< s(5550) s(5561) =< s(5549) s(5562) =< s(5549) s(5563) =< s(5562)*s(5545) s(5564) =< s(5561) s(5565) =< s(5556) s(5566) =< s(5565)*s(5543) s(5567) =< s(5557) s(5568) =< s(5567)*aux(380) s(5704) =< aux(389) with precondition: [V1>=1,V>=0,Out>=0,2*V1>=Out] * Chain [92]: 1*s(5804)+1*s(5805)+4*s(5806)+4*s(5807)+2*s(5808)+4*s(5809)+10*s(5810)+1*s(5811)+1*s(5812)+4*s(5813)+1*s(5822)+1*s(5823)+2*s(5824)+1*s(5825)+1*s(5826)+16*s(5829)+55*s(5830)+2*s(5831)+33*s(5833)+3*s(5834)+6*s(5835)+19*s(5836)+1*s(5837)+20*s(5838)+1*s(5839)+1*s(5840)+1 Such that:s(5840) =< 2 s(5795) =< V s(5796) =< 2*V s(5797) =< 2/3*V s(5798) =< 2/5*V s(5799) =< 3/4*V s(5800) =< 3/5*V s(5801) =< 4/5*V s(5802) =< 4/7*V s(5803) =< 4/9*V s(5804) =< s(5795) s(5805) =< s(5795) s(5806) =< s(5795) s(5807) =< s(5795) s(5808) =< s(5795) s(5809) =< s(5795) s(5810) =< s(5795) s(5811) =< s(5795) s(5812) =< s(5795) s(5813) =< s(5795) s(5808) =< s(5797) s(5809) =< s(5797) s(5811) =< s(5797) s(5813) =< s(5797) s(5806) =< s(5798) s(5805) =< s(5799) s(5804) =< s(5800) s(5812) =< s(5801) s(5813) =< s(5801) s(5811) =< s(5802) s(5813) =< s(5802) s(5807) =< s(5803) s(5809) =< s(5803) s(5814) =< s(5796)+1 s(5815) =< s(5796)+2 s(5816) =< s(5796)+3 s(5817) =< s(5796) s(5818) =< s(5796)-1 s(5819) =< s(5810)*s(5814) s(5820) =< s(5810)*s(5815) s(5821) =< s(5810)*s(5816) s(5822) =< s(5813)*s(5817) s(5823) =< s(5811)*s(5818) s(5824) =< s(5808)*s(5817) s(5825) =< s(5809)*s(5818) s(5826) =< s(5809)*s(5817) s(5827) =< s(5807)*s(5814) s(5828) =< s(5806)*s(5817) s(5829) =< s(5819) s(5830) =< s(5821) s(5831) =< s(5830)*s(5816) s(5832) =< s(5821) s(5833) =< s(5821) s(5832) =< s(5820) s(5833) =< s(5820) s(5834) =< s(5833)*s(5816) s(5835) =< s(5832) s(5836) =< s(5827) s(5837) =< s(5836)*s(5814) s(5838) =< s(5828) s(5839) =< s(5838)*s(5796) with precondition: [V1=2,1>=Out,V>=1,Out>=0] * Chain [91]: 1*s(5850)+1*s(5851)+4*s(5852)+4*s(5853)+2*s(5854)+4*s(5855)+10*s(5856)+1*s(5857)+1*s(5858)+4*s(5859)+1*s(5868)+1*s(5869)+2*s(5870)+1*s(5871)+1*s(5872)+16*s(5875)+55*s(5876)+2*s(5877)+33*s(5879)+3*s(5880)+6*s(5881)+19*s(5882)+1*s(5883)+20*s(5884)+1*s(5885)+2*s(5886)+0 Such that:s(5841) =< V1 s(5842) =< 2*V1 s(5843) =< 2/3*V1 s(5844) =< 2/5*V1 s(5845) =< 3/4*V1 s(5846) =< 3/5*V1 s(5847) =< 4/5*V1 s(5848) =< 4/7*V1 s(5849) =< 4/9*V1 aux(397) =< 2 s(5886) =< aux(397) s(5850) =< s(5841) s(5851) =< s(5841) s(5852) =< s(5841) s(5853) =< s(5841) s(5854) =< s(5841) s(5855) =< s(5841) s(5856) =< s(5841) s(5857) =< s(5841) s(5858) =< s(5841) s(5859) =< s(5841) s(5854) =< s(5843) s(5855) =< s(5843) s(5857) =< s(5843) s(5859) =< s(5843) s(5852) =< s(5844) s(5851) =< s(5845) s(5850) =< s(5846) s(5858) =< s(5847) s(5859) =< s(5847) s(5857) =< s(5848) s(5859) =< s(5848) s(5853) =< s(5849) s(5855) =< s(5849) s(5860) =< s(5842)+1 s(5861) =< s(5842)+2 s(5862) =< s(5842)+3 s(5863) =< s(5842) s(5864) =< s(5842)-1 s(5865) =< s(5856)*s(5860) s(5866) =< s(5856)*s(5861) s(5867) =< s(5856)*s(5862) s(5868) =< s(5859)*s(5863) s(5869) =< s(5857)*s(5864) s(5870) =< s(5854)*s(5863) s(5871) =< s(5855)*s(5864) s(5872) =< s(5855)*s(5863) s(5873) =< s(5853)*s(5860) s(5874) =< s(5852)*s(5863) s(5875) =< s(5865) s(5876) =< s(5867) s(5877) =< s(5876)*s(5862) s(5878) =< s(5867) s(5879) =< s(5867) s(5878) =< s(5866) s(5879) =< s(5866) s(5880) =< s(5879)*s(5862) s(5881) =< s(5878) s(5882) =< s(5873) s(5883) =< s(5882)*s(5860) s(5884) =< s(5874) s(5885) =< s(5884)*s(5842) with precondition: [V=2,Out=0,V1>=0] * Chain [90]: 1*s(5897)+1*s(5898)+4*s(5899)+4*s(5900)+2*s(5901)+4*s(5902)+10*s(5903)+1*s(5904)+1*s(5905)+4*s(5906)+1*s(5915)+1*s(5916)+2*s(5917)+1*s(5918)+1*s(5919)+16*s(5922)+55*s(5923)+2*s(5924)+33*s(5926)+3*s(5927)+6*s(5928)+19*s(5929)+1*s(5930)+20*s(5931)+1*s(5932)+1*s(5933)+1 Such that:s(5933) =< 2 s(5888) =< V1 s(5889) =< 2*V1 s(5890) =< 2/3*V1 s(5891) =< 2/5*V1 s(5892) =< 3/4*V1 s(5893) =< 3/5*V1 s(5894) =< 4/5*V1 s(5895) =< 4/7*V1 s(5896) =< 4/9*V1 s(5897) =< s(5888) s(5898) =< s(5888) s(5899) =< s(5888) s(5900) =< s(5888) s(5901) =< s(5888) s(5902) =< s(5888) s(5903) =< s(5888) s(5904) =< s(5888) s(5905) =< s(5888) s(5906) =< s(5888) s(5901) =< s(5890) s(5902) =< s(5890) s(5904) =< s(5890) s(5906) =< s(5890) s(5899) =< s(5891) s(5898) =< s(5892) s(5897) =< s(5893) s(5905) =< s(5894) s(5906) =< s(5894) s(5904) =< s(5895) s(5906) =< s(5895) s(5900) =< s(5896) s(5902) =< s(5896) s(5907) =< s(5889)+1 s(5908) =< s(5889)+2 s(5909) =< s(5889)+3 s(5910) =< s(5889) s(5911) =< s(5889)-1 s(5912) =< s(5903)*s(5907) s(5913) =< s(5903)*s(5908) s(5914) =< s(5903)*s(5909) s(5915) =< s(5906)*s(5910) s(5916) =< s(5904)*s(5911) s(5917) =< s(5901)*s(5910) s(5918) =< s(5902)*s(5911) s(5919) =< s(5902)*s(5910) s(5920) =< s(5900)*s(5907) s(5921) =< s(5899)*s(5910) s(5922) =< s(5912) s(5923) =< s(5914) s(5924) =< s(5923)*s(5909) s(5925) =< s(5914) s(5926) =< s(5914) s(5925) =< s(5913) s(5926) =< s(5913) s(5927) =< s(5926)*s(5909) s(5928) =< s(5925) s(5929) =< s(5920) s(5930) =< s(5929)*s(5907) s(5931) =< s(5921) s(5932) =< s(5931)*s(5889) with precondition: [V=2,Out>=0,2*V1>=Out+2] #### Cost of chains of fun7(V1,V,Out): * Chain [100]: 3*s(6220)+3*s(6221)+12*s(6222)+12*s(6223)+6*s(6224)+12*s(6225)+30*s(6226)+3*s(6227)+3*s(6228)+12*s(6229)+3*s(6238)+3*s(6239)+6*s(6240)+3*s(6241)+3*s(6242)+48*s(6245)+165*s(6246)+6*s(6247)+99*s(6249)+9*s(6250)+18*s(6251)+57*s(6252)+3*s(6253)+60*s(6254)+3*s(6255)+5*s(6265)+5*s(6266)+20*s(6267)+20*s(6268)+10*s(6269)+20*s(6270)+50*s(6271)+5*s(6272)+5*s(6273)+20*s(6274)+5*s(6283)+5*s(6284)+10*s(6285)+5*s(6286)+5*s(6287)+80*s(6290)+275*s(6291)+10*s(6292)+165*s(6294)+15*s(6295)+30*s(6296)+95*s(6297)+5*s(6298)+100*s(6299)+5*s(6300)+74*s(6305)+42*s(6306)+66*s(6308)+6*s(6311)+12*s(6312)+8*s(6410)+2*s(6412)+102*s(6524)+66*s(6527)+6*s(6530)+12*s(6531)+2*s(6586)+22*s(6601)+2*s(6602)+4*s(6603)+4 Such that:aux(428) =< 1 aux(429) =< 2 aux(430) =< 3 aux(431) =< V1 aux(432) =< 2*V1 aux(433) =< 2*V1+1 aux(434) =< 2/3*V1 aux(435) =< 2/5*V1 aux(436) =< 3/4*V1 aux(437) =< 3/5*V1 aux(438) =< 4/5*V1 aux(439) =< 4/7*V1 aux(440) =< 4/9*V1 aux(441) =< V aux(442) =< 2*V aux(443) =< 2/3*V aux(444) =< 2/5*V aux(445) =< 3/4*V aux(446) =< 3/5*V aux(447) =< 4/5*V aux(448) =< 4/7*V aux(449) =< 4/9*V s(6410) =< aux(428) s(6305) =< aux(432) s(6412) =< s(6305)*aux(432) s(6265) =< aux(441) s(6266) =< aux(441) s(6267) =< aux(441) s(6268) =< aux(441) s(6269) =< aux(441) s(6270) =< aux(441) s(6271) =< aux(441) s(6272) =< aux(441) s(6273) =< aux(441) s(6274) =< aux(441) s(6269) =< aux(443) s(6270) =< aux(443) s(6272) =< aux(443) s(6274) =< aux(443) s(6267) =< aux(444) s(6266) =< aux(445) s(6265) =< aux(446) s(6273) =< aux(447) s(6274) =< aux(447) s(6272) =< aux(448) s(6274) =< aux(448) s(6268) =< aux(449) s(6270) =< aux(449) s(6275) =< aux(442)+1 s(6276) =< aux(442)+2 s(6277) =< aux(442)+3 s(6278) =< aux(442) s(6279) =< aux(442)-1 s(6280) =< s(6271)*s(6275) s(6281) =< s(6271)*s(6276) s(6282) =< s(6271)*s(6277) s(6283) =< s(6274)*s(6278) s(6284) =< s(6272)*s(6279) s(6285) =< s(6269)*s(6278) s(6286) =< s(6270)*s(6279) s(6287) =< s(6270)*s(6278) s(6288) =< s(6268)*s(6275) s(6289) =< s(6267)*s(6278) s(6290) =< s(6280) s(6291) =< s(6282) s(6292) =< s(6291)*s(6277) s(6293) =< s(6282) s(6294) =< s(6282) s(6293) =< s(6281) s(6294) =< s(6281) s(6295) =< s(6294)*s(6277) s(6296) =< s(6293) s(6297) =< s(6288) s(6298) =< s(6297)*s(6275) s(6299) =< s(6289) s(6300) =< s(6299)*aux(442) s(6220) =< aux(431) s(6221) =< aux(431) s(6222) =< aux(431) s(6223) =< aux(431) s(6224) =< aux(431) s(6225) =< aux(431) s(6226) =< aux(431) s(6227) =< aux(431) s(6228) =< aux(431) s(6229) =< aux(431) s(6224) =< aux(434) s(6225) =< aux(434) s(6227) =< aux(434) s(6229) =< aux(434) s(6222) =< aux(435) s(6221) =< aux(436) s(6220) =< aux(437) s(6228) =< aux(438) s(6229) =< aux(438) s(6227) =< aux(439) s(6229) =< aux(439) s(6223) =< aux(440) s(6225) =< aux(440) s(6230) =< aux(432)+1 s(6231) =< aux(432)+2 s(6232) =< aux(432)+3 s(6233) =< aux(432) s(6234) =< aux(432)-1 s(6235) =< s(6226)*s(6230) s(6236) =< s(6226)*s(6231) s(6237) =< s(6226)*s(6232) s(6238) =< s(6229)*s(6233) s(6239) =< s(6227)*s(6234) s(6240) =< s(6224)*s(6233) s(6241) =< s(6225)*s(6234) s(6242) =< s(6225)*s(6233) s(6243) =< s(6223)*s(6230) s(6244) =< s(6222)*s(6233) s(6245) =< s(6235) s(6246) =< s(6237) s(6247) =< s(6246)*s(6232) s(6248) =< s(6237) s(6249) =< s(6237) s(6248) =< s(6236) s(6249) =< s(6236) s(6250) =< s(6249)*s(6232) s(6251) =< s(6248) s(6252) =< s(6243) s(6253) =< s(6252)*s(6230) s(6254) =< s(6244) s(6255) =< s(6254)*aux(432) s(6524) =< aux(429) s(6586) =< s(6524)*aux(429) s(6600) =< aux(429) s(6601) =< aux(429) s(6600) =< aux(428) s(6601) =< aux(428) s(6602) =< s(6601)*aux(429) s(6603) =< s(6600) s(6306) =< aux(442) s(6526) =< aux(429) s(6527) =< aux(429) s(6526) =< aux(430) s(6527) =< aux(430) s(6530) =< s(6527)*aux(429) s(6531) =< s(6526) s(6307) =< aux(432) s(6308) =< aux(432) s(6307) =< aux(433) s(6308) =< aux(433) s(6311) =< s(6308)*aux(432) s(6312) =< s(6307) with precondition: [Out=0,V1>=0,V>=0] * Chain [99]: 1*s(6709)+1*s(6710)+4*s(6711)+4*s(6712)+2*s(6713)+4*s(6714)+10*s(6715)+1*s(6716)+1*s(6717)+4*s(6718)+1*s(6727)+1*s(6728)+2*s(6729)+1*s(6730)+1*s(6731)+16*s(6734)+55*s(6735)+2*s(6736)+33*s(6738)+3*s(6739)+6*s(6740)+19*s(6741)+1*s(6742)+20*s(6743)+1*s(6744)+2*s(6754)+2*s(6755)+8*s(6756)+8*s(6757)+4*s(6758)+8*s(6759)+20*s(6760)+2*s(6761)+2*s(6762)+8*s(6763)+2*s(6772)+2*s(6773)+4*s(6774)+2*s(6775)+2*s(6776)+32*s(6779)+110*s(6780)+4*s(6781)+66*s(6783)+6*s(6784)+12*s(6785)+38*s(6786)+2*s(6787)+40*s(6788)+2*s(6789)+3*s(6790)+1*s(6838)+4 Such that:s(6838) =< 2 s(6700) =< V1 s(6701) =< 2*V1 s(6702) =< 2/3*V1 s(6703) =< 2/5*V1 s(6704) =< 3/4*V1 s(6705) =< 3/5*V1 s(6706) =< 4/5*V1 s(6707) =< 4/7*V1 s(6708) =< 4/9*V1 aux(452) =< V aux(453) =< 2*V aux(454) =< 2/3*V aux(455) =< 2/5*V aux(456) =< 3/4*V aux(457) =< 3/5*V aux(458) =< 4/5*V aux(459) =< 4/7*V aux(460) =< 4/9*V s(6790) =< aux(453) s(6754) =< aux(452) s(6755) =< aux(452) s(6756) =< aux(452) s(6757) =< aux(452) s(6758) =< aux(452) s(6759) =< aux(452) s(6760) =< aux(452) s(6761) =< aux(452) s(6762) =< aux(452) s(6763) =< aux(452) s(6758) =< aux(454) s(6759) =< aux(454) s(6761) =< aux(454) s(6763) =< aux(454) s(6756) =< aux(455) s(6755) =< aux(456) s(6754) =< aux(457) s(6762) =< aux(458) s(6763) =< aux(458) s(6761) =< aux(459) s(6763) =< aux(459) s(6757) =< aux(460) s(6759) =< aux(460) s(6764) =< aux(453)+1 s(6765) =< aux(453)+2 s(6766) =< aux(453)+3 s(6767) =< aux(453) s(6768) =< aux(453)-1 s(6769) =< s(6760)*s(6764) s(6770) =< s(6760)*s(6765) s(6771) =< s(6760)*s(6766) s(6772) =< s(6763)*s(6767) s(6773) =< s(6761)*s(6768) s(6774) =< s(6758)*s(6767) s(6775) =< s(6759)*s(6768) s(6776) =< s(6759)*s(6767) s(6777) =< s(6757)*s(6764) s(6778) =< s(6756)*s(6767) s(6779) =< s(6769) s(6780) =< s(6771) s(6781) =< s(6780)*s(6766) s(6782) =< s(6771) s(6783) =< s(6771) s(6782) =< s(6770) s(6783) =< s(6770) s(6784) =< s(6783)*s(6766) s(6785) =< s(6782) s(6786) =< s(6777) s(6787) =< s(6786)*s(6764) s(6788) =< s(6778) s(6789) =< s(6788)*aux(453) s(6709) =< s(6700) s(6710) =< s(6700) s(6711) =< s(6700) s(6712) =< s(6700) s(6713) =< s(6700) s(6714) =< s(6700) s(6715) =< s(6700) s(6716) =< s(6700) s(6717) =< s(6700) s(6718) =< s(6700) s(6713) =< s(6702) s(6714) =< s(6702) s(6716) =< s(6702) s(6718) =< s(6702) s(6711) =< s(6703) s(6710) =< s(6704) s(6709) =< s(6705) s(6717) =< s(6706) s(6718) =< s(6706) s(6716) =< s(6707) s(6718) =< s(6707) s(6712) =< s(6708) s(6714) =< s(6708) s(6719) =< s(6701)+1 s(6720) =< s(6701)+2 s(6721) =< s(6701)+3 s(6722) =< s(6701) s(6723) =< s(6701)-1 s(6724) =< s(6715)*s(6719) s(6725) =< s(6715)*s(6720) s(6726) =< s(6715)*s(6721) s(6727) =< s(6718)*s(6722) s(6728) =< s(6716)*s(6723) s(6729) =< s(6713)*s(6722) s(6730) =< s(6714)*s(6723) s(6731) =< s(6714)*s(6722) s(6732) =< s(6712)*s(6719) s(6733) =< s(6711)*s(6722) s(6734) =< s(6724) s(6735) =< s(6726) s(6736) =< s(6735)*s(6721) s(6737) =< s(6726) s(6738) =< s(6726) s(6737) =< s(6725) s(6738) =< s(6725) s(6739) =< s(6738)*s(6721) s(6740) =< s(6737) s(6741) =< s(6732) s(6742) =< s(6741)*s(6719) s(6743) =< s(6733) s(6744) =< s(6743)*s(6701) with precondition: [Out>=2,2*V1>=Out,2*V>=Out+1] * Chain [98]: 1*s(6848)+1*s(6849)+4*s(6850)+4*s(6851)+2*s(6852)+4*s(6853)+10*s(6854)+1*s(6855)+1*s(6856)+4*s(6857)+1*s(6866)+1*s(6867)+2*s(6868)+1*s(6869)+1*s(6870)+16*s(6873)+55*s(6874)+2*s(6875)+33*s(6877)+3*s(6878)+6*s(6879)+19*s(6880)+1*s(6881)+20*s(6882)+1*s(6883)+58*s(6888)+28*s(6889)+3*s(6894)+4 Such that:s(6839) =< V1 aux(461) =< 2*V1 s(6841) =< 2/3*V1 s(6842) =< 2/5*V1 s(6843) =< 3/4*V1 s(6844) =< 3/5*V1 s(6845) =< 4/5*V1 s(6846) =< 4/7*V1 s(6847) =< 4/9*V1 aux(463) =< 2 s(6888) =< aux(461) s(6889) =< aux(463) s(6894) =< s(6888)*aux(461) s(6848) =< s(6839) s(6849) =< s(6839) s(6850) =< s(6839) s(6851) =< s(6839) s(6852) =< s(6839) s(6853) =< s(6839) s(6854) =< s(6839) s(6855) =< s(6839) s(6856) =< s(6839) s(6857) =< s(6839) s(6852) =< s(6841) s(6853) =< s(6841) s(6855) =< s(6841) s(6857) =< s(6841) s(6850) =< s(6842) s(6849) =< s(6843) s(6848) =< s(6844) s(6856) =< s(6845) s(6857) =< s(6845) s(6855) =< s(6846) s(6857) =< s(6846) s(6851) =< s(6847) s(6853) =< s(6847) s(6858) =< aux(461)+1 s(6859) =< aux(461)+2 s(6860) =< aux(461)+3 s(6861) =< aux(461) s(6862) =< aux(461)-1 s(6863) =< s(6854)*s(6858) s(6864) =< s(6854)*s(6859) s(6865) =< s(6854)*s(6860) s(6866) =< s(6857)*s(6861) s(6867) =< s(6855)*s(6862) s(6868) =< s(6852)*s(6861) s(6869) =< s(6853)*s(6862) s(6870) =< s(6853)*s(6861) s(6871) =< s(6851)*s(6858) s(6872) =< s(6850)*s(6861) s(6873) =< s(6863) s(6874) =< s(6865) s(6875) =< s(6874)*s(6860) s(6876) =< s(6865) s(6877) =< s(6865) s(6876) =< s(6864) s(6877) =< s(6864) s(6878) =< s(6877)*s(6860) s(6879) =< s(6876) s(6880) =< s(6871) s(6881) =< s(6880)*s(6858) s(6882) =< s(6872) s(6883) =< s(6882)*aux(461) with precondition: [V=2,Out=0,V1>=0] * Chain [97]: 2*s(6927)+2*s(6928)+8*s(6929)+8*s(6930)+4*s(6931)+8*s(6932)+20*s(6933)+2*s(6934)+2*s(6935)+8*s(6936)+2*s(6945)+2*s(6946)+4*s(6947)+2*s(6948)+2*s(6949)+32*s(6952)+110*s(6953)+4*s(6954)+66*s(6956)+6*s(6957)+12*s(6958)+38*s(6959)+2*s(6960)+40*s(6961)+2*s(6962)+1*s(6972)+1*s(6973)+4*s(6974)+4*s(6975)+2*s(6976)+4*s(6977)+10*s(6978)+1*s(6979)+1*s(6980)+4*s(6981)+1*s(6990)+1*s(6991)+2*s(6992)+1*s(6993)+1*s(6994)+16*s(6997)+55*s(6998)+2*s(6999)+33*s(7001)+3*s(7002)+6*s(7003)+19*s(7004)+1*s(7005)+20*s(7006)+1*s(7007)+1*s(7008)+1*s(7054)+4 Such that:s(7054) =< 2 s(6963) =< V aux(464) =< 2*V s(6965) =< 2/3*V s(6966) =< 2/5*V s(6967) =< 3/4*V s(6968) =< 3/5*V s(6969) =< 4/5*V s(6970) =< 4/7*V s(6971) =< 4/9*V aux(465) =< V1 aux(466) =< 2*V1 aux(467) =< 2/3*V1 aux(468) =< 2/5*V1 aux(469) =< 3/4*V1 aux(470) =< 3/5*V1 aux(471) =< 4/5*V1 aux(472) =< 4/7*V1 aux(473) =< 4/9*V1 s(6927) =< aux(465) s(6928) =< aux(465) s(6929) =< aux(465) s(6930) =< aux(465) s(6931) =< aux(465) s(6932) =< aux(465) s(6933) =< aux(465) s(6934) =< aux(465) s(6935) =< aux(465) s(6936) =< aux(465) s(6931) =< aux(467) s(6932) =< aux(467) s(6934) =< aux(467) s(6936) =< aux(467) s(6929) =< aux(468) s(6928) =< aux(469) s(6927) =< aux(470) s(6935) =< aux(471) s(6936) =< aux(471) s(6934) =< aux(472) s(6936) =< aux(472) s(6930) =< aux(473) s(6932) =< aux(473) s(6937) =< aux(466)+1 s(6938) =< aux(466)+2 s(6939) =< aux(466)+3 s(6940) =< aux(466) s(6941) =< aux(466)-1 s(6942) =< s(6933)*s(6937) s(6943) =< s(6933)*s(6938) s(6944) =< s(6933)*s(6939) s(6945) =< s(6936)*s(6940) s(6946) =< s(6934)*s(6941) s(6947) =< s(6931)*s(6940) s(6948) =< s(6932)*s(6941) s(6949) =< s(6932)*s(6940) s(6950) =< s(6930)*s(6937) s(6951) =< s(6929)*s(6940) s(6952) =< s(6942) s(6953) =< s(6944) s(6954) =< s(6953)*s(6939) s(6955) =< s(6944) s(6956) =< s(6944) s(6955) =< s(6943) s(6956) =< s(6943) s(6957) =< s(6956)*s(6939) s(6958) =< s(6955) s(6959) =< s(6950) s(6960) =< s(6959)*s(6937) s(6961) =< s(6951) s(6962) =< s(6961)*aux(466) s(7008) =< aux(464) s(6972) =< s(6963) s(6973) =< s(6963) s(6974) =< s(6963) s(6975) =< s(6963) s(6976) =< s(6963) s(6977) =< s(6963) s(6978) =< s(6963) s(6979) =< s(6963) s(6980) =< s(6963) s(6981) =< s(6963) s(6976) =< s(6965) s(6977) =< s(6965) s(6979) =< s(6965) s(6981) =< s(6965) s(6974) =< s(6966) s(6973) =< s(6967) s(6972) =< s(6968) s(6980) =< s(6969) s(6981) =< s(6969) s(6979) =< s(6970) s(6981) =< s(6970) s(6975) =< s(6971) s(6977) =< s(6971) s(6982) =< aux(464)+1 s(6983) =< aux(464)+2 s(6984) =< aux(464)+3 s(6985) =< aux(464) s(6986) =< aux(464)-1 s(6987) =< s(6978)*s(6982) s(6988) =< s(6978)*s(6983) s(6989) =< s(6978)*s(6984) s(6990) =< s(6981)*s(6985) s(6991) =< s(6979)*s(6986) s(6992) =< s(6976)*s(6985) s(6993) =< s(6977)*s(6986) s(6994) =< s(6977)*s(6985) s(6995) =< s(6975)*s(6982) s(6996) =< s(6974)*s(6985) s(6997) =< s(6987) s(6998) =< s(6989) s(6999) =< s(6998)*s(6984) s(7000) =< s(6989) s(7001) =< s(6989) s(7000) =< s(6988) s(7001) =< s(6988) s(7002) =< s(7001)*s(6984) s(7003) =< s(7000) s(7004) =< s(6995) s(7005) =< s(7004)*s(6982) s(7006) =< s(6996) s(7007) =< s(7006)*aux(464) with precondition: [Out=1,V1>=1,V>=1] * Chain [96]: 2*s(7064)+2*s(7065)+8*s(7066)+8*s(7067)+4*s(7068)+8*s(7069)+20*s(7070)+2*s(7071)+2*s(7072)+8*s(7073)+2*s(7082)+2*s(7083)+4*s(7084)+2*s(7085)+2*s(7086)+32*s(7089)+110*s(7090)+4*s(7091)+66*s(7093)+6*s(7094)+12*s(7095)+38*s(7096)+2*s(7097)+40*s(7098)+2*s(7099)+1*s(7109)+1*s(7110)+4*s(7111)+4*s(7112)+2*s(7113)+4*s(7114)+10*s(7115)+1*s(7116)+1*s(7117)+4*s(7118)+1*s(7127)+1*s(7128)+2*s(7129)+1*s(7130)+1*s(7131)+16*s(7134)+55*s(7135)+2*s(7136)+33*s(7138)+3*s(7139)+6*s(7140)+19*s(7141)+1*s(7142)+20*s(7143)+1*s(7144)+1*s(7146)+11*s(7149)+23*s(7150)+1*s(7151)+2*s(7152)+1*s(7199)+1*s(7204)+4 Such that:s(7199) =< 2 aux(475) =< 2*V1+1 s(7100) =< V s(7101) =< 2*V s(7102) =< 2/3*V s(7103) =< 2/5*V s(7104) =< 3/4*V s(7105) =< 3/5*V s(7106) =< 4/5*V s(7107) =< 4/7*V s(7108) =< 4/9*V aux(477) =< V1 aux(478) =< 2*V1 aux(479) =< 2/3*V1 aux(480) =< 2/5*V1 aux(481) =< 3/4*V1 aux(482) =< 3/5*V1 aux(483) =< 4/5*V1 aux(484) =< 4/7*V1 aux(485) =< 4/9*V1 s(7150) =< aux(478) s(7204) =< s(7150)*aux(478) s(7064) =< aux(477) s(7065) =< aux(477) s(7066) =< aux(477) s(7067) =< aux(477) s(7068) =< aux(477) s(7069) =< aux(477) s(7070) =< aux(477) s(7071) =< aux(477) s(7072) =< aux(477) s(7073) =< aux(477) s(7068) =< aux(479) s(7069) =< aux(479) s(7071) =< aux(479) s(7073) =< aux(479) s(7066) =< aux(480) s(7065) =< aux(481) s(7064) =< aux(482) s(7072) =< aux(483) s(7073) =< aux(483) s(7071) =< aux(484) s(7073) =< aux(484) s(7067) =< aux(485) s(7069) =< aux(485) s(7074) =< aux(478)+1 s(7075) =< aux(478)+2 s(7076) =< aux(478)+3 s(7077) =< aux(478) s(7078) =< aux(478)-1 s(7079) =< s(7070)*s(7074) s(7080) =< s(7070)*s(7075) s(7081) =< s(7070)*s(7076) s(7082) =< s(7073)*s(7077) s(7083) =< s(7071)*s(7078) s(7084) =< s(7068)*s(7077) s(7085) =< s(7069)*s(7078) s(7086) =< s(7069)*s(7077) s(7087) =< s(7067)*s(7074) s(7088) =< s(7066)*s(7077) s(7089) =< s(7079) s(7090) =< s(7081) s(7091) =< s(7090)*s(7076) s(7092) =< s(7081) s(7093) =< s(7081) s(7092) =< s(7080) s(7093) =< s(7080) s(7094) =< s(7093)*s(7076) s(7095) =< s(7092) s(7096) =< s(7087) s(7097) =< s(7096)*s(7074) s(7098) =< s(7088) s(7099) =< s(7098)*aux(478) s(7146) =< aux(475) s(7148) =< aux(478) s(7149) =< aux(478) s(7148) =< aux(475) s(7149) =< aux(475) s(7151) =< s(7149)*aux(478) s(7152) =< s(7148) s(7109) =< s(7100) s(7110) =< s(7100) s(7111) =< s(7100) s(7112) =< s(7100) s(7113) =< s(7100) s(7114) =< s(7100) s(7115) =< s(7100) s(7116) =< s(7100) s(7117) =< s(7100) s(7118) =< s(7100) s(7113) =< s(7102) s(7114) =< s(7102) s(7116) =< s(7102) s(7118) =< s(7102) s(7111) =< s(7103) s(7110) =< s(7104) s(7109) =< s(7105) s(7117) =< s(7106) s(7118) =< s(7106) s(7116) =< s(7107) s(7118) =< s(7107) s(7112) =< s(7108) s(7114) =< s(7108) s(7119) =< s(7101)+1 s(7120) =< s(7101)+2 s(7121) =< s(7101)+3 s(7122) =< s(7101) s(7123) =< s(7101)-1 s(7124) =< s(7115)*s(7119) s(7125) =< s(7115)*s(7120) s(7126) =< s(7115)*s(7121) s(7127) =< s(7118)*s(7122) s(7128) =< s(7116)*s(7123) s(7129) =< s(7113)*s(7122) s(7130) =< s(7114)*s(7123) s(7131) =< s(7114)*s(7122) s(7132) =< s(7112)*s(7119) s(7133) =< s(7111)*s(7122) s(7134) =< s(7124) s(7135) =< s(7126) s(7136) =< s(7135)*s(7121) s(7137) =< s(7126) s(7138) =< s(7126) s(7137) =< s(7125) s(7138) =< s(7125) s(7139) =< s(7138)*s(7121) s(7140) =< s(7137) s(7141) =< s(7132) s(7142) =< s(7141)*s(7119) s(7143) =< s(7133) s(7144) =< s(7143)*s(7101) with precondition: [1>=Out,V>=1,Out>=0,2*V1>=3] * Chain [95]: 1*s(7215)+1*s(7216)+4*s(7217)+4*s(7218)+2*s(7219)+4*s(7220)+10*s(7221)+1*s(7222)+1*s(7223)+4*s(7224)+1*s(7233)+1*s(7234)+2*s(7235)+1*s(7236)+1*s(7237)+16*s(7240)+55*s(7241)+2*s(7242)+33*s(7244)+3*s(7245)+6*s(7246)+19*s(7247)+1*s(7248)+20*s(7249)+1*s(7250)+1*s(7260)+1*s(7261)+4*s(7262)+4*s(7263)+2*s(7264)+4*s(7265)+10*s(7266)+1*s(7267)+1*s(7268)+4*s(7269)+1*s(7278)+1*s(7279)+2*s(7280)+1*s(7281)+1*s(7282)+16*s(7285)+55*s(7286)+2*s(7287)+33*s(7289)+3*s(7290)+6*s(7291)+19*s(7292)+1*s(7293)+20*s(7294)+1*s(7295)+1*s(7297)+6*s(7299)+11*s(7301)+1*s(7302)+2*s(7303)+4 Such that:s(7206) =< V1 s(7208) =< 2/3*V1 s(7209) =< 2/5*V1 s(7210) =< 3/4*V1 s(7211) =< 3/5*V1 s(7212) =< 4/5*V1 s(7213) =< 4/7*V1 s(7214) =< 4/9*V1 s(7251) =< V s(7252) =< 2*V s(7253) =< 2/3*V s(7254) =< 2/5*V s(7255) =< 3/4*V s(7256) =< 3/5*V s(7257) =< 4/5*V s(7258) =< 4/7*V s(7259) =< 4/9*V aux(486) =< 2*V1 aux(487) =< 2*V1+1 s(7297) =< aux(487) s(7299) =< aux(486) s(7300) =< aux(486) s(7301) =< aux(486) s(7300) =< aux(487) s(7301) =< aux(487) s(7302) =< s(7301)*aux(486) s(7303) =< s(7300) s(7260) =< s(7251) s(7261) =< s(7251) s(7262) =< s(7251) s(7263) =< s(7251) s(7264) =< s(7251) s(7265) =< s(7251) s(7266) =< s(7251) s(7267) =< s(7251) s(7268) =< s(7251) s(7269) =< s(7251) s(7264) =< s(7253) s(7265) =< s(7253) s(7267) =< s(7253) s(7269) =< s(7253) s(7262) =< s(7254) s(7261) =< s(7255) s(7260) =< s(7256) s(7268) =< s(7257) s(7269) =< s(7257) s(7267) =< s(7258) s(7269) =< s(7258) s(7263) =< s(7259) s(7265) =< s(7259) s(7270) =< s(7252)+1 s(7271) =< s(7252)+2 s(7272) =< s(7252)+3 s(7273) =< s(7252) s(7274) =< s(7252)-1 s(7275) =< s(7266)*s(7270) s(7276) =< s(7266)*s(7271) s(7277) =< s(7266)*s(7272) s(7278) =< s(7269)*s(7273) s(7279) =< s(7267)*s(7274) s(7280) =< s(7264)*s(7273) s(7281) =< s(7265)*s(7274) s(7282) =< s(7265)*s(7273) s(7283) =< s(7263)*s(7270) s(7284) =< s(7262)*s(7273) s(7285) =< s(7275) s(7286) =< s(7277) s(7287) =< s(7286)*s(7272) s(7288) =< s(7277) s(7289) =< s(7277) s(7288) =< s(7276) s(7289) =< s(7276) s(7290) =< s(7289)*s(7272) s(7291) =< s(7288) s(7292) =< s(7283) s(7293) =< s(7292)*s(7270) s(7294) =< s(7284) s(7295) =< s(7294)*s(7252) s(7215) =< s(7206) s(7216) =< s(7206) s(7217) =< s(7206) s(7218) =< s(7206) s(7219) =< s(7206) s(7220) =< s(7206) s(7221) =< s(7206) s(7222) =< s(7206) s(7223) =< s(7206) s(7224) =< s(7206) s(7219) =< s(7208) s(7220) =< s(7208) s(7222) =< s(7208) s(7224) =< s(7208) s(7217) =< s(7209) s(7216) =< s(7210) s(7215) =< s(7211) s(7223) =< s(7212) s(7224) =< s(7212) s(7222) =< s(7213) s(7224) =< s(7213) s(7218) =< s(7214) s(7220) =< s(7214) s(7225) =< aux(486)+1 s(7226) =< aux(486)+2 s(7227) =< aux(486)+3 s(7228) =< aux(486) s(7229) =< aux(486)-1 s(7230) =< s(7221)*s(7225) s(7231) =< s(7221)*s(7226) s(7232) =< s(7221)*s(7227) s(7233) =< s(7224)*s(7228) s(7234) =< s(7222)*s(7229) s(7235) =< s(7219)*s(7228) s(7236) =< s(7220)*s(7229) s(7237) =< s(7220)*s(7228) s(7238) =< s(7218)*s(7225) s(7239) =< s(7217)*s(7228) s(7240) =< s(7230) s(7241) =< s(7232) s(7242) =< s(7241)*s(7227) s(7243) =< s(7232) s(7244) =< s(7232) s(7243) =< s(7231) s(7244) =< s(7231) s(7245) =< s(7244)*s(7227) s(7246) =< s(7243) s(7247) =< s(7238) s(7248) =< s(7247)*s(7225) s(7249) =< s(7239) s(7250) =< s(7249)*aux(486) with precondition: [Out>=0,2*V1>=5,2*V>=3,2*V1>=2*Out+1,2*V>=Out+1] #### Cost of chains of start(V1,V,V8): * Chain [101]: 492*s(7465)+643*s(7467)+11*s(7478)+1*s(7480)+1*s(7481)+2*s(7482)+4*s(7483)+44*s(7485)+4*s(7486)+8*s(7487)+13*s(7490)+2*s(7492)+58*s(7520)+58*s(7521)+232*s(7522)+232*s(7523)+116*s(7524)+232*s(7525)+58*s(7527)+58*s(7528)+232*s(7529)+58*s(7538)+58*s(7539)+116*s(7540)+58*s(7541)+58*s(7542)+928*s(7545)+3190*s(7546)+116*s(7547)+1914*s(7549)+174*s(7550)+348*s(7551)+1102*s(7552)+58*s(7553)+1160*s(7554)+58*s(7555)+146*s(7575)+54*s(7576)+47*s(7577)+47*s(7578)+188*s(7579)+188*s(7580)+94*s(7581)+188*s(7582)+47*s(7584)+47*s(7585)+188*s(7586)+47*s(7595)+47*s(7596)+94*s(7597)+47*s(7598)+47*s(7599)+752*s(7602)+2585*s(7603)+94*s(7604)+1551*s(7606)+141*s(7607)+282*s(7608)+893*s(7609)+47*s(7610)+940*s(7611)+47*s(7612)+162*s(7741)+18*s(7907)+18*s(7908)+72*s(7909)+72*s(7910)+36*s(7911)+72*s(7912)+180*s(7913)+18*s(7914)+18*s(7915)+72*s(7916)+18*s(7925)+18*s(7926)+36*s(7927)+18*s(7928)+18*s(7929)+288*s(7932)+990*s(7933)+36*s(7934)+594*s(7936)+54*s(7937)+108*s(7938)+342*s(7939)+18*s(7940)+360*s(7941)+18*s(7942)+6*s(8720)+2*s(8794)+22*s(8796)+2*s(8797)+4*s(8798)+66*s(8801)+6*s(8802)+12*s(8803)+88*s(8805)+8*s(8806)+16*s(8807)+2*s(8958)+4 Such that:s(8697) =< 3 s(7471) =< V1-V aux(498) =< 1 aux(499) =< 2 aux(500) =< V1 aux(501) =< V1-V+1 aux(502) =< 2*V1 aux(503) =< 2*V1+1 aux(504) =< 2/3*V1 aux(505) =< 2/5*V1 aux(506) =< 3/4*V1 aux(507) =< 3/5*V1 aux(508) =< 4/5*V1 aux(509) =< 4/7*V1 aux(510) =< 4/9*V1 aux(511) =< V aux(512) =< 2*V aux(513) =< 2/3*V aux(514) =< 2/5*V aux(515) =< 3/4*V aux(516) =< 3/5*V aux(517) =< 4/5*V aux(518) =< 4/7*V aux(519) =< 4/9*V aux(520) =< V8 aux(521) =< 2*V8 aux(522) =< 2/3*V8 aux(523) =< 2/5*V8 aux(524) =< 3/4*V8 aux(525) =< 3/5*V8 aux(526) =< 4/5*V8 aux(527) =< 4/7*V8 aux(528) =< 4/9*V8 s(7490) =< aux(498) s(7575) =< aux(499) s(7467) =< aux(500) s(7465) =< aux(511) s(7492) =< s(7467)*aux(500) s(7577) =< aux(511) s(7578) =< aux(511) s(7579) =< aux(511) s(7580) =< aux(511) s(7581) =< aux(511) s(7582) =< aux(511) s(7584) =< aux(511) s(7585) =< aux(511) s(7586) =< aux(511) s(7581) =< aux(513) s(7582) =< aux(513) s(7584) =< aux(513) s(7586) =< aux(513) s(7579) =< aux(514) s(7578) =< aux(515) s(7577) =< aux(516) s(7585) =< aux(517) s(7586) =< aux(517) s(7584) =< aux(518) s(7586) =< aux(518) s(7580) =< aux(519) s(7582) =< aux(519) s(7587) =< aux(512)+1 s(7588) =< aux(512)+2 s(7589) =< aux(512)+3 s(7590) =< aux(512) s(7591) =< aux(512)-1 s(7592) =< s(7465)*s(7587) s(7593) =< s(7465)*s(7588) s(7594) =< s(7465)*s(7589) s(7595) =< s(7586)*s(7590) s(7596) =< s(7584)*s(7591) s(7597) =< s(7581)*s(7590) s(7598) =< s(7582)*s(7591) s(7599) =< s(7582)*s(7590) s(7600) =< s(7580)*s(7587) s(7601) =< s(7579)*s(7590) s(7602) =< s(7592) s(7603) =< s(7594) s(7604) =< s(7603)*s(7589) s(7605) =< s(7594) s(7606) =< s(7594) s(7605) =< s(7593) s(7606) =< s(7593) s(7607) =< s(7606)*s(7589) s(7608) =< s(7605) s(7609) =< s(7600) s(7610) =< s(7609)*s(7587) s(7611) =< s(7601) s(7612) =< s(7611)*aux(512) s(7520) =< aux(500) s(7521) =< aux(500) s(7522) =< aux(500) s(7523) =< aux(500) s(7524) =< aux(500) s(7525) =< aux(500) s(7527) =< aux(500) s(7528) =< aux(500) s(7529) =< aux(500) s(7524) =< aux(504) s(7525) =< aux(504) s(7527) =< aux(504) s(7529) =< aux(504) s(7522) =< aux(505) s(7521) =< aux(506) s(7520) =< aux(507) s(7528) =< aux(508) s(7529) =< aux(508) s(7527) =< aux(509) s(7529) =< aux(509) s(7523) =< aux(510) s(7525) =< aux(510) s(7530) =< aux(502)+1 s(7531) =< aux(502)+2 s(7532) =< aux(502)+3 s(7533) =< aux(502) s(7534) =< aux(502)-1 s(7535) =< s(7467)*s(7530) s(7536) =< s(7467)*s(7531) s(7537) =< s(7467)*s(7532) s(7538) =< s(7529)*s(7533) s(7539) =< s(7527)*s(7534) s(7540) =< s(7524)*s(7533) s(7541) =< s(7525)*s(7534) s(7542) =< s(7525)*s(7533) s(7543) =< s(7523)*s(7530) s(7544) =< s(7522)*s(7533) s(7545) =< s(7535) s(7546) =< s(7537) s(7547) =< s(7546)*s(7532) s(7548) =< s(7537) s(7549) =< s(7537) s(7548) =< s(7536) s(7549) =< s(7536) s(7550) =< s(7549)*s(7532) s(7551) =< s(7548) s(7552) =< s(7543) s(7553) =< s(7552)*s(7530) s(7554) =< s(7544) s(7555) =< s(7554)*aux(502) s(7741) =< aux(502) s(8720) =< s(7741)*aux(502) s(8794) =< s(7575)*aux(499) s(8795) =< aux(499) s(8796) =< aux(499) s(8795) =< aux(498) s(8796) =< aux(498) s(8797) =< s(8796)*aux(499) s(8798) =< s(8795) s(7576) =< aux(512) s(8800) =< aux(499) s(8801) =< aux(499) s(8800) =< s(8697) s(8801) =< s(8697) s(8802) =< s(8801)*aux(499) s(8803) =< s(8800) s(8804) =< aux(502) s(8805) =< aux(502) s(8804) =< aux(503) s(8805) =< aux(503) s(8806) =< s(8805)*aux(502) s(8807) =< s(8804) s(8958) =< aux(503) s(7477) =< aux(500) s(7478) =< aux(500) s(7479) =< aux(500) s(7480) =< aux(500) s(7477) =< aux(501) s(7478) =< aux(501) s(7477) =< s(7471) s(7478) =< s(7471) s(7479) =< s(7471) s(7480) =< s(7471) s(7481) =< s(7478)*aux(500) s(7482) =< s(7477) s(7483) =< s(7479) s(7484) =< aux(500) s(7485) =< aux(500) s(7484) =< aux(501) s(7485) =< aux(501) s(7486) =< s(7485)*aux(500) s(7487) =< s(7484) s(7907) =< aux(520) s(7908) =< aux(520) s(7909) =< aux(520) s(7910) =< aux(520) s(7911) =< aux(520) s(7912) =< aux(520) s(7913) =< aux(520) s(7914) =< aux(520) s(7915) =< aux(520) s(7916) =< aux(520) s(7911) =< aux(522) s(7912) =< aux(522) s(7914) =< aux(522) s(7916) =< aux(522) s(7909) =< aux(523) s(7908) =< aux(524) s(7907) =< aux(525) s(7915) =< aux(526) s(7916) =< aux(526) s(7914) =< aux(527) s(7916) =< aux(527) s(7910) =< aux(528) s(7912) =< aux(528) s(7917) =< aux(521)+1 s(7918) =< aux(521)+2 s(7919) =< aux(521)+3 s(7920) =< aux(521) s(7921) =< aux(521)-1 s(7922) =< s(7913)*s(7917) s(7923) =< s(7913)*s(7918) s(7924) =< s(7913)*s(7919) s(7925) =< s(7916)*s(7920) s(7926) =< s(7914)*s(7921) s(7927) =< s(7911)*s(7920) s(7928) =< s(7912)*s(7921) s(7929) =< s(7912)*s(7920) s(7930) =< s(7910)*s(7917) s(7931) =< s(7909)*s(7920) s(7932) =< s(7922) s(7933) =< s(7924) s(7934) =< s(7933)*s(7919) s(7935) =< s(7924) s(7936) =< s(7924) s(7935) =< s(7923) s(7936) =< s(7923) s(7937) =< s(7936)*s(7919) s(7938) =< s(7935) s(7939) =< s(7930) s(7940) =< s(7939)*s(7917) s(7941) =< s(7931) s(7942) =< s(7941)*aux(521) with precondition: [] Closed-form bounds of start(V1,V,V8): ------------------------------------- * Chain [101] with precondition: [] - Upper bound: nat(V1)*23043+557+nat(V1)*7*nat(V1)+nat(V1)*116*nat(nat(2*V1)+ -1)+nat(V1)*10730*nat(2*V1)+nat(V1)*406*nat(2*V1)*nat(2*V1)+nat(V)*18587+nat(V)*94*nat(nat(2*V)+ -1)+nat(V)*8695*nat(2*V)+nat(V)*329*nat(2*V)*nat(2*V)+nat(V8)*7110+nat(V8)*36*nat(nat(2*V8)+ -1)+nat(V8)*3330*nat(2*V8)+nat(V8)*126*nat(2*V8)*nat(2*V8)+nat(2*V1)*266+nat(2*V1)*14*nat(2*V1)+nat(2*V)*54+nat(2*V1+1)*2 - Complexity: n^3 ### Maximum cost of start(V1,V,V8): nat(V1)*23043+557+nat(V1)*7*nat(V1)+nat(V1)*116*nat(nat(2*V1)+ -1)+nat(V1)*10730*nat(2*V1)+nat(V1)*406*nat(2*V1)*nat(2*V1)+nat(V)*18587+nat(V)*94*nat(nat(2*V)+ -1)+nat(V)*8695*nat(2*V)+nat(V)*329*nat(2*V)*nat(2*V)+nat(V8)*7110+nat(V8)*36*nat(nat(2*V8)+ -1)+nat(V8)*3330*nat(2*V8)+nat(V8)*126*nat(2*V8)*nat(2*V8)+nat(2*V1)*266+nat(2*V1)*14*nat(2*V1)+nat(2*V)*54+nat(2*V1+1)*2 Asymptotic class: n^3 * Total analysis performed in 30922 ms. ---------------------------------------- (16) BOUNDS(1, n^3) ---------------------------------------- (17) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (18) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: leq(0', y) -> true leq(s(x), 0') -> false leq(s(x), s(y)) -> leq(x, y) if(true, x, y) -> x if(false, x, y) -> y -(x, 0') -> x -(s(x), s(y)) -> -(x, y) mod(0', y) -> 0' mod(s(x), 0') -> 0' mod(s(x), s(y)) -> if(leq(y, x), mod(-(s(x), s(y)), s(y)), s(x)) The (relative) TRS S consists of the following rules: encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_leq(x_1, x_2)) -> leq(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)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_mod(x_1, x_2)) -> mod(encArg(x_1), encArg(x_2)) encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_mod(x_1, x_2) -> mod(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (19) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (20) Obligation: Innermost TRS: Rules: leq(0', y) -> true leq(s(x), 0') -> false leq(s(x), s(y)) -> leq(x, y) if(true, x, y) -> x if(false, x, y) -> y -(x, 0') -> x -(s(x), s(y)) -> -(x, y) mod(0', y) -> 0' mod(s(x), 0') -> 0' mod(s(x), s(y)) -> if(leq(y, x), mod(-(s(x), s(y)), s(y)), s(x)) encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_leq(x_1, x_2)) -> leq(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)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_mod(x_1, x_2)) -> mod(encArg(x_1), encArg(x_2)) encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_mod(x_1, x_2) -> mod(encArg(x_1), encArg(x_2)) Types: leq :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod 0' :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod true :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod s :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod false :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod if :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod - :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod mod :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encArg :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_leq :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_if :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_- :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_mod :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_leq :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_0 :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_true :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_s :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_false :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_if :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_- :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_mod :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod hole_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod1_4 :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4 :: Nat -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod ---------------------------------------- (21) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: leq, -, mod, encArg They will be analysed ascendingly in the following order: leq < mod leq < encArg - < mod - < encArg mod < encArg ---------------------------------------- (22) Obligation: Innermost TRS: Rules: leq(0', y) -> true leq(s(x), 0') -> false leq(s(x), s(y)) -> leq(x, y) if(true, x, y) -> x if(false, x, y) -> y -(x, 0') -> x -(s(x), s(y)) -> -(x, y) mod(0', y) -> 0' mod(s(x), 0') -> 0' mod(s(x), s(y)) -> if(leq(y, x), mod(-(s(x), s(y)), s(y)), s(x)) encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_leq(x_1, x_2)) -> leq(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)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_mod(x_1, x_2)) -> mod(encArg(x_1), encArg(x_2)) encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_mod(x_1, x_2) -> mod(encArg(x_1), encArg(x_2)) Types: leq :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod 0' :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod true :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod s :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod false :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod if :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod - :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod mod :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encArg :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_leq :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_if :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_- :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_mod :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_leq :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_0 :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_true :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_s :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_false :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_if :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_- :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_mod :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod hole_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod1_4 :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4 :: Nat -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod Generator Equations: gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(0) <=> 0' gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(+(x, 1)) <=> s(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(x)) The following defined symbols remain to be analysed: leq, -, mod, encArg They will be analysed ascendingly in the following order: leq < mod leq < encArg - < mod - < encArg mod < encArg ---------------------------------------- (23) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: leq(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n4_4), gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n4_4)) -> true, rt in Omega(1 + n4_4) Induction Base: leq(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(0), gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(0)) ->_R^Omega(1) true Induction Step: leq(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(+(n4_4, 1)), gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(+(n4_4, 1))) ->_R^Omega(1) leq(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n4_4), gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_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). ---------------------------------------- (24) Complex Obligation (BEST) ---------------------------------------- (25) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: leq(0', y) -> true leq(s(x), 0') -> false leq(s(x), s(y)) -> leq(x, y) if(true, x, y) -> x if(false, x, y) -> y -(x, 0') -> x -(s(x), s(y)) -> -(x, y) mod(0', y) -> 0' mod(s(x), 0') -> 0' mod(s(x), s(y)) -> if(leq(y, x), mod(-(s(x), s(y)), s(y)), s(x)) encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_leq(x_1, x_2)) -> leq(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)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_mod(x_1, x_2)) -> mod(encArg(x_1), encArg(x_2)) encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_mod(x_1, x_2) -> mod(encArg(x_1), encArg(x_2)) Types: leq :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod 0' :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod true :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod s :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod false :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod if :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod - :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod mod :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encArg :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_leq :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_if :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_- :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_mod :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_leq :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_0 :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_true :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_s :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_false :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_if :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_- :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_mod :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod hole_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod1_4 :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4 :: Nat -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod Generator Equations: gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(0) <=> 0' gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(+(x, 1)) <=> s(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(x)) The following defined symbols remain to be analysed: leq, -, mod, encArg They will be analysed ascendingly in the following order: leq < mod leq < encArg - < mod - < encArg mod < encArg ---------------------------------------- (26) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (27) BOUNDS(n^1, INF) ---------------------------------------- (28) Obligation: Innermost TRS: Rules: leq(0', y) -> true leq(s(x), 0') -> false leq(s(x), s(y)) -> leq(x, y) if(true, x, y) -> x if(false, x, y) -> y -(x, 0') -> x -(s(x), s(y)) -> -(x, y) mod(0', y) -> 0' mod(s(x), 0') -> 0' mod(s(x), s(y)) -> if(leq(y, x), mod(-(s(x), s(y)), s(y)), s(x)) encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_leq(x_1, x_2)) -> leq(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)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_mod(x_1, x_2)) -> mod(encArg(x_1), encArg(x_2)) encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_mod(x_1, x_2) -> mod(encArg(x_1), encArg(x_2)) Types: leq :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod 0' :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod true :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod s :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod false :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod if :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod - :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod mod :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encArg :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_leq :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_if :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_- :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_mod :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_leq :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_0 :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_true :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_s :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_false :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_if :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_- :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_mod :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod hole_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod1_4 :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4 :: Nat -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod Lemmas: leq(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n4_4), gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n4_4)) -> true, rt in Omega(1 + n4_4) Generator Equations: gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(0) <=> 0' gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(+(x, 1)) <=> s(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(x)) The following defined symbols remain to be analysed: -, mod, encArg They will be analysed ascendingly in the following order: - < mod - < encArg mod < encArg ---------------------------------------- (29) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: -(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n503_4), gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n503_4)) -> gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(0), rt in Omega(1 + n503_4) Induction Base: -(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(0), gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(0)) ->_R^Omega(1) gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(0) Induction Step: -(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(+(n503_4, 1)), gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(+(n503_4, 1))) ->_R^Omega(1) -(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n503_4), gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n503_4)) ->_IH gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(0) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (30) Obligation: Innermost TRS: Rules: leq(0', y) -> true leq(s(x), 0') -> false leq(s(x), s(y)) -> leq(x, y) if(true, x, y) -> x if(false, x, y) -> y -(x, 0') -> x -(s(x), s(y)) -> -(x, y) mod(0', y) -> 0' mod(s(x), 0') -> 0' mod(s(x), s(y)) -> if(leq(y, x), mod(-(s(x), s(y)), s(y)), s(x)) encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_leq(x_1, x_2)) -> leq(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)) encArg(cons_-(x_1, x_2)) -> -(encArg(x_1), encArg(x_2)) encArg(cons_mod(x_1, x_2)) -> mod(encArg(x_1), encArg(x_2)) encode_leq(x_1, x_2) -> leq(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_-(x_1, x_2) -> -(encArg(x_1), encArg(x_2)) encode_mod(x_1, x_2) -> mod(encArg(x_1), encArg(x_2)) Types: leq :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod 0' :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod true :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod s :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod false :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod if :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod - :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod mod :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encArg :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_leq :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_if :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_- :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod cons_mod :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_leq :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_0 :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_true :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_s :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_false :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_if :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_- :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod encode_mod :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod hole_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod1_4 :: 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4 :: Nat -> 0':true:s:false:cons_leq:cons_if:cons_-:cons_mod Lemmas: leq(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n4_4), gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n4_4)) -> true, rt in Omega(1 + n4_4) -(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n503_4), gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n503_4)) -> gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(0), rt in Omega(1 + n503_4) Generator Equations: gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(0) <=> 0' gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(+(x, 1)) <=> s(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(x)) The following defined symbols remain to be analysed: mod, encArg They will be analysed ascendingly in the following order: mod < encArg ---------------------------------------- (31) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n1317_4)) -> gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n1317_4), rt in Omega(0) Induction Base: encArg(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(0)) ->_R^Omega(0) 0' Induction Step: encArg(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(+(n1317_4, 1))) ->_R^Omega(0) s(encArg(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(n1317_4))) ->_IH s(gen_0':true:s:false:cons_leq:cons_if:cons_-:cons_mod2_4(c1318_4)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (32) BOUNDS(1, INF)