/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 207 ms] (4) CpxRelTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 32.4 s] (14) BOUNDS(1, n^3) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRelTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 0 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 260 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 343 ms] (28) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: p(0) -> 0 p(s(x)) -> x le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) minus(x, 0) -> x minus(x, s(y)) -> if(le(x, s(y)), 0, p(minus(x, p(s(y))))) if(true, x, y) -> x if(false, x, y) -> y S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: p(0) -> 0 p(s(x)) -> x le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) minus(x, 0) -> x minus(x, s(y)) -> if(le(x, s(y)), 0, p(minus(x, p(s(y))))) if(true, x, y) -> x if(false, x, y) -> y The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: p(0) -> 0 p(s(x)) -> x le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) minus(x, 0) -> x minus(x, s(y)) -> if(le(x, s(y)), 0, p(minus(x, p(s(y))))) if(true, x, y) -> x if(false, x, y) -> y The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). The TRS R consists of the following rules: p(0) -> 0 [1] p(s(x)) -> x [1] le(0, y) -> true [1] le(s(x), 0) -> false [1] le(s(x), s(y)) -> le(x, y) [1] minus(x, 0) -> x [1] minus(x, s(y)) -> if(le(x, s(y)), 0, p(minus(x, p(s(y))))) [1] if(true, x, y) -> x [1] if(false, x, y) -> y [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) [0] encode_true -> true [0] encode_false -> false [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: p(0) -> 0 [1] p(s(x)) -> x [1] le(0, y) -> true [1] le(s(x), 0) -> false [1] le(s(x), s(y)) -> le(x, y) [1] minus(x, 0) -> x [1] minus(x, s(y)) -> if(le(x, s(y)), 0, p(minus(x, p(s(y))))) [1] if(true, x, y) -> x [1] if(false, x, y) -> y [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) [0] encode_true -> true [0] encode_false -> false [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] The TRS has the following type information: p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if 0 :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if s :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if true :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if false :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if minus :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encArg :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if cons_p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if cons_le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if cons_minus :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if cons_if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_0 :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_s :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_true :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_false :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_minus :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if encode_if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if Rewrite Strategy: INNERMOST ---------------------------------------- (9) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: encArg(v0) -> null_encArg [0] encode_p(v0) -> null_encode_p [0] encode_0 -> null_encode_0 [0] encode_s(v0) -> null_encode_s [0] encode_le(v0, v1) -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_minus(v0, v1) -> null_encode_minus [0] encode_if(v0, v1, v2) -> null_encode_if [0] p(v0) -> null_p [0] le(v0, v1) -> null_le [0] minus(v0, v1) -> null_minus [0] if(v0, v1, v2) -> null_if [0] And the following fresh constants: null_encArg, null_encode_p, null_encode_0, null_encode_s, null_encode_le, null_encode_true, null_encode_false, null_encode_minus, null_encode_if, null_p, null_le, null_minus, null_if ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: p(0) -> 0 [1] p(s(x)) -> x [1] le(0, y) -> true [1] le(s(x), 0) -> false [1] le(s(x), s(y)) -> le(x, y) [1] minus(x, 0) -> x [1] minus(x, s(y)) -> if(le(x, s(y)), 0, p(minus(x, p(s(y))))) [1] if(true, x, y) -> x [1] if(false, x, y) -> y [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) [0] encode_true -> true [0] encode_false -> false [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(v0) -> null_encArg [0] encode_p(v0) -> null_encode_p [0] encode_0 -> null_encode_0 [0] encode_s(v0) -> null_encode_s [0] encode_le(v0, v1) -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_minus(v0, v1) -> null_encode_minus [0] encode_if(v0, v1, v2) -> null_encode_if [0] p(v0) -> null_p [0] le(v0, v1) -> null_le [0] minus(v0, v1) -> null_minus [0] if(v0, v1, v2) -> null_if [0] The TRS has the following type information: p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if 0 :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if s :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if true :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if false :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if minus :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if encArg :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if cons_p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if cons_le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if cons_minus :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if cons_if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if encode_p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if encode_0 :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if encode_s :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if encode_le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if encode_true :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if encode_false :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if encode_minus :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if encode_if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if -> 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if null_encArg :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if null_encode_p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if null_encode_0 :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if null_encode_s :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if null_encode_le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if null_encode_true :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if null_encode_false :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if null_encode_minus :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if null_encode_if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if null_p :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if null_le :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if null_minus :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if null_if :: 0:s:true:false:cons_p:cons_le:cons_minus:cons_if:null_encArg:null_encode_p:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_minus:null_encode_if:null_p:null_le:null_minus:null_if Rewrite Strategy: INNERMOST ---------------------------------------- (11) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 true => 2 false => 1 null_encArg => 0 null_encode_p => 0 null_encode_0 => 0 null_encode_s => 0 null_encode_le => 0 null_encode_true => 0 null_encode_false => 0 null_encode_minus => 0 null_encode_if => 0 null_p => 0 null_le => 0 null_minus => 0 null_if => 0 ---------------------------------------- (12) Obligation: Complexity RNTS consisting of the following rules: encArg(z) -{ 0 }-> p(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> minus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> le(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encArg(z) -{ 0 }-> 2 :|: z = 2 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0 encode_0 -{ 0 }-> 0 :|: encode_false -{ 0 }-> 1 :|: encode_false -{ 0 }-> 0 :|: encode_if(z, z', z'') -{ 0 }-> if(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3 encode_if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_le(z, z') -{ 0 }-> le(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_le(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_minus(z, z') -{ 0 }-> minus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_p(z) -{ 0 }-> p(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_s(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 encode_true -{ 0 }-> 2 :|: encode_true -{ 0 }-> 0 :|: if(z, z', z'') -{ 1 }-> 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 le(z, z') -{ 1 }-> le(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x le(z, z') -{ 1 }-> 2 :|: y >= 0, z = 0, z' = y le(z, z') -{ 1 }-> 1 :|: x >= 0, z = 1 + x, z' = 0 le(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 minus(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0 minus(z, z') -{ 1 }-> if(le(x, 1 + y), 0, p(minus(x, p(1 + y)))) :|: z' = 1 + y, x >= 0, y >= 0, z = x minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 p(z) -{ 1 }-> x :|: x >= 0, z = 1 + x p(z) -{ 1 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (13) CompleteCoflocoProof (FINISHED) Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: eq(start(V, V2, V11),0,[p(V, Out)],[V >= 0]). eq(start(V, V2, V11),0,[le(V, V2, Out)],[V >= 0,V2 >= 0]). eq(start(V, V2, V11),0,[minus(V, V2, Out)],[V >= 0,V2 >= 0]). eq(start(V, V2, V11),0,[if(V, V2, V11, Out)],[V >= 0,V2 >= 0,V11 >= 0]). eq(start(V, V2, V11),0,[encArg(V, Out)],[V >= 0]). eq(start(V, V2, V11),0,[fun(V, Out)],[V >= 0]). eq(start(V, V2, V11),0,[fun1(Out)],[]). eq(start(V, V2, V11),0,[fun2(V, Out)],[V >= 0]). eq(start(V, V2, V11),0,[fun3(V, V2, Out)],[V >= 0,V2 >= 0]). eq(start(V, V2, V11),0,[fun4(Out)],[]). eq(start(V, V2, V11),0,[fun5(Out)],[]). eq(start(V, V2, V11),0,[fun6(V, V2, Out)],[V >= 0,V2 >= 0]). eq(start(V, V2, V11),0,[fun7(V, V2, V11, Out)],[V >= 0,V2 >= 0,V11 >= 0]). eq(p(V, Out),1,[],[Out = 0,V = 0]). eq(p(V, Out),1,[],[Out = V1,V1 >= 0,V = 1 + V1]). eq(le(V, V2, Out),1,[],[Out = 2,V3 >= 0,V = 0,V2 = V3]). eq(le(V, V2, Out),1,[],[Out = 1,V4 >= 0,V = 1 + V4,V2 = 0]). eq(le(V, V2, Out),1,[le(V5, V6, Ret)],[Out = Ret,V2 = 1 + V6,V5 >= 0,V6 >= 0,V = 1 + V5]). eq(minus(V, V2, Out),1,[],[Out = V7,V7 >= 0,V = V7,V2 = 0]). eq(minus(V, V2, Out),1,[le(V8, 1 + V9, Ret0),p(1 + V9, Ret201),minus(V8, Ret201, Ret20),p(Ret20, Ret2),if(Ret0, 0, Ret2, Ret1)],[Out = Ret1,V2 = 1 + V9,V8 >= 0,V9 >= 0,V = V8]). eq(if(V, V2, V11, Out),1,[],[Out = V12,V = 2,V2 = V12,V11 = V10,V12 >= 0,V10 >= 0]). eq(if(V, V2, V11, Out),1,[],[Out = V13,V2 = V14,V11 = V13,V = 1,V14 >= 0,V13 >= 0]). eq(encArg(V, Out),0,[],[Out = 0,V = 0]). eq(encArg(V, Out),0,[encArg(V15, Ret11)],[Out = 1 + Ret11,V = 1 + V15,V15 >= 0]). eq(encArg(V, Out),0,[],[Out = 2,V = 2]). eq(encArg(V, Out),0,[],[Out = 1,V = 1]). eq(encArg(V, Out),0,[encArg(V16, Ret01),p(Ret01, Ret3)],[Out = Ret3,V = 1 + V16,V16 >= 0]). eq(encArg(V, Out),0,[encArg(V17, Ret02),encArg(V18, Ret12),le(Ret02, Ret12, Ret4)],[Out = Ret4,V17 >= 0,V = 1 + V17 + V18,V18 >= 0]). eq(encArg(V, Out),0,[encArg(V20, Ret03),encArg(V19, Ret13),minus(Ret03, Ret13, Ret5)],[Out = Ret5,V20 >= 0,V = 1 + V19 + V20,V19 >= 0]). eq(encArg(V, Out),0,[encArg(V23, Ret04),encArg(V22, Ret14),encArg(V21, Ret21),if(Ret04, Ret14, Ret21, Ret6)],[Out = Ret6,V23 >= 0,V = 1 + V21 + V22 + V23,V21 >= 0,V22 >= 0]). eq(fun(V, Out),0,[encArg(V24, Ret05),p(Ret05, Ret7)],[Out = Ret7,V24 >= 0,V = V24]). eq(fun1(Out),0,[],[Out = 0]). eq(fun2(V, Out),0,[encArg(V25, Ret15)],[Out = 1 + Ret15,V25 >= 0,V = V25]). eq(fun3(V, V2, Out),0,[encArg(V27, Ret06),encArg(V26, Ret16),le(Ret06, Ret16, Ret8)],[Out = Ret8,V27 >= 0,V26 >= 0,V = V27,V2 = V26]). eq(fun4(Out),0,[],[Out = 2]). eq(fun5(Out),0,[],[Out = 1]). eq(fun6(V, V2, Out),0,[encArg(V29, Ret07),encArg(V28, Ret17),minus(Ret07, Ret17, Ret9)],[Out = Ret9,V29 >= 0,V28 >= 0,V = V29,V2 = V28]). eq(fun7(V, V2, V11, Out),0,[encArg(V30, Ret08),encArg(V32, Ret18),encArg(V31, Ret22),if(Ret08, Ret18, Ret22, Ret10)],[Out = Ret10,V30 >= 0,V31 >= 0,V32 >= 0,V = V30,V2 = V32,V11 = V31]). eq(encArg(V, Out),0,[],[Out = 0,V33 >= 0,V = V33]). eq(fun(V, Out),0,[],[Out = 0,V34 >= 0,V = V34]). eq(fun2(V, Out),0,[],[Out = 0,V35 >= 0,V = V35]). eq(fun3(V, V2, Out),0,[],[Out = 0,V36 >= 0,V37 >= 0,V = V36,V2 = V37]). eq(fun4(Out),0,[],[Out = 0]). eq(fun5(Out),0,[],[Out = 0]). eq(fun6(V, V2, Out),0,[],[Out = 0,V38 >= 0,V39 >= 0,V = V38,V2 = V39]). eq(fun7(V, V2, V11, Out),0,[],[Out = 0,V40 >= 0,V11 = V42,V41 >= 0,V = V40,V2 = V41,V42 >= 0]). eq(p(V, Out),0,[],[Out = 0,V43 >= 0,V = V43]). eq(le(V, V2, Out),0,[],[Out = 0,V44 >= 0,V45 >= 0,V = V44,V2 = V45]). eq(minus(V, V2, Out),0,[],[Out = 0,V46 >= 0,V47 >= 0,V = V46,V2 = V47]). eq(if(V, V2, V11, Out),0,[],[Out = 0,V49 >= 0,V11 = V50,V48 >= 0,V = V49,V2 = V48,V50 >= 0]). input_output_vars(p(V,Out),[V],[Out]). input_output_vars(le(V,V2,Out),[V,V2],[Out]). input_output_vars(minus(V,V2,Out),[V,V2],[Out]). input_output_vars(if(V,V2,V11,Out),[V,V2,V11],[Out]). input_output_vars(encArg(V,Out),[V],[Out]). input_output_vars(fun(V,Out),[V],[Out]). input_output_vars(fun1(Out),[],[Out]). input_output_vars(fun2(V,Out),[V],[Out]). input_output_vars(fun3(V,V2,Out),[V,V2],[Out]). input_output_vars(fun4(Out),[],[Out]). input_output_vars(fun5(Out),[],[Out]). input_output_vars(fun6(V,V2,Out),[V,V2],[Out]). input_output_vars(fun7(V,V2,V11,Out),[V,V2,V11],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. non_recursive : [if/4] 1. recursive : [le/3] 2. non_recursive : [p/2] 3. recursive [non_tail] : [minus/3] 4. recursive [non_tail,multiple] : [encArg/2] 5. non_recursive : [fun/2] 6. non_recursive : [fun1/1] 7. non_recursive : [fun2/2] 8. non_recursive : [fun3/3] 9. non_recursive : [fun4/1] 10. non_recursive : [fun5/1] 11. non_recursive : [fun6/3] 12. non_recursive : [fun7/4] 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 le/3 2. SCC is partially evaluated into p/2 3. SCC is partially evaluated into minus/3 4. SCC is partially evaluated into encArg/2 5. SCC is partially evaluated into fun/2 6. SCC is completely evaluated into other SCCs 7. SCC is partially evaluated into fun2/2 8. SCC is partially evaluated into fun3/3 9. SCC is partially evaluated into fun4/1 10. SCC is partially evaluated into fun5/1 11. SCC is partially evaluated into fun6/3 12. SCC is partially evaluated into fun7/4 13. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations if/4 * CE 26 is refined into CE [49] * CE 24 is refined into CE [50] * CE 25 is refined into CE [51] ### Cost equations --> "Loop" of if/4 * CEs [49] --> Loop 29 * CEs [50] --> Loop 30 * CEs [51] --> Loop 31 ### Ranking functions of CR if(V,V2,V11,Out) #### Partial ranking functions of CR if(V,V2,V11,Out) ### Specialization of cost equations le/3 * CE 20 is refined into CE [52] * CE 18 is refined into CE [53] * CE 17 is refined into CE [54] * CE 19 is refined into CE [55] ### Cost equations --> "Loop" of le/3 * CEs [55] --> Loop 32 * CEs [52] --> Loop 33 * CEs [53] --> Loop 34 * CEs [54] --> Loop 35 ### Ranking functions of CR le(V,V2,Out) * RF of phase [32]: [V,V2] #### Partial ranking functions of CR le(V,V2,Out) * Partial RF of phase [32]: - RF of loop [32:1]: V V2 ### Specialization of cost equations p/2 * CE 15 is refined into CE [56] * CE 14 is refined into CE [57] * CE 16 is refined into CE [58] ### Cost equations --> "Loop" of p/2 * CEs [56] --> Loop 36 * CEs [57,58] --> Loop 37 ### Ranking functions of CR p(V,Out) #### Partial ranking functions of CR p(V,Out) ### Specialization of cost equations minus/3 * CE 23 is refined into CE [59] * CE 21 is refined into CE [60] * CE 22 is refined into CE [61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88] ### Cost equations --> "Loop" of minus/3 * CEs [79] --> Loop 38 * CEs [75] --> Loop 39 * CEs [65,66,67,68,71,72,77,78,80,85,86,87,88] --> Loop 40 * CEs [61,62,63,64,69,70,73,74,76,81,82,83,84] --> Loop 41 * CEs [59] --> Loop 42 * CEs [60] --> Loop 43 ### Ranking functions of CR minus(V,V2,Out) * RF of phase [38]: [V2] * RF of phase [40]: [V2] #### Partial ranking functions of CR minus(V,V2,Out) * Partial RF of phase [38]: - RF of loop [38:1]: V2 * Partial RF of phase [40]: - RF of loop [40:1]: V2 ### Specialization of cost equations encArg/2 * CE 27 is refined into CE [89] * CE 29 is refined into CE [90] * CE 30 is refined into CE [91] * CE 34 is refined into CE [92,93,94] * CE 32 is refined into CE [95,96,97,98,99] * CE 33 is refined into CE [100,101,102,103,104] * CE 28 is refined into CE [105] * CE 31 is refined into CE [106,107] ### Cost equations --> "Loop" of encArg/2 * CEs [105] --> Loop 44 * CEs [107] --> Loop 45 * CEs [106] --> Loop 46 * CEs [104] --> Loop 47 * CEs [103] --> Loop 48 * CEs [102] --> Loop 49 * CEs [100] --> Loop 50 * CEs [99] --> Loop 51 * CEs [95] --> Loop 52 * CEs [98] --> Loop 53 * CEs [96] --> Loop 54 * CEs [97,101] --> Loop 55 * CEs [93] --> Loop 56 * CEs [92] --> Loop 57 * CEs [94] --> Loop 58 * CEs [89] --> Loop 59 * CEs [90] --> Loop 60 * CEs [91] --> Loop 61 ### Ranking functions of CR encArg(V,Out) * RF of phase [44,45,46,47,48,49,50,51,52,53,54,55,56,57,58]: [V] #### Partial ranking functions of CR encArg(V,Out) * Partial RF of phase [44,45,46,47,48,49,50,51,52,53,54,55,56,57,58]: - RF of loop [44:1,45:1,46:1,47:1,47:2,48:1,48:2,49:1,49:2,50:1,50:2,51:1,51:2,52:1,52:2,53:1,53:2,54:1,54:2,55:1,55:2,56:1,56:2,56:3,57:1,57:2,57:3,58:1,58:2,58:3]: V ### Specialization of cost equations fun/2 * CE 35 is refined into CE [108,109,110,111,112] * CE 36 is refined into CE [113] ### Cost equations --> "Loop" of fun/2 * CEs [109,111] --> Loop 62 * CEs [108,110,112,113] --> Loop 63 ### Ranking functions of CR fun(V,Out) #### Partial ranking functions of CR fun(V,Out) ### Specialization of cost equations fun2/2 * CE 37 is refined into CE [114,115,116] * CE 38 is refined into CE [117] ### Cost equations --> "Loop" of fun2/2 * CEs [116] --> Loop 64 * CEs [117] --> Loop 65 * CEs [114,115] --> Loop 66 ### Ranking functions of CR fun2(V,Out) #### Partial ranking functions of CR fun2(V,Out) ### Specialization of cost equations fun3/3 * CE 39 is refined into CE [118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143] * CE 40 is refined into CE [144] ### Cost equations --> "Loop" of fun3/3 * CEs [123,126,140] --> Loop 67 * CEs [125] --> Loop 68 * CEs [124,141] --> Loop 69 * CEs [119,121,128,130,132,136] --> Loop 70 * CEs [118,122,127,133,135,138,142] --> Loop 71 * CEs [120,129,131,134,137,139,143,144] --> Loop 72 ### Ranking functions of CR fun3(V,V2,Out) #### Partial ranking functions of CR fun3(V,V2,Out) ### Specialization of cost equations fun4/1 * CE 41 is refined into CE [145] * CE 42 is refined into CE [146] ### Cost equations --> "Loop" of fun4/1 * CEs [145] --> Loop 73 * CEs [146] --> Loop 74 ### Ranking functions of CR fun4(Out) #### Partial ranking functions of CR fun4(Out) ### Specialization of cost equations fun5/1 * CE 43 is refined into CE [147] * CE 44 is refined into CE [148] ### Cost equations --> "Loop" of fun5/1 * CEs [147] --> Loop 75 * CEs [148] --> Loop 76 ### Ranking functions of CR fun5(Out) #### Partial ranking functions of CR fun5(Out) ### Specialization of cost equations fun6/3 * CE 45 is refined into CE [149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171] * CE 46 is refined into CE [172] ### Cost equations --> "Loop" of fun6/3 * CEs [155] --> Loop 77 * CEs [156,157] --> Loop 78 * CEs [154,169] --> Loop 79 * CEs [160,165] --> Loop 80 * CEs [149,151,152,153,158,162,163] --> Loop 81 * CEs [150,159,161,164,166,167,168,170,171,172] --> Loop 82 ### Ranking functions of CR fun6(V,V2,Out) #### Partial ranking functions of CR fun6(V,V2,Out) ### Specialization of cost equations fun7/4 * CE 47 is refined into CE [173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226] * CE 48 is refined into CE [227] ### Cost equations --> "Loop" of fun7/4 * CEs [176,194] --> Loop 83 * CEs [173,182,191] --> Loop 84 * CEs [183,185,186,189] --> Loop 85 * CEs [184,187,188,190,221,222,223] --> Loop 86 * CEs [177,202] --> Loop 87 * CEs [178,195,196,203,214,215,219,225] --> Loop 88 * CEs [174,180,200,204,206,208,210] --> Loop 89 * CEs [175,179,181,192,193,197,198,199,201,205,207,209,211,212,213,216,217,218,220,224,226,227] --> Loop 90 ### Ranking functions of CR fun7(V,V2,V11,Out) #### Partial ranking functions of CR fun7(V,V2,V11,Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [228,229] * CE 2 is refined into CE [230,231,232,233,234] * CE 3 is refined into CE [235,236,237,238,239] * CE 4 is refined into CE [240,241,242] * CE 5 is refined into CE [243,244,245] * CE 6 is refined into CE [246,247] * CE 7 is refined into CE [248] * CE 8 is refined into CE [249,250,251] * CE 9 is refined into CE [252,253,254] * CE 10 is refined into CE [255,256] * CE 11 is refined into CE [257,258] * CE 12 is refined into CE [259,260,261,262] * CE 13 is refined into CE [263,264,265,266,267] ### Cost equations --> "Loop" of start/3 * CEs [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] --> Loop 91 ### Ranking functions of CR start(V,V2,V11) #### Partial ranking functions of CR start(V,V2,V11) Computing Bounds ===================================== #### Cost of chains of if(V,V2,V11,Out): * Chain [31]: 1 with precondition: [V=1,V11=Out,V2>=0,V11>=0] * Chain [30]: 1 with precondition: [V=2,V2=Out,V2>=0,V11>=0] * Chain [29]: 0 with precondition: [Out=0,V>=0,V2>=0,V11>=0] #### Cost of chains of le(V,V2,Out): * Chain [[32],35]: 1*it(32)+1 Such that:it(32) =< V with precondition: [Out=2,V>=1,V2>=V] * Chain [[32],34]: 1*it(32)+1 Such that:it(32) =< V2 with precondition: [Out=1,V2>=1,V>=V2+1] * Chain [[32],33]: 1*it(32)+0 Such that:it(32) =< V2 with precondition: [Out=0,V>=1,V2>=1] * Chain [35]: 1 with precondition: [V=0,Out=2,V2>=0] * Chain [34]: 1 with precondition: [V2=0,Out=1,V>=1] * Chain [33]: 0 with precondition: [Out=0,V>=0,V2>=0] #### Cost of chains of p(V,Out): * Chain [37]: 1 with precondition: [Out=0,V>=0] * Chain [36]: 1 with precondition: [V=Out+1,V>=1] #### Cost of chains of minus(V,V2,Out): * Chain [[40],[38],43]: 10*it(38)+2*s(4)+4*s(20)+4*s(21)+1 Such that:aux(7) =< V aux(10) =< V2 it(38) =< aux(10) s(4) =< it(38)*aux(10) aux(8) =< aux(10) s(23) =< it(38)*aux(7) s(22) =< it(38)*aux(8) s(21) =< s(23) s(20) =< s(22) with precondition: [Out=0,V>=2,V2>=2] * Chain [[40],[38],39,43]: 10*it(38)+2*s(4)+4*s(20)+4*s(21)+1*s(24)+6 Such that:aux(7) =< V aux(11) =< V2 aux(12) =< V2+1 it(38) =< aux(12) s(24) =< aux(12) it(38) =< aux(11) s(4) =< it(38)*aux(11) aux(8) =< aux(11) s(23) =< it(38)*aux(7) s(22) =< it(38)*aux(8) s(21) =< s(23) s(20) =< s(22) with precondition: [Out=0,V>=3,V2>=3] * Chain [[40],43]: 5*it(40)+1*s(19)+4*s(20)+4*s(21)+1 Such that:aux(7) =< V aux(13) =< V2 it(40) =< aux(13) aux(8) =< aux(13) s(23) =< it(40)*aux(7) s(19) =< it(40)*aux(13) s(22) =< it(40)*aux(8) s(21) =< s(23) s(20) =< s(22) with precondition: [Out=0,V>=0,V2>=1] * Chain [[40],42]: 5*it(40)+1*s(19)+4*s(20)+4*s(21)+0 Such that:aux(7) =< V aux(14) =< V2 it(40) =< aux(14) aux(8) =< aux(14) s(23) =< it(40)*aux(7) s(19) =< it(40)*aux(14) s(22) =< it(40)*aux(8) s(21) =< s(23) s(20) =< s(22) with precondition: [Out=0,V>=0,V2>=1] * Chain [[40],41,43]: 10*it(40)+1*s(19)+4*s(20)+4*s(21)+4*s(30)+6 Such that:aux(17) =< V aux(18) =< V2 it(40) =< aux(18) s(30) =< aux(17) aux(8) =< aux(18) s(23) =< it(40)*aux(17) s(19) =< it(40)*aux(18) s(22) =< it(40)*aux(8) s(21) =< s(23) s(20) =< s(22) with precondition: [Out=0,V>=0,V2>=2] * Chain [[40],41,42]: 10*it(40)+1*s(19)+4*s(20)+4*s(21)+4*s(30)+5 Such that:aux(19) =< V aux(20) =< V2 it(40) =< aux(20) s(30) =< aux(19) aux(8) =< aux(20) s(23) =< it(40)*aux(19) s(19) =< it(40)*aux(20) s(22) =< it(40)*aux(8) s(21) =< s(23) s(20) =< s(22) with precondition: [Out=0,V>=0,V2>=2] * Chain [[40],39,43]: 6*it(40)+1*s(19)+4*s(20)+4*s(21)+6 Such that:aux(7) =< V aux(21) =< V2 it(40) =< aux(21) aux(8) =< aux(21) s(23) =< it(40)*aux(7) s(19) =< it(40)*aux(21) s(22) =< it(40)*aux(8) s(21) =< s(23) s(20) =< s(22) with precondition: [Out=0,V>=2,V2>=2] * Chain [[38],43]: 5*it(38)+1*s(4)+1 Such that:aux(3) =< V-Out it(38) =< aux(3) s(4) =< it(38)*aux(3) with precondition: [V=Out+V2,V2>=1,V>=V2+1] * Chain [[38],39,43]: 5*it(38)+1*s(4)+1*s(24)+6 Such that:s(24) =< -V+V2+Out+1 it(38) =< V-Out aux(2) =< V2 it(38) =< aux(2) s(4) =< it(38)*aux(2) with precondition: [V>=V2+1,V>=Out+2,Out+V2>=V] * Chain [43]: 1 with precondition: [V2=0,V=Out,V>=0] * Chain [42]: 0 with precondition: [Out=0,V>=0,V2>=0] * Chain [41,43]: 5*s(25)+4*s(30)+6 Such that:aux(15) =< V aux(16) =< V2 s(30) =< aux(15) s(25) =< aux(16) with precondition: [Out=0,V>=0,V2>=1] * Chain [41,42]: 5*s(25)+4*s(30)+5 Such that:aux(15) =< V aux(16) =< V2 s(30) =< aux(15) s(25) =< aux(16) with precondition: [Out=0,V>=0,V2>=1] * Chain [39,43]: 1*s(24)+6 Such that:s(24) =< V2 with precondition: [V=Out+1,V2>=1,V>=V2+1] #### Cost of chains of encArg(V,Out): * Chain [61]: 0 with precondition: [V=1,Out=1] * Chain [60]: 0 with precondition: [V=2,Out=2] * Chain [59]: 0 with precondition: [Out=0,V>=0] * Chain [multiple([44,45,46,47,48,49,50,51,52,53,54,55,56,57,58],[[61],[60],[59]])]: 10*it(45)+6*it(47)+7*it(48)+1*it(51)+1*it(53)+1*it(54)+1*it(56)+1*it(57)+6*s(165)+1*s(166)+5*s(168)+1*s(169)+1*s(171)+1*s(172)+1*s(173)+57*s(174)+16*s(175)+7*s(176)+24*s(177)+24*s(178)+10*s(179)+1*s(180)+2*s(181)+4*s(182)+4*s(183)+0 Such that:s(119) =< 2*V aux(49) =< V aux(50) =< 2/3*V aux(51) =< 3/4*V aux(52) =< 3/5*V aux(53) =< 4/5*V aux(54) =< 4/7*V aux(55) =< 4/9*V it(45) =< aux(49) it(47) =< aux(49) it(48) =< aux(49) it(51) =< aux(49) it(53) =< aux(49) it(54) =< aux(49) it(56) =< aux(49) it(57) =< aux(49) it(51) =< aux(50) it(53) =< aux(50) it(56) =< aux(50) it(57) =< aux(51) it(56) =< aux(52) it(54) =< aux(53) it(56) =< aux(53) it(57) =< aux(53) it(48) =< aux(54) it(53) =< aux(54) it(47) =< aux(55) aux(39) =< s(119)+3 aux(27) =< s(119)+2 aux(37) =< s(119)+4 aux(29) =< s(119) aux(33) =< s(119)+1 s(187) =< it(45)*aux(39) s(186) =< it(45)*aux(27) s(190) =< it(45)*aux(37) s(173) =< it(53)*aux(29) s(172) =< it(51)*aux(33) s(171) =< it(48)*aux(29) s(170) =< it(48)*aux(29) s(167) =< it(47)*aux(27) s(174) =< s(186) s(175) =< s(190) s(152) =< aux(27) s(189) =< s(174)*aux(37) s(176) =< s(174)*aux(27) s(188) =< s(174)*s(152) s(177) =< s(189) s(178) =< s(188) s(179) =< s(187) s(180) =< s(187) s(179) =< s(186) s(181) =< s(179)*aux(27) s(185) =< s(179)*aux(37) s(184) =< s(179)*s(152) s(182) =< s(185) s(183) =< s(184) s(168) =< s(170) s(169) =< s(168)*s(119) s(165) =< s(167) s(166) =< s(165)*aux(27) with precondition: [V>=1,Out>=0,2*V>=Out] #### Cost of chains of fun(V,Out): * Chain [63]: 10*s(247)+6*s(248)+7*s(249)+1*s(250)+1*s(251)+1*s(252)+1*s(253)+1*s(254)+1*s(263)+1*s(264)+1*s(265)+57*s(268)+16*s(269)+7*s(272)+24*s(274)+24*s(275)+10*s(276)+1*s(277)+2*s(278)+4*s(281)+4*s(282)+5*s(283)+1*s(284)+6*s(285)+1*s(286)+1 Such that:s(239) =< V s(240) =< 2*V s(241) =< 2/3*V s(242) =< 3/4*V s(243) =< 3/5*V s(244) =< 4/5*V s(245) =< 4/7*V s(246) =< 4/9*V s(247) =< s(239) s(248) =< s(239) s(249) =< s(239) s(250) =< s(239) s(251) =< s(239) s(252) =< s(239) s(253) =< s(239) s(254) =< s(239) s(250) =< s(241) s(251) =< s(241) s(253) =< s(241) s(254) =< s(242) s(253) =< s(243) s(252) =< s(244) s(253) =< s(244) s(254) =< s(244) s(249) =< s(245) s(251) =< s(245) s(248) =< s(246) s(255) =< s(240)+3 s(256) =< s(240)+2 s(257) =< s(240)+4 s(258) =< s(240) s(259) =< s(240)+1 s(260) =< s(247)*s(255) s(261) =< s(247)*s(256) s(262) =< s(247)*s(257) s(263) =< s(251)*s(258) s(264) =< s(250)*s(259) s(265) =< s(249)*s(258) s(266) =< s(249)*s(258) s(267) =< s(248)*s(256) s(268) =< s(261) s(269) =< s(262) s(270) =< s(256) s(271) =< s(268)*s(257) s(272) =< s(268)*s(256) s(273) =< s(268)*s(270) s(274) =< s(271) s(275) =< s(273) s(276) =< s(260) s(277) =< s(260) s(276) =< s(261) s(278) =< s(276)*s(256) s(279) =< s(276)*s(257) s(280) =< s(276)*s(270) s(281) =< s(279) s(282) =< s(280) s(283) =< s(266) s(284) =< s(283)*s(240) s(285) =< s(267) s(286) =< s(285)*s(256) with precondition: [Out=0,V>=0] * Chain [62]: 10*s(295)+6*s(296)+7*s(297)+1*s(298)+1*s(299)+1*s(300)+1*s(301)+1*s(302)+1*s(311)+1*s(312)+1*s(313)+57*s(316)+16*s(317)+7*s(320)+24*s(322)+24*s(323)+10*s(324)+1*s(325)+2*s(326)+4*s(329)+4*s(330)+5*s(331)+1*s(332)+6*s(333)+1*s(334)+1 Such that:s(287) =< V s(288) =< 2*V s(289) =< 2/3*V s(290) =< 3/4*V s(291) =< 3/5*V s(292) =< 4/5*V s(293) =< 4/7*V s(294) =< 4/9*V s(295) =< s(287) s(296) =< s(287) s(297) =< s(287) s(298) =< s(287) s(299) =< s(287) s(300) =< s(287) s(301) =< s(287) s(302) =< s(287) s(298) =< s(289) s(299) =< s(289) s(301) =< s(289) s(302) =< s(290) s(301) =< s(291) s(300) =< s(292) s(301) =< s(292) s(302) =< s(292) s(297) =< s(293) s(299) =< s(293) s(296) =< s(294) s(303) =< s(288)+3 s(304) =< s(288)+2 s(305) =< s(288)+4 s(306) =< s(288) s(307) =< s(288)+1 s(308) =< s(295)*s(303) s(309) =< s(295)*s(304) s(310) =< s(295)*s(305) s(311) =< s(299)*s(306) s(312) =< s(298)*s(307) s(313) =< s(297)*s(306) s(314) =< s(297)*s(306) s(315) =< s(296)*s(304) s(316) =< s(309) s(317) =< s(310) s(318) =< s(304) s(319) =< s(316)*s(305) s(320) =< s(316)*s(304) s(321) =< s(316)*s(318) s(322) =< s(319) s(323) =< s(321) s(324) =< s(308) s(325) =< s(308) s(324) =< s(309) s(326) =< s(324)*s(304) s(327) =< s(324)*s(305) s(328) =< s(324)*s(318) s(329) =< s(327) s(330) =< s(328) s(331) =< s(314) s(332) =< s(331)*s(288) s(333) =< s(315) s(334) =< s(333)*s(304) with precondition: [V>=1,Out>=0,2*V>=Out+1] #### Cost of chains of fun2(V,Out): * Chain [66]: 10*s(343)+6*s(344)+7*s(345)+1*s(346)+1*s(347)+1*s(348)+1*s(349)+1*s(350)+1*s(359)+1*s(360)+1*s(361)+57*s(364)+16*s(365)+7*s(368)+24*s(370)+24*s(371)+10*s(372)+1*s(373)+2*s(374)+4*s(377)+4*s(378)+5*s(379)+1*s(380)+6*s(381)+1*s(382)+0 Such that:s(335) =< V s(336) =< 2*V s(337) =< 2/3*V s(338) =< 3/4*V s(339) =< 3/5*V s(340) =< 4/5*V s(341) =< 4/7*V s(342) =< 4/9*V s(343) =< s(335) s(344) =< s(335) s(345) =< s(335) s(346) =< s(335) s(347) =< s(335) s(348) =< s(335) s(349) =< s(335) s(350) =< s(335) s(346) =< s(337) s(347) =< s(337) s(349) =< s(337) s(350) =< s(338) s(349) =< s(339) s(348) =< s(340) s(349) =< s(340) s(350) =< s(340) s(345) =< s(341) s(347) =< s(341) s(344) =< s(342) s(351) =< s(336)+3 s(352) =< s(336)+2 s(353) =< s(336)+4 s(354) =< s(336) s(355) =< s(336)+1 s(356) =< s(343)*s(351) s(357) =< s(343)*s(352) s(358) =< s(343)*s(353) s(359) =< s(347)*s(354) s(360) =< s(346)*s(355) s(361) =< s(345)*s(354) s(362) =< s(345)*s(354) s(363) =< s(344)*s(352) s(364) =< s(357) s(365) =< s(358) s(366) =< s(352) s(367) =< s(364)*s(353) s(368) =< s(364)*s(352) s(369) =< s(364)*s(366) s(370) =< s(367) s(371) =< s(369) s(372) =< s(356) s(373) =< s(356) s(372) =< s(357) s(374) =< s(372)*s(352) s(375) =< s(372)*s(353) s(376) =< s(372)*s(366) s(377) =< s(375) s(378) =< s(376) s(379) =< s(362) s(380) =< s(379)*s(336) s(381) =< s(363) s(382) =< s(381)*s(352) with precondition: [V>=1,Out>=1,2*V+1>=Out] * Chain [65]: 0 with precondition: [Out=0,V>=0] * Chain [64]: 0 with precondition: [Out=1,V>=0] #### Cost of chains of fun3(V,V2,Out): * Chain [72]: 20*s(391)+12*s(392)+14*s(393)+2*s(394)+2*s(395)+2*s(396)+2*s(397)+2*s(398)+2*s(407)+2*s(408)+2*s(409)+114*s(412)+32*s(413)+14*s(416)+48*s(418)+48*s(419)+20*s(420)+2*s(421)+4*s(422)+8*s(425)+8*s(426)+10*s(427)+2*s(428)+12*s(429)+2*s(430)+30*s(439)+18*s(440)+21*s(441)+3*s(442)+3*s(443)+3*s(444)+3*s(445)+3*s(446)+3*s(455)+3*s(456)+3*s(457)+171*s(460)+48*s(461)+21*s(464)+72*s(466)+72*s(467)+30*s(468)+3*s(469)+6*s(470)+12*s(473)+12*s(474)+15*s(475)+3*s(476)+18*s(477)+3*s(478)+3*s(479)+1*s(578)+0 Such that:s(578) =< 2 aux(59) =< V aux(60) =< 2*V aux(61) =< 2/3*V aux(62) =< 3/4*V aux(63) =< 3/5*V aux(64) =< 4/5*V aux(65) =< 4/7*V aux(66) =< 4/9*V aux(67) =< V2 aux(68) =< 2*V2 aux(69) =< 2/3*V2 aux(70) =< 3/4*V2 aux(71) =< 3/5*V2 aux(72) =< 4/5*V2 aux(73) =< 4/7*V2 aux(74) =< 4/9*V2 s(479) =< aux(68) s(439) =< aux(67) s(440) =< aux(67) s(441) =< aux(67) s(442) =< aux(67) s(443) =< aux(67) s(444) =< aux(67) s(445) =< aux(67) s(446) =< aux(67) s(442) =< aux(69) s(443) =< aux(69) s(445) =< aux(69) s(446) =< aux(70) s(445) =< aux(71) s(444) =< aux(72) s(445) =< aux(72) s(446) =< aux(72) s(441) =< aux(73) s(443) =< aux(73) s(440) =< aux(74) s(447) =< aux(68)+3 s(448) =< aux(68)+2 s(449) =< aux(68)+4 s(450) =< aux(68) s(451) =< aux(68)+1 s(452) =< s(439)*s(447) s(453) =< s(439)*s(448) s(454) =< s(439)*s(449) s(455) =< s(443)*s(450) s(456) =< s(442)*s(451) s(457) =< s(441)*s(450) s(458) =< s(441)*s(450) s(459) =< s(440)*s(448) s(460) =< s(453) s(461) =< s(454) s(462) =< s(448) s(463) =< s(460)*s(449) s(464) =< s(460)*s(448) s(465) =< s(460)*s(462) s(466) =< s(463) s(467) =< s(465) s(468) =< s(452) s(469) =< s(452) s(468) =< s(453) s(470) =< s(468)*s(448) s(471) =< s(468)*s(449) s(472) =< s(468)*s(462) s(473) =< s(471) s(474) =< s(472) s(475) =< s(458) s(476) =< s(475)*aux(68) s(477) =< s(459) s(478) =< s(477)*s(448) s(391) =< aux(59) s(392) =< aux(59) s(393) =< aux(59) s(394) =< aux(59) s(395) =< aux(59) s(396) =< aux(59) s(397) =< aux(59) s(398) =< aux(59) s(394) =< aux(61) s(395) =< aux(61) s(397) =< aux(61) s(398) =< aux(62) s(397) =< aux(63) s(396) =< aux(64) s(397) =< aux(64) s(398) =< aux(64) s(393) =< aux(65) s(395) =< aux(65) s(392) =< aux(66) s(399) =< aux(60)+3 s(400) =< aux(60)+2 s(401) =< aux(60)+4 s(402) =< aux(60) s(403) =< aux(60)+1 s(404) =< s(391)*s(399) s(405) =< s(391)*s(400) s(406) =< s(391)*s(401) s(407) =< s(395)*s(402) s(408) =< s(394)*s(403) s(409) =< s(393)*s(402) s(410) =< s(393)*s(402) s(411) =< s(392)*s(400) s(412) =< s(405) s(413) =< s(406) s(414) =< s(400) s(415) =< s(412)*s(401) s(416) =< s(412)*s(400) s(417) =< s(412)*s(414) s(418) =< s(415) s(419) =< s(417) s(420) =< s(404) s(421) =< s(404) s(420) =< s(405) s(422) =< s(420)*s(400) s(423) =< s(420)*s(401) s(424) =< s(420)*s(414) s(425) =< s(423) s(426) =< s(424) s(427) =< s(410) s(428) =< s(427)*aux(60) s(429) =< s(411) s(430) =< s(429)*s(400) with precondition: [Out=0,V>=0,V2>=0] * Chain [71]: 30*s(638)+18*s(639)+21*s(640)+3*s(641)+3*s(642)+3*s(643)+3*s(644)+3*s(645)+3*s(654)+3*s(655)+3*s(656)+171*s(659)+48*s(660)+21*s(663)+72*s(665)+72*s(666)+30*s(667)+3*s(668)+6*s(669)+12*s(672)+12*s(673)+15*s(674)+3*s(675)+18*s(676)+3*s(677)+40*s(686)+24*s(687)+28*s(688)+4*s(689)+4*s(690)+4*s(691)+4*s(692)+4*s(693)+4*s(702)+4*s(703)+4*s(704)+228*s(707)+64*s(708)+28*s(711)+96*s(713)+96*s(714)+40*s(715)+4*s(716)+8*s(717)+16*s(720)+16*s(721)+20*s(722)+4*s(723)+24*s(724)+4*s(725)+1*s(822)+2*s(919)+1 Such that:aux(76) =< 2 aux(77) =< V aux(78) =< 2*V aux(79) =< 2/3*V aux(80) =< 3/4*V aux(81) =< 3/5*V aux(82) =< 4/5*V aux(83) =< 4/7*V aux(84) =< 4/9*V aux(85) =< V2 aux(86) =< 2*V2 aux(87) =< 2/3*V2 aux(88) =< 3/4*V2 aux(89) =< 3/5*V2 aux(90) =< 4/5*V2 aux(91) =< 4/7*V2 aux(92) =< 4/9*V2 s(919) =< aux(76) s(686) =< aux(85) s(687) =< aux(85) s(688) =< aux(85) s(689) =< aux(85) s(690) =< aux(85) s(691) =< aux(85) s(692) =< aux(85) s(693) =< aux(85) s(689) =< aux(87) s(690) =< aux(87) s(692) =< aux(87) s(693) =< aux(88) s(692) =< aux(89) s(691) =< aux(90) s(692) =< aux(90) s(693) =< aux(90) s(688) =< aux(91) s(690) =< aux(91) s(687) =< aux(92) s(694) =< aux(86)+3 s(695) =< aux(86)+2 s(696) =< aux(86)+4 s(697) =< aux(86) s(698) =< aux(86)+1 s(699) =< s(686)*s(694) s(700) =< s(686)*s(695) s(701) =< s(686)*s(696) s(702) =< s(690)*s(697) s(703) =< s(689)*s(698) s(704) =< s(688)*s(697) s(705) =< s(688)*s(697) s(706) =< s(687)*s(695) s(707) =< s(700) s(708) =< s(701) s(709) =< s(695) s(710) =< s(707)*s(696) s(711) =< s(707)*s(695) s(712) =< s(707)*s(709) s(713) =< s(710) s(714) =< s(712) s(715) =< s(699) s(716) =< s(699) s(715) =< s(700) s(717) =< s(715)*s(695) s(718) =< s(715)*s(696) s(719) =< s(715)*s(709) s(720) =< s(718) s(721) =< s(719) s(722) =< s(705) s(723) =< s(722)*aux(86) s(724) =< s(706) s(725) =< s(724)*s(695) s(638) =< aux(77) s(639) =< aux(77) s(640) =< aux(77) s(641) =< aux(77) s(642) =< aux(77) s(643) =< aux(77) s(644) =< aux(77) s(645) =< aux(77) s(641) =< aux(79) s(642) =< aux(79) s(644) =< aux(79) s(645) =< aux(80) s(644) =< aux(81) s(643) =< aux(82) s(644) =< aux(82) s(645) =< aux(82) s(640) =< aux(83) s(642) =< aux(83) s(639) =< aux(84) s(646) =< aux(78)+3 s(647) =< aux(78)+2 s(648) =< aux(78)+4 s(649) =< aux(78) s(650) =< aux(78)+1 s(651) =< s(638)*s(646) s(652) =< s(638)*s(647) s(653) =< s(638)*s(648) s(654) =< s(642)*s(649) s(655) =< s(641)*s(650) s(656) =< s(640)*s(649) s(657) =< s(640)*s(649) s(658) =< s(639)*s(647) s(659) =< s(652) s(660) =< s(653) s(661) =< s(647) s(662) =< s(659)*s(648) s(663) =< s(659)*s(647) s(664) =< s(659)*s(661) s(665) =< s(662) s(666) =< s(664) s(667) =< s(651) s(668) =< s(651) s(667) =< s(652) s(669) =< s(667)*s(647) s(670) =< s(667)*s(648) s(671) =< s(667)*s(661) s(672) =< s(670) s(673) =< s(671) s(674) =< s(657) s(675) =< s(674)*aux(78) s(676) =< s(658) s(677) =< s(676)*s(647) s(822) =< aux(86) with precondition: [Out=2,V>=0,V2>=0] * Chain [70]: 30*s(977)+18*s(978)+21*s(979)+3*s(980)+3*s(981)+3*s(982)+3*s(983)+3*s(984)+3*s(993)+3*s(994)+3*s(995)+171*s(998)+48*s(999)+21*s(1002)+72*s(1004)+72*s(1005)+30*s(1006)+3*s(1007)+6*s(1008)+12*s(1011)+12*s(1012)+15*s(1013)+3*s(1014)+18*s(1015)+3*s(1016)+40*s(1025)+24*s(1026)+28*s(1027)+4*s(1028)+4*s(1029)+4*s(1030)+4*s(1031)+4*s(1032)+4*s(1041)+4*s(1042)+4*s(1043)+228*s(1046)+64*s(1047)+28*s(1050)+96*s(1052)+96*s(1053)+40*s(1054)+4*s(1055)+8*s(1056)+16*s(1059)+16*s(1060)+20*s(1061)+4*s(1062)+24*s(1063)+4*s(1064)+1*s(1161)+1*s(1306)+1 Such that:s(1306) =< 1 aux(94) =< V aux(95) =< 2*V aux(96) =< 2/3*V aux(97) =< 3/4*V aux(98) =< 3/5*V aux(99) =< 4/5*V aux(100) =< 4/7*V aux(101) =< 4/9*V aux(102) =< V2 aux(103) =< 2*V2 aux(104) =< 2/3*V2 aux(105) =< 3/4*V2 aux(106) =< 3/5*V2 aux(107) =< 4/5*V2 aux(108) =< 4/7*V2 aux(109) =< 4/9*V2 s(1025) =< aux(102) s(1026) =< aux(102) s(1027) =< aux(102) s(1028) =< aux(102) s(1029) =< aux(102) s(1030) =< aux(102) s(1031) =< aux(102) s(1032) =< aux(102) s(1028) =< aux(104) s(1029) =< aux(104) s(1031) =< aux(104) s(1032) =< aux(105) s(1031) =< aux(106) s(1030) =< aux(107) s(1031) =< aux(107) s(1032) =< aux(107) s(1027) =< aux(108) s(1029) =< aux(108) s(1026) =< aux(109) s(1033) =< aux(103)+3 s(1034) =< aux(103)+2 s(1035) =< aux(103)+4 s(1036) =< aux(103) s(1037) =< aux(103)+1 s(1038) =< s(1025)*s(1033) s(1039) =< s(1025)*s(1034) s(1040) =< s(1025)*s(1035) s(1041) =< s(1029)*s(1036) s(1042) =< s(1028)*s(1037) s(1043) =< s(1027)*s(1036) s(1044) =< s(1027)*s(1036) s(1045) =< s(1026)*s(1034) s(1046) =< s(1039) s(1047) =< s(1040) s(1048) =< s(1034) s(1049) =< s(1046)*s(1035) s(1050) =< s(1046)*s(1034) s(1051) =< s(1046)*s(1048) s(1052) =< s(1049) s(1053) =< s(1051) s(1054) =< s(1038) s(1055) =< s(1038) s(1054) =< s(1039) s(1056) =< s(1054)*s(1034) s(1057) =< s(1054)*s(1035) s(1058) =< s(1054)*s(1048) s(1059) =< s(1057) s(1060) =< s(1058) s(1061) =< s(1044) s(1062) =< s(1061)*aux(103) s(1063) =< s(1045) s(1064) =< s(1063)*s(1034) s(977) =< aux(94) s(978) =< aux(94) s(979) =< aux(94) s(980) =< aux(94) s(981) =< aux(94) s(982) =< aux(94) s(983) =< aux(94) s(984) =< aux(94) s(980) =< aux(96) s(981) =< aux(96) s(983) =< aux(96) s(984) =< aux(97) s(983) =< aux(98) s(982) =< aux(99) s(983) =< aux(99) s(984) =< aux(99) s(979) =< aux(100) s(981) =< aux(100) s(978) =< aux(101) s(985) =< aux(95)+3 s(986) =< aux(95)+2 s(987) =< aux(95)+4 s(988) =< aux(95) s(989) =< aux(95)+1 s(990) =< s(977)*s(985) s(991) =< s(977)*s(986) s(992) =< s(977)*s(987) s(993) =< s(981)*s(988) s(994) =< s(980)*s(989) s(995) =< s(979)*s(988) s(996) =< s(979)*s(988) s(997) =< s(978)*s(986) s(998) =< s(991) s(999) =< s(992) s(1000) =< s(986) s(1001) =< s(998)*s(987) s(1002) =< s(998)*s(986) s(1003) =< s(998)*s(1000) s(1004) =< s(1001) s(1005) =< s(1003) s(1006) =< s(990) s(1007) =< s(990) s(1006) =< s(991) s(1008) =< s(1006)*s(986) s(1009) =< s(1006)*s(987) s(1010) =< s(1006)*s(1000) s(1011) =< s(1009) s(1012) =< s(1010) s(1013) =< s(996) s(1014) =< s(1013)*aux(95) s(1015) =< s(997) s(1016) =< s(1015)*s(986) s(1161) =< aux(95) with precondition: [Out=1,V>=1,V2>=0] * Chain [69]: 10*s(1315)+6*s(1316)+7*s(1317)+1*s(1318)+1*s(1319)+1*s(1320)+1*s(1321)+1*s(1322)+1*s(1331)+1*s(1332)+1*s(1333)+57*s(1336)+16*s(1337)+7*s(1340)+24*s(1342)+24*s(1343)+10*s(1344)+1*s(1345)+2*s(1346)+4*s(1349)+4*s(1350)+5*s(1351)+1*s(1352)+6*s(1353)+1*s(1354)+2*s(1355)+0 Such that:s(1307) =< V s(1308) =< 2*V s(1309) =< 2/3*V s(1310) =< 3/4*V s(1311) =< 3/5*V s(1312) =< 4/5*V s(1313) =< 4/7*V s(1314) =< 4/9*V aux(110) =< 2 s(1355) =< aux(110) s(1315) =< s(1307) s(1316) =< s(1307) s(1317) =< s(1307) s(1318) =< s(1307) s(1319) =< s(1307) s(1320) =< s(1307) s(1321) =< s(1307) s(1322) =< s(1307) s(1318) =< s(1309) s(1319) =< s(1309) s(1321) =< s(1309) s(1322) =< s(1310) s(1321) =< s(1311) s(1320) =< s(1312) s(1321) =< s(1312) s(1322) =< s(1312) s(1317) =< s(1313) s(1319) =< s(1313) s(1316) =< s(1314) s(1323) =< s(1308)+3 s(1324) =< s(1308)+2 s(1325) =< s(1308)+4 s(1326) =< s(1308) s(1327) =< s(1308)+1 s(1328) =< s(1315)*s(1323) s(1329) =< s(1315)*s(1324) s(1330) =< s(1315)*s(1325) s(1331) =< s(1319)*s(1326) s(1332) =< s(1318)*s(1327) s(1333) =< s(1317)*s(1326) s(1334) =< s(1317)*s(1326) s(1335) =< s(1316)*s(1324) s(1336) =< s(1329) s(1337) =< s(1330) s(1338) =< s(1324) s(1339) =< s(1336)*s(1325) s(1340) =< s(1336)*s(1324) s(1341) =< s(1336)*s(1338) s(1342) =< s(1339) s(1343) =< s(1341) s(1344) =< s(1328) s(1345) =< s(1328) s(1344) =< s(1329) s(1346) =< s(1344)*s(1324) s(1347) =< s(1344)*s(1325) s(1348) =< s(1344)*s(1338) s(1349) =< s(1347) s(1350) =< s(1348) s(1351) =< s(1334) s(1352) =< s(1351)*s(1308) s(1353) =< s(1335) s(1354) =< s(1353)*s(1324) with precondition: [V2=2,Out=0,V>=0] * Chain [68]: 10*s(1365)+6*s(1366)+7*s(1367)+1*s(1368)+1*s(1369)+1*s(1370)+1*s(1371)+1*s(1372)+1*s(1381)+1*s(1382)+1*s(1383)+57*s(1386)+16*s(1387)+7*s(1390)+24*s(1392)+24*s(1393)+10*s(1394)+1*s(1395)+2*s(1396)+4*s(1399)+4*s(1400)+5*s(1401)+1*s(1402)+6*s(1403)+1*s(1404)+1*s(1405)+1 Such that:s(1405) =< 2 s(1357) =< V s(1358) =< 2*V s(1359) =< 2/3*V s(1360) =< 3/4*V s(1361) =< 3/5*V s(1362) =< 4/5*V s(1363) =< 4/7*V s(1364) =< 4/9*V s(1365) =< s(1357) s(1366) =< s(1357) s(1367) =< s(1357) s(1368) =< s(1357) s(1369) =< s(1357) s(1370) =< s(1357) s(1371) =< s(1357) s(1372) =< s(1357) s(1368) =< s(1359) s(1369) =< s(1359) s(1371) =< s(1359) s(1372) =< s(1360) s(1371) =< s(1361) s(1370) =< s(1362) s(1371) =< s(1362) s(1372) =< s(1362) s(1367) =< s(1363) s(1369) =< s(1363) s(1366) =< s(1364) s(1373) =< s(1358)+3 s(1374) =< s(1358)+2 s(1375) =< s(1358)+4 s(1376) =< s(1358) s(1377) =< s(1358)+1 s(1378) =< s(1365)*s(1373) s(1379) =< s(1365)*s(1374) s(1380) =< s(1365)*s(1375) s(1381) =< s(1369)*s(1376) s(1382) =< s(1368)*s(1377) s(1383) =< s(1367)*s(1376) s(1384) =< s(1367)*s(1376) s(1385) =< s(1366)*s(1374) s(1386) =< s(1379) s(1387) =< s(1380) s(1388) =< s(1374) s(1389) =< s(1386)*s(1375) s(1390) =< s(1386)*s(1374) s(1391) =< s(1386)*s(1388) s(1392) =< s(1389) s(1393) =< s(1391) s(1394) =< s(1378) s(1395) =< s(1378) s(1394) =< s(1379) s(1396) =< s(1394)*s(1374) s(1397) =< s(1394)*s(1375) s(1398) =< s(1394)*s(1388) s(1399) =< s(1397) s(1400) =< s(1398) s(1401) =< s(1384) s(1402) =< s(1401)*s(1358) s(1403) =< s(1385) s(1404) =< s(1403)*s(1374) with precondition: [V2=2,Out=1,2*V>=3] * Chain [67]: 20*s(1414)+12*s(1415)+14*s(1416)+2*s(1417)+2*s(1418)+2*s(1419)+2*s(1420)+2*s(1421)+2*s(1430)+2*s(1431)+2*s(1432)+114*s(1435)+32*s(1436)+14*s(1439)+48*s(1441)+48*s(1442)+20*s(1443)+2*s(1444)+4*s(1445)+8*s(1448)+8*s(1449)+10*s(1450)+2*s(1451)+12*s(1452)+2*s(1453)+1*s(1502)+1 Such that:s(1502) =< 2 aux(111) =< V aux(112) =< 2*V aux(113) =< 2/3*V aux(114) =< 3/4*V aux(115) =< 3/5*V aux(116) =< 4/5*V aux(117) =< 4/7*V aux(118) =< 4/9*V s(1414) =< aux(111) s(1415) =< aux(111) s(1416) =< aux(111) s(1417) =< aux(111) s(1418) =< aux(111) s(1419) =< aux(111) s(1420) =< aux(111) s(1421) =< aux(111) s(1417) =< aux(113) s(1418) =< aux(113) s(1420) =< aux(113) s(1421) =< aux(114) s(1420) =< aux(115) s(1419) =< aux(116) s(1420) =< aux(116) s(1421) =< aux(116) s(1416) =< aux(117) s(1418) =< aux(117) s(1415) =< aux(118) s(1422) =< aux(112)+3 s(1423) =< aux(112)+2 s(1424) =< aux(112)+4 s(1425) =< aux(112) s(1426) =< aux(112)+1 s(1427) =< s(1414)*s(1422) s(1428) =< s(1414)*s(1423) s(1429) =< s(1414)*s(1424) s(1430) =< s(1418)*s(1425) s(1431) =< s(1417)*s(1426) s(1432) =< s(1416)*s(1425) s(1433) =< s(1416)*s(1425) s(1434) =< s(1415)*s(1423) s(1435) =< s(1428) s(1436) =< s(1429) s(1437) =< s(1423) s(1438) =< s(1435)*s(1424) s(1439) =< s(1435)*s(1423) s(1440) =< s(1435)*s(1437) s(1441) =< s(1438) s(1442) =< s(1440) s(1443) =< s(1427) s(1444) =< s(1427) s(1443) =< s(1428) s(1445) =< s(1443)*s(1423) s(1446) =< s(1443)*s(1424) s(1447) =< s(1443)*s(1437) s(1448) =< s(1446) s(1449) =< s(1447) s(1450) =< s(1433) s(1451) =< s(1450)*aux(112) s(1452) =< s(1434) s(1453) =< s(1452)*s(1423) with precondition: [V2=2,Out=2,V>=0] #### Cost of chains of fun4(Out): * Chain [74]: 0 with precondition: [Out=0] * Chain [73]: 0 with precondition: [Out=2] #### Cost of chains of fun5(Out): * Chain [76]: 0 with precondition: [Out=0] * Chain [75]: 0 with precondition: [Out=1] #### Cost of chains of fun6(V,V2,Out): * Chain [82]: 20*s(1954)+12*s(1955)+14*s(1956)+2*s(1957)+2*s(1958)+2*s(1959)+2*s(1960)+2*s(1961)+2*s(1970)+2*s(1971)+2*s(1972)+114*s(1975)+32*s(1976)+14*s(1979)+48*s(1981)+48*s(1982)+20*s(1983)+2*s(1984)+4*s(1985)+8*s(1988)+8*s(1989)+10*s(1990)+2*s(1991)+12*s(1992)+2*s(1993)+40*s(2002)+24*s(2003)+28*s(2004)+4*s(2005)+4*s(2006)+4*s(2007)+4*s(2008)+4*s(2009)+4*s(2018)+4*s(2019)+4*s(2020)+228*s(2023)+64*s(2024)+28*s(2027)+96*s(2029)+96*s(2030)+40*s(2031)+4*s(2032)+8*s(2033)+16*s(2036)+16*s(2037)+20*s(2038)+4*s(2039)+24*s(2040)+4*s(2041)+32*s(2045)+168*s(2046)+21*s(2049)+24*s(2051)+72*s(2052)+30*s(2053)+3*s(2054)+6*s(2055)+4*s(2058)+12*s(2059)+3*s(2120)+104*s(2177)+24*s(2183)+4*s(2190)+7*s(2199)+24*s(2201)+24*s(2202)+10*s(2203)+1*s(2204)+2*s(2205)+4*s(2208)+4*s(2209)+6 Such that:s(2192) =< 3 aux(152) =< 1 aux(153) =< 2 aux(154) =< V aux(155) =< 2*V aux(156) =< 2/3*V aux(157) =< 3/4*V aux(158) =< 3/5*V aux(159) =< 4/5*V aux(160) =< 4/7*V aux(161) =< 4/9*V aux(162) =< V2 aux(163) =< 2*V2 aux(164) =< 2*V2+1 aux(165) =< 2/3*V2 aux(166) =< 3/4*V2 aux(167) =< 3/5*V2 aux(168) =< 4/5*V2 aux(169) =< 4/7*V2 aux(170) =< 4/9*V2 s(2045) =< aux(155) s(2120) =< aux(152) s(1954) =< aux(154) s(1955) =< aux(154) s(1956) =< aux(154) s(1957) =< aux(154) s(1958) =< aux(154) s(1959) =< aux(154) s(1960) =< aux(154) s(1961) =< aux(154) s(1957) =< aux(156) s(1958) =< aux(156) s(1960) =< aux(156) s(1961) =< aux(157) s(1960) =< aux(158) s(1959) =< aux(159) s(1960) =< aux(159) s(1961) =< aux(159) s(1956) =< aux(160) s(1958) =< aux(160) s(1955) =< aux(161) s(1962) =< aux(155)+3 s(1963) =< aux(155)+2 s(1964) =< aux(155)+4 s(1965) =< aux(155) s(1966) =< aux(155)+1 s(1967) =< s(1954)*s(1962) s(1968) =< s(1954)*s(1963) s(1969) =< s(1954)*s(1964) s(1970) =< s(1958)*s(1965) s(1971) =< s(1957)*s(1966) s(1972) =< s(1956)*s(1965) s(1973) =< s(1956)*s(1965) s(1974) =< s(1955)*s(1963) s(1975) =< s(1968) s(1976) =< s(1969) s(1977) =< s(1963) s(1978) =< s(1975)*s(1964) s(1979) =< s(1975)*s(1963) s(1980) =< s(1975)*s(1977) s(1981) =< s(1978) s(1982) =< s(1980) s(1983) =< s(1967) s(1984) =< s(1967) s(1983) =< s(1968) s(1985) =< s(1983)*s(1963) s(1986) =< s(1983)*s(1964) s(1987) =< s(1983)*s(1977) s(1988) =< s(1986) s(1989) =< s(1987) s(1990) =< s(1973) s(1991) =< s(1990)*aux(155) s(1992) =< s(1974) s(1993) =< s(1992)*s(1963) s(2177) =< aux(153) s(2046) =< aux(163) s(2013) =< aux(163) s(2180) =< s(2046)*aux(153) s(2049) =< s(2046)*aux(163) s(2050) =< s(2046)*s(2013) s(2183) =< s(2180) s(2052) =< s(2050) s(2053) =< aux(164) s(2054) =< aux(164) s(2053) =< aux(163) s(2055) =< s(2053)*aux(163) s(2188) =< s(2053)*aux(153) s(2057) =< s(2053)*s(2013) s(2190) =< s(2188) s(2059) =< s(2057) s(2002) =< aux(162) s(2003) =< aux(162) s(2004) =< aux(162) s(2005) =< aux(162) s(2006) =< aux(162) s(2007) =< aux(162) s(2008) =< aux(162) s(2009) =< aux(162) s(2005) =< aux(165) s(2006) =< aux(165) s(2008) =< aux(165) s(2009) =< aux(166) s(2008) =< aux(167) s(2007) =< aux(168) s(2008) =< aux(168) s(2009) =< aux(168) s(2004) =< aux(169) s(2006) =< aux(169) s(2003) =< aux(170) s(2010) =< aux(163)+3 s(2011) =< aux(163)+2 s(2012) =< aux(163)+4 s(2014) =< aux(163)+1 s(2015) =< s(2002)*s(2010) s(2016) =< s(2002)*s(2011) s(2017) =< s(2002)*s(2012) s(2018) =< s(2006)*s(2013) s(2019) =< s(2005)*s(2014) s(2020) =< s(2004)*s(2013) s(2021) =< s(2004)*s(2013) s(2022) =< s(2003)*s(2011) s(2023) =< s(2016) s(2024) =< s(2017) s(2025) =< s(2011) s(2026) =< s(2023)*s(2012) s(2027) =< s(2023)*s(2011) s(2028) =< s(2023)*s(2025) s(2029) =< s(2026) s(2030) =< s(2028) s(2031) =< s(2015) s(2032) =< s(2015) s(2031) =< s(2016) s(2033) =< s(2031)*s(2011) s(2034) =< s(2031)*s(2012) s(2035) =< s(2031)*s(2025) s(2036) =< s(2034) s(2037) =< s(2035) s(2038) =< s(2021) s(2039) =< s(2038)*aux(163) s(2040) =< s(2022) s(2041) =< s(2040)*s(2011) s(2197) =< aux(153) s(2198) =< s(2177)*aux(153) s(2199) =< s(2177)*aux(153) s(2200) =< s(2177)*s(2197) s(2201) =< s(2198) s(2202) =< s(2200) s(2203) =< s(2192) s(2204) =< s(2192) s(2203) =< aux(153) s(2205) =< s(2203)*aux(153) s(2206) =< s(2203)*aux(153) s(2207) =< s(2203)*s(2197) s(2208) =< s(2206) s(2209) =< s(2207) s(2048) =< s(2046)*aux(155) s(2051) =< s(2048) s(2056) =< s(2053)*aux(155) s(2058) =< s(2056) with precondition: [Out=0,V>=0,V2>=0] * Chain [81]: 50*s(2368)+30*s(2369)+35*s(2370)+5*s(2371)+5*s(2372)+5*s(2373)+5*s(2374)+5*s(2375)+5*s(2384)+5*s(2385)+5*s(2386)+285*s(2389)+80*s(2390)+35*s(2393)+120*s(2395)+120*s(2396)+50*s(2397)+5*s(2398)+10*s(2399)+20*s(2402)+20*s(2403)+25*s(2404)+5*s(2405)+30*s(2406)+5*s(2407)+60*s(2416)+36*s(2417)+42*s(2418)+6*s(2419)+6*s(2420)+6*s(2421)+6*s(2422)+6*s(2423)+6*s(2432)+6*s(2433)+6*s(2434)+342*s(2437)+96*s(2438)+42*s(2441)+144*s(2443)+144*s(2444)+60*s(2445)+6*s(2446)+12*s(2447)+24*s(2450)+24*s(2451)+30*s(2452)+6*s(2453)+36*s(2454)+6*s(2455)+6*s(2552)+1*s(2651)+1*s(2748)+5*s(2749)+1*s(2751)+6*s(2848)+1*s(2899)+6 Such that:aux(174) =< 2*V2+1 aux(175) =< 1 aux(176) =< V aux(177) =< 2*V aux(178) =< 2/3*V aux(179) =< 3/4*V aux(180) =< 3/5*V aux(181) =< 4/5*V aux(182) =< 4/7*V aux(183) =< 4/9*V aux(184) =< V2 aux(185) =< 2*V2 aux(186) =< 2/3*V2 aux(187) =< 3/4*V2 aux(188) =< 3/5*V2 aux(189) =< 4/5*V2 aux(190) =< 4/7*V2 aux(191) =< 4/9*V2 s(2848) =< aux(175) s(2416) =< aux(184) s(2417) =< aux(184) s(2418) =< aux(184) s(2419) =< aux(184) s(2420) =< aux(184) s(2421) =< aux(184) s(2422) =< aux(184) s(2423) =< aux(184) s(2419) =< aux(186) s(2420) =< aux(186) s(2422) =< aux(186) s(2423) =< aux(187) s(2422) =< aux(188) s(2421) =< aux(189) s(2422) =< aux(189) s(2423) =< aux(189) s(2418) =< aux(190) s(2420) =< aux(190) s(2417) =< aux(191) s(2424) =< aux(185)+3 s(2425) =< aux(185)+2 s(2426) =< aux(185)+4 s(2427) =< aux(185) s(2428) =< aux(185)+1 s(2429) =< s(2416)*s(2424) s(2430) =< s(2416)*s(2425) s(2431) =< s(2416)*s(2426) s(2432) =< s(2420)*s(2427) s(2433) =< s(2419)*s(2428) s(2434) =< s(2418)*s(2427) s(2435) =< s(2418)*s(2427) s(2436) =< s(2417)*s(2425) s(2437) =< s(2430) s(2438) =< s(2431) s(2439) =< s(2425) s(2440) =< s(2437)*s(2426) s(2441) =< s(2437)*s(2425) s(2442) =< s(2437)*s(2439) s(2443) =< s(2440) s(2444) =< s(2442) s(2445) =< s(2429) s(2446) =< s(2429) s(2445) =< s(2430) s(2447) =< s(2445)*s(2425) s(2448) =< s(2445)*s(2426) s(2449) =< s(2445)*s(2439) s(2450) =< s(2448) s(2451) =< s(2449) s(2452) =< s(2435) s(2453) =< s(2452)*aux(185) s(2454) =< s(2436) s(2455) =< s(2454)*s(2425) s(2899) =< s(2848)*aux(175) s(2368) =< aux(176) s(2369) =< aux(176) s(2370) =< aux(176) s(2371) =< aux(176) s(2372) =< aux(176) s(2373) =< aux(176) s(2374) =< aux(176) s(2375) =< aux(176) s(2371) =< aux(178) s(2372) =< aux(178) s(2374) =< aux(178) s(2375) =< aux(179) s(2374) =< aux(180) s(2373) =< aux(181) s(2374) =< aux(181) s(2375) =< aux(181) s(2370) =< aux(182) s(2372) =< aux(182) s(2369) =< aux(183) s(2376) =< aux(177)+3 s(2377) =< aux(177)+2 s(2378) =< aux(177)+4 s(2379) =< aux(177) s(2380) =< aux(177)+1 s(2381) =< s(2368)*s(2376) s(2382) =< s(2368)*s(2377) s(2383) =< s(2368)*s(2378) s(2384) =< s(2372)*s(2379) s(2385) =< s(2371)*s(2380) s(2386) =< s(2370)*s(2379) s(2387) =< s(2370)*s(2379) s(2388) =< s(2369)*s(2377) s(2389) =< s(2382) s(2390) =< s(2383) s(2391) =< s(2377) s(2392) =< s(2389)*s(2378) s(2393) =< s(2389)*s(2377) s(2394) =< s(2389)*s(2391) s(2395) =< s(2392) s(2396) =< s(2394) s(2397) =< s(2381) s(2398) =< s(2381) s(2397) =< s(2382) s(2399) =< s(2397)*s(2377) s(2400) =< s(2397)*s(2378) s(2401) =< s(2397)*s(2391) s(2402) =< s(2400) s(2403) =< s(2401) s(2404) =< s(2387) s(2405) =< s(2404)*aux(177) s(2406) =< s(2388) s(2407) =< s(2406)*s(2377) s(2552) =< aux(177) s(2651) =< s(2552)*aux(177) s(2748) =< aux(174) s(2749) =< aux(174) s(2749) =< aux(185) s(2751) =< s(2749)*aux(185) with precondition: [V>=1,V2>=0,Out>=0,2*V>=Out] * Chain [80]: 10*s(2908)+6*s(2909)+7*s(2910)+1*s(2911)+1*s(2912)+1*s(2913)+1*s(2914)+1*s(2915)+1*s(2924)+1*s(2925)+1*s(2926)+57*s(2929)+16*s(2930)+7*s(2933)+24*s(2935)+24*s(2936)+10*s(2937)+1*s(2938)+2*s(2939)+4*s(2942)+4*s(2943)+5*s(2944)+1*s(2945)+6*s(2946)+1*s(2947)+1 Such that:s(2900) =< V2 s(2901) =< 2*V2 s(2902) =< 2/3*V2 s(2903) =< 3/4*V2 s(2904) =< 3/5*V2 s(2905) =< 4/5*V2 s(2906) =< 4/7*V2 s(2907) =< 4/9*V2 s(2908) =< s(2900) s(2909) =< s(2900) s(2910) =< s(2900) s(2911) =< s(2900) s(2912) =< s(2900) s(2913) =< s(2900) s(2914) =< s(2900) s(2915) =< s(2900) s(2911) =< s(2902) s(2912) =< s(2902) s(2914) =< s(2902) s(2915) =< s(2903) s(2914) =< s(2904) s(2913) =< s(2905) s(2914) =< s(2905) s(2915) =< s(2905) s(2910) =< s(2906) s(2912) =< s(2906) s(2909) =< s(2907) s(2916) =< s(2901)+3 s(2917) =< s(2901)+2 s(2918) =< s(2901)+4 s(2919) =< s(2901) s(2920) =< s(2901)+1 s(2921) =< s(2908)*s(2916) s(2922) =< s(2908)*s(2917) s(2923) =< s(2908)*s(2918) s(2924) =< s(2912)*s(2919) s(2925) =< s(2911)*s(2920) s(2926) =< s(2910)*s(2919) s(2927) =< s(2910)*s(2919) s(2928) =< s(2909)*s(2917) s(2929) =< s(2922) s(2930) =< s(2923) s(2931) =< s(2917) s(2932) =< s(2929)*s(2918) s(2933) =< s(2929)*s(2917) s(2934) =< s(2929)*s(2931) s(2935) =< s(2932) s(2936) =< s(2934) s(2937) =< s(2921) s(2938) =< s(2921) s(2937) =< s(2922) s(2939) =< s(2937)*s(2917) s(2940) =< s(2937)*s(2918) s(2941) =< s(2937)*s(2931) s(2942) =< s(2940) s(2943) =< s(2941) s(2944) =< s(2927) s(2945) =< s(2944)*s(2901) s(2946) =< s(2928) s(2947) =< s(2946)*s(2917) with precondition: [V=2,Out=2,V2>=0] * Chain [79]: 10*s(2956)+6*s(2957)+7*s(2958)+1*s(2959)+1*s(2960)+1*s(2961)+1*s(2962)+1*s(2963)+1*s(2972)+1*s(2973)+1*s(2974)+57*s(2977)+16*s(2978)+7*s(2981)+24*s(2983)+24*s(2984)+10*s(2985)+1*s(2986)+2*s(2987)+4*s(2990)+4*s(2991)+5*s(2992)+1*s(2993)+6*s(2994)+1*s(2995)+16*s(2999)+112*s(3000)+14*s(3003)+24*s(3005)+48*s(3006)+20*s(3007)+2*s(3008)+4*s(3009)+4*s(3012)+8*s(3013)+6 Such that:s(2948) =< V aux(192) =< 2*V s(2950) =< 2/3*V s(2951) =< 3/4*V s(2952) =< 3/5*V s(2953) =< 4/5*V s(2954) =< 4/7*V s(2955) =< 4/9*V aux(193) =< 2 aux(194) =< 3 s(2999) =< aux(192) s(3000) =< aux(193) s(3001) =< aux(193) s(3002) =< s(3000)*aux(192) s(3003) =< s(3000)*aux(193) s(3004) =< s(3000)*s(3001) s(3005) =< s(3002) s(3006) =< s(3004) s(3007) =< aux(194) s(3008) =< aux(194) s(3007) =< aux(193) s(3009) =< s(3007)*aux(193) s(3010) =< s(3007)*aux(192) s(3011) =< s(3007)*s(3001) s(3012) =< s(3010) s(3013) =< s(3011) s(2956) =< s(2948) s(2957) =< s(2948) s(2958) =< s(2948) s(2959) =< s(2948) s(2960) =< s(2948) s(2961) =< s(2948) s(2962) =< s(2948) s(2963) =< s(2948) s(2959) =< s(2950) s(2960) =< s(2950) s(2962) =< s(2950) s(2963) =< s(2951) s(2962) =< s(2952) s(2961) =< s(2953) s(2962) =< s(2953) s(2963) =< s(2953) s(2958) =< s(2954) s(2960) =< s(2954) s(2957) =< s(2955) s(2964) =< aux(192)+3 s(2965) =< aux(192)+2 s(2966) =< aux(192)+4 s(2967) =< aux(192) s(2968) =< aux(192)+1 s(2969) =< s(2956)*s(2964) s(2970) =< s(2956)*s(2965) s(2971) =< s(2956)*s(2966) s(2972) =< s(2960)*s(2967) s(2973) =< s(2959)*s(2968) s(2974) =< s(2958)*s(2967) s(2975) =< s(2958)*s(2967) s(2976) =< s(2957)*s(2965) s(2977) =< s(2970) s(2978) =< s(2971) s(2979) =< s(2965) s(2980) =< s(2977)*s(2966) s(2981) =< s(2977)*s(2965) s(2982) =< s(2977)*s(2979) s(2983) =< s(2980) s(2984) =< s(2982) s(2985) =< s(2969) s(2986) =< s(2969) s(2985) =< s(2970) s(2987) =< s(2985)*s(2965) s(2988) =< s(2985)*s(2966) s(2989) =< s(2985)*s(2979) s(2990) =< s(2988) s(2991) =< s(2989) s(2992) =< s(2975) s(2993) =< s(2992)*aux(192) s(2994) =< s(2976) s(2995) =< s(2994)*s(2965) with precondition: [V2=2,Out=0,V>=0] * Chain [78]: 20*s(3040)+12*s(3041)+14*s(3042)+2*s(3043)+2*s(3044)+2*s(3045)+2*s(3046)+2*s(3047)+2*s(3056)+2*s(3057)+2*s(3058)+114*s(3061)+32*s(3062)+14*s(3065)+48*s(3067)+48*s(3068)+20*s(3069)+2*s(3070)+4*s(3071)+8*s(3074)+8*s(3075)+10*s(3076)+2*s(3077)+12*s(3078)+2*s(3079)+10*s(3081)+2*s(3082)+1*s(3131)+6 Such that:s(3131) =< 1 aux(196) =< 2 aux(197) =< V aux(198) =< 2*V aux(199) =< 2/3*V aux(200) =< 3/4*V aux(201) =< 3/5*V aux(202) =< 4/5*V aux(203) =< 4/7*V aux(204) =< 4/9*V s(3081) =< aux(196) s(3082) =< s(3081)*aux(196) s(3040) =< aux(197) s(3041) =< aux(197) s(3042) =< aux(197) s(3043) =< aux(197) s(3044) =< aux(197) s(3045) =< aux(197) s(3046) =< aux(197) s(3047) =< aux(197) s(3043) =< aux(199) s(3044) =< aux(199) s(3046) =< aux(199) s(3047) =< aux(200) s(3046) =< aux(201) s(3045) =< aux(202) s(3046) =< aux(202) s(3047) =< aux(202) s(3042) =< aux(203) s(3044) =< aux(203) s(3041) =< aux(204) s(3048) =< aux(198)+3 s(3049) =< aux(198)+2 s(3050) =< aux(198)+4 s(3051) =< aux(198) s(3052) =< aux(198)+1 s(3053) =< s(3040)*s(3048) s(3054) =< s(3040)*s(3049) s(3055) =< s(3040)*s(3050) s(3056) =< s(3044)*s(3051) s(3057) =< s(3043)*s(3052) s(3058) =< s(3042)*s(3051) s(3059) =< s(3042)*s(3051) s(3060) =< s(3041)*s(3049) s(3061) =< s(3054) s(3062) =< s(3055) s(3063) =< s(3049) s(3064) =< s(3061)*s(3050) s(3065) =< s(3061)*s(3049) s(3066) =< s(3061)*s(3063) s(3067) =< s(3064) s(3068) =< s(3066) s(3069) =< s(3053) s(3070) =< s(3053) s(3069) =< s(3054) s(3071) =< s(3069)*s(3049) s(3072) =< s(3069)*s(3050) s(3073) =< s(3069)*s(3063) s(3074) =< s(3072) s(3075) =< s(3073) s(3076) =< s(3059) s(3077) =< s(3076)*aux(198) s(3078) =< s(3060) s(3079) =< s(3078)*s(3049) with precondition: [V2=2,Out>=1,2*V>=Out+2] * Chain [77]: 10*s(3143)+6*s(3144)+7*s(3145)+1*s(3146)+1*s(3147)+1*s(3148)+1*s(3149)+1*s(3150)+1*s(3159)+1*s(3160)+1*s(3161)+57*s(3164)+16*s(3165)+7*s(3168)+24*s(3170)+24*s(3171)+10*s(3172)+1*s(3173)+2*s(3174)+4*s(3177)+4*s(3178)+5*s(3179)+1*s(3180)+6*s(3181)+1*s(3182)+1*s(3183)+6 Such that:s(3183) =< 2 s(3135) =< V s(3136) =< 2*V s(3137) =< 2/3*V s(3138) =< 3/4*V s(3139) =< 3/5*V s(3140) =< 4/5*V s(3141) =< 4/7*V s(3142) =< 4/9*V s(3143) =< s(3135) s(3144) =< s(3135) s(3145) =< s(3135) s(3146) =< s(3135) s(3147) =< s(3135) s(3148) =< s(3135) s(3149) =< s(3135) s(3150) =< s(3135) s(3146) =< s(3137) s(3147) =< s(3137) s(3149) =< s(3137) s(3150) =< s(3138) s(3149) =< s(3139) s(3148) =< s(3140) s(3149) =< s(3140) s(3150) =< s(3140) s(3145) =< s(3141) s(3147) =< s(3141) s(3144) =< s(3142) s(3151) =< s(3136)+3 s(3152) =< s(3136)+2 s(3153) =< s(3136)+4 s(3154) =< s(3136) s(3155) =< s(3136)+1 s(3156) =< s(3143)*s(3151) s(3157) =< s(3143)*s(3152) s(3158) =< s(3143)*s(3153) s(3159) =< s(3147)*s(3154) s(3160) =< s(3146)*s(3155) s(3161) =< s(3145)*s(3154) s(3162) =< s(3145)*s(3154) s(3163) =< s(3144)*s(3152) s(3164) =< s(3157) s(3165) =< s(3158) s(3166) =< s(3152) s(3167) =< s(3164)*s(3153) s(3168) =< s(3164)*s(3152) s(3169) =< s(3164)*s(3166) s(3170) =< s(3167) s(3171) =< s(3169) s(3172) =< s(3156) s(3173) =< s(3156) s(3172) =< s(3157) s(3174) =< s(3172)*s(3152) s(3175) =< s(3172)*s(3153) s(3176) =< s(3172)*s(3166) s(3177) =< s(3175) s(3178) =< s(3176) s(3179) =< s(3162) s(3180) =< s(3179)*s(3136) s(3181) =< s(3163) s(3182) =< s(3181)*s(3152) with precondition: [V2=2,Out>=2,2*V>=Out+1] #### Cost of chains of fun7(V,V2,V11,Out): * Chain [90]: 80*s(3543)+48*s(3544)+56*s(3545)+8*s(3546)+8*s(3547)+8*s(3548)+8*s(3549)+8*s(3550)+8*s(3559)+8*s(3560)+8*s(3561)+456*s(3564)+128*s(3565)+56*s(3568)+192*s(3570)+192*s(3571)+80*s(3572)+8*s(3573)+16*s(3574)+32*s(3577)+32*s(3578)+40*s(3579)+8*s(3580)+48*s(3581)+8*s(3582)+70*s(3591)+42*s(3592)+49*s(3593)+7*s(3594)+7*s(3595)+7*s(3596)+7*s(3597)+7*s(3598)+7*s(3607)+7*s(3608)+7*s(3609)+399*s(3612)+112*s(3613)+49*s(3616)+168*s(3618)+168*s(3619)+70*s(3620)+7*s(3621)+14*s(3622)+28*s(3625)+28*s(3626)+35*s(3627)+7*s(3628)+42*s(3629)+7*s(3630)+90*s(3639)+54*s(3640)+63*s(3641)+9*s(3642)+9*s(3643)+9*s(3644)+9*s(3645)+9*s(3646)+9*s(3655)+9*s(3656)+9*s(3657)+513*s(3660)+144*s(3661)+63*s(3664)+216*s(3666)+216*s(3667)+90*s(3668)+9*s(3669)+18*s(3670)+36*s(3673)+36*s(3674)+45*s(3675)+9*s(3676)+54*s(3677)+9*s(3678)+1 Such that:aux(223) =< V aux(224) =< 2*V aux(225) =< 2/3*V aux(226) =< 3/4*V aux(227) =< 3/5*V aux(228) =< 4/5*V aux(229) =< 4/7*V aux(230) =< 4/9*V aux(231) =< V2 aux(232) =< 2*V2 aux(233) =< 2/3*V2 aux(234) =< 3/4*V2 aux(235) =< 3/5*V2 aux(236) =< 4/5*V2 aux(237) =< 4/7*V2 aux(238) =< 4/9*V2 aux(239) =< V11 aux(240) =< 2*V11 aux(241) =< 2/3*V11 aux(242) =< 3/4*V11 aux(243) =< 3/5*V11 aux(244) =< 4/5*V11 aux(245) =< 4/7*V11 aux(246) =< 4/9*V11 s(3639) =< aux(239) s(3640) =< aux(239) s(3641) =< aux(239) s(3642) =< aux(239) s(3643) =< aux(239) s(3644) =< aux(239) s(3645) =< aux(239) s(3646) =< aux(239) s(3642) =< aux(241) s(3643) =< aux(241) s(3645) =< aux(241) s(3646) =< aux(242) s(3645) =< aux(243) s(3644) =< aux(244) s(3645) =< aux(244) s(3646) =< aux(244) s(3641) =< aux(245) s(3643) =< aux(245) s(3640) =< aux(246) s(3647) =< aux(240)+3 s(3648) =< aux(240)+2 s(3649) =< aux(240)+4 s(3650) =< aux(240) s(3651) =< aux(240)+1 s(3652) =< s(3639)*s(3647) s(3653) =< s(3639)*s(3648) s(3654) =< s(3639)*s(3649) s(3655) =< s(3643)*s(3650) s(3656) =< s(3642)*s(3651) s(3657) =< s(3641)*s(3650) s(3658) =< s(3641)*s(3650) s(3659) =< s(3640)*s(3648) s(3660) =< s(3653) s(3661) =< s(3654) s(3662) =< s(3648) s(3663) =< s(3660)*s(3649) s(3664) =< s(3660)*s(3648) s(3665) =< s(3660)*s(3662) s(3666) =< s(3663) s(3667) =< s(3665) s(3668) =< s(3652) s(3669) =< s(3652) s(3668) =< s(3653) s(3670) =< s(3668)*s(3648) s(3671) =< s(3668)*s(3649) s(3672) =< s(3668)*s(3662) s(3673) =< s(3671) s(3674) =< s(3672) s(3675) =< s(3658) s(3676) =< s(3675)*aux(240) s(3677) =< s(3659) s(3678) =< s(3677)*s(3648) s(3591) =< aux(231) s(3592) =< aux(231) s(3593) =< aux(231) s(3594) =< aux(231) s(3595) =< aux(231) s(3596) =< aux(231) s(3597) =< aux(231) s(3598) =< aux(231) s(3594) =< aux(233) s(3595) =< aux(233) s(3597) =< aux(233) s(3598) =< aux(234) s(3597) =< aux(235) s(3596) =< aux(236) s(3597) =< aux(236) s(3598) =< aux(236) s(3593) =< aux(237) s(3595) =< aux(237) s(3592) =< aux(238) s(3599) =< aux(232)+3 s(3600) =< aux(232)+2 s(3601) =< aux(232)+4 s(3602) =< aux(232) s(3603) =< aux(232)+1 s(3604) =< s(3591)*s(3599) s(3605) =< s(3591)*s(3600) s(3606) =< s(3591)*s(3601) s(3607) =< s(3595)*s(3602) s(3608) =< s(3594)*s(3603) s(3609) =< s(3593)*s(3602) s(3610) =< s(3593)*s(3602) s(3611) =< s(3592)*s(3600) s(3612) =< s(3605) s(3613) =< s(3606) s(3614) =< s(3600) s(3615) =< s(3612)*s(3601) s(3616) =< s(3612)*s(3600) s(3617) =< s(3612)*s(3614) s(3618) =< s(3615) s(3619) =< s(3617) s(3620) =< s(3604) s(3621) =< s(3604) s(3620) =< s(3605) s(3622) =< s(3620)*s(3600) s(3623) =< s(3620)*s(3601) s(3624) =< s(3620)*s(3614) s(3625) =< s(3623) s(3626) =< s(3624) s(3627) =< s(3610) s(3628) =< s(3627)*aux(232) s(3629) =< s(3611) s(3630) =< s(3629)*s(3600) s(3543) =< aux(223) s(3544) =< aux(223) s(3545) =< aux(223) s(3546) =< aux(223) s(3547) =< aux(223) s(3548) =< aux(223) s(3549) =< aux(223) s(3550) =< aux(223) s(3546) =< aux(225) s(3547) =< aux(225) s(3549) =< aux(225) s(3550) =< aux(226) s(3549) =< aux(227) s(3548) =< aux(228) s(3549) =< aux(228) s(3550) =< aux(228) s(3545) =< aux(229) s(3547) =< aux(229) s(3544) =< aux(230) s(3551) =< aux(224)+3 s(3552) =< aux(224)+2 s(3553) =< aux(224)+4 s(3554) =< aux(224) s(3555) =< aux(224)+1 s(3556) =< s(3543)*s(3551) s(3557) =< s(3543)*s(3552) s(3558) =< s(3543)*s(3553) s(3559) =< s(3547)*s(3554) s(3560) =< s(3546)*s(3555) s(3561) =< s(3545)*s(3554) s(3562) =< s(3545)*s(3554) s(3563) =< s(3544)*s(3552) s(3564) =< s(3557) s(3565) =< s(3558) s(3566) =< s(3552) s(3567) =< s(3564)*s(3553) s(3568) =< s(3564)*s(3552) s(3569) =< s(3564)*s(3566) s(3570) =< s(3567) s(3571) =< s(3569) s(3572) =< s(3556) s(3573) =< s(3556) s(3572) =< s(3557) s(3574) =< s(3572)*s(3552) s(3575) =< s(3572)*s(3553) s(3576) =< s(3572)*s(3566) s(3577) =< s(3575) s(3578) =< s(3576) s(3579) =< s(3562) s(3580) =< s(3579)*aux(224) s(3581) =< s(3563) s(3582) =< s(3581)*s(3552) with precondition: [Out=0,V>=0,V2>=0,V11>=0] * Chain [89]: 20*s(4695)+12*s(4696)+14*s(4697)+2*s(4698)+2*s(4699)+2*s(4700)+2*s(4701)+2*s(4702)+2*s(4711)+2*s(4712)+2*s(4713)+114*s(4716)+32*s(4717)+14*s(4720)+48*s(4722)+48*s(4723)+20*s(4724)+2*s(4725)+4*s(4726)+8*s(4729)+8*s(4730)+10*s(4731)+2*s(4732)+12*s(4733)+2*s(4734)+40*s(4743)+24*s(4744)+28*s(4745)+4*s(4746)+4*s(4747)+4*s(4748)+4*s(4749)+4*s(4750)+4*s(4759)+4*s(4760)+4*s(4761)+228*s(4764)+64*s(4765)+28*s(4768)+96*s(4770)+96*s(4771)+40*s(4772)+4*s(4773)+8*s(4774)+16*s(4777)+16*s(4778)+20*s(4779)+4*s(4780)+24*s(4781)+4*s(4782)+30*s(4791)+18*s(4792)+21*s(4793)+3*s(4794)+3*s(4795)+3*s(4796)+3*s(4797)+3*s(4798)+3*s(4807)+3*s(4808)+3*s(4809)+171*s(4812)+48*s(4813)+21*s(4816)+72*s(4818)+72*s(4819)+30*s(4820)+3*s(4821)+6*s(4822)+12*s(4825)+12*s(4826)+15*s(4827)+3*s(4828)+18*s(4829)+3*s(4830)+1 Such that:aux(247) =< V aux(248) =< 2*V aux(249) =< 2/3*V aux(250) =< 3/4*V aux(251) =< 3/5*V aux(252) =< 4/5*V aux(253) =< 4/7*V aux(254) =< 4/9*V aux(255) =< V2 aux(256) =< 2*V2 aux(257) =< 2/3*V2 aux(258) =< 3/4*V2 aux(259) =< 3/5*V2 aux(260) =< 4/5*V2 aux(261) =< 4/7*V2 aux(262) =< 4/9*V2 aux(263) =< V11 aux(264) =< 2*V11 aux(265) =< 2/3*V11 aux(266) =< 3/4*V11 aux(267) =< 3/5*V11 aux(268) =< 4/5*V11 aux(269) =< 4/7*V11 aux(270) =< 4/9*V11 s(4791) =< aux(263) s(4792) =< aux(263) s(4793) =< aux(263) s(4794) =< aux(263) s(4795) =< aux(263) s(4796) =< aux(263) s(4797) =< aux(263) s(4798) =< aux(263) s(4794) =< aux(265) s(4795) =< aux(265) s(4797) =< aux(265) s(4798) =< aux(266) s(4797) =< aux(267) s(4796) =< aux(268) s(4797) =< aux(268) s(4798) =< aux(268) s(4793) =< aux(269) s(4795) =< aux(269) s(4792) =< aux(270) s(4799) =< aux(264)+3 s(4800) =< aux(264)+2 s(4801) =< aux(264)+4 s(4802) =< aux(264) s(4803) =< aux(264)+1 s(4804) =< s(4791)*s(4799) s(4805) =< s(4791)*s(4800) s(4806) =< s(4791)*s(4801) s(4807) =< s(4795)*s(4802) s(4808) =< s(4794)*s(4803) s(4809) =< s(4793)*s(4802) s(4810) =< s(4793)*s(4802) s(4811) =< s(4792)*s(4800) s(4812) =< s(4805) s(4813) =< s(4806) s(4814) =< s(4800) s(4815) =< s(4812)*s(4801) s(4816) =< s(4812)*s(4800) s(4817) =< s(4812)*s(4814) s(4818) =< s(4815) s(4819) =< s(4817) s(4820) =< s(4804) s(4821) =< s(4804) s(4820) =< s(4805) s(4822) =< s(4820)*s(4800) s(4823) =< s(4820)*s(4801) s(4824) =< s(4820)*s(4814) s(4825) =< s(4823) s(4826) =< s(4824) s(4827) =< s(4810) s(4828) =< s(4827)*aux(264) s(4829) =< s(4811) s(4830) =< s(4829)*s(4800) s(4743) =< aux(255) s(4744) =< aux(255) s(4745) =< aux(255) s(4746) =< aux(255) s(4747) =< aux(255) s(4748) =< aux(255) s(4749) =< aux(255) s(4750) =< aux(255) s(4746) =< aux(257) s(4747) =< aux(257) s(4749) =< aux(257) s(4750) =< aux(258) s(4749) =< aux(259) s(4748) =< aux(260) s(4749) =< aux(260) s(4750) =< aux(260) s(4745) =< aux(261) s(4747) =< aux(261) s(4744) =< aux(262) s(4751) =< aux(256)+3 s(4752) =< aux(256)+2 s(4753) =< aux(256)+4 s(4754) =< aux(256) s(4755) =< aux(256)+1 s(4756) =< s(4743)*s(4751) s(4757) =< s(4743)*s(4752) s(4758) =< s(4743)*s(4753) s(4759) =< s(4747)*s(4754) s(4760) =< s(4746)*s(4755) s(4761) =< s(4745)*s(4754) s(4762) =< s(4745)*s(4754) s(4763) =< s(4744)*s(4752) s(4764) =< s(4757) s(4765) =< s(4758) s(4766) =< s(4752) s(4767) =< s(4764)*s(4753) s(4768) =< s(4764)*s(4752) s(4769) =< s(4764)*s(4766) s(4770) =< s(4767) s(4771) =< s(4769) s(4772) =< s(4756) s(4773) =< s(4756) s(4772) =< s(4757) s(4774) =< s(4772)*s(4752) s(4775) =< s(4772)*s(4753) s(4776) =< s(4772)*s(4766) s(4777) =< s(4775) s(4778) =< s(4776) s(4779) =< s(4762) s(4780) =< s(4779)*aux(256) s(4781) =< s(4763) s(4782) =< s(4781)*s(4752) s(4695) =< aux(247) s(4696) =< aux(247) s(4697) =< aux(247) s(4698) =< aux(247) s(4699) =< aux(247) s(4700) =< aux(247) s(4701) =< aux(247) s(4702) =< aux(247) s(4698) =< aux(249) s(4699) =< aux(249) s(4701) =< aux(249) s(4702) =< aux(250) s(4701) =< aux(251) s(4700) =< aux(252) s(4701) =< aux(252) s(4702) =< aux(252) s(4697) =< aux(253) s(4699) =< aux(253) s(4696) =< aux(254) s(4703) =< aux(248)+3 s(4704) =< aux(248)+2 s(4705) =< aux(248)+4 s(4706) =< aux(248) s(4707) =< aux(248)+1 s(4708) =< s(4695)*s(4703) s(4709) =< s(4695)*s(4704) s(4710) =< s(4695)*s(4705) s(4711) =< s(4699)*s(4706) s(4712) =< s(4698)*s(4707) s(4713) =< s(4697)*s(4706) s(4714) =< s(4697)*s(4706) s(4715) =< s(4696)*s(4704) s(4716) =< s(4709) s(4717) =< s(4710) s(4718) =< s(4704) s(4719) =< s(4716)*s(4705) s(4720) =< s(4716)*s(4704) s(4721) =< s(4716)*s(4718) s(4722) =< s(4719) s(4723) =< s(4721) s(4724) =< s(4708) s(4725) =< s(4708) s(4724) =< s(4709) s(4726) =< s(4724)*s(4704) s(4727) =< s(4724)*s(4705) s(4728) =< s(4724)*s(4718) s(4729) =< s(4727) s(4730) =< s(4728) s(4731) =< s(4714) s(4732) =< s(4731)*aux(248) s(4733) =< s(4715) s(4734) =< s(4733)*s(4704) with precondition: [V>=1,V2>=1,V11>=0,Out>=0,2*V2>=Out] * Chain [88]: 30*s(5127)+18*s(5128)+21*s(5129)+3*s(5130)+3*s(5131)+3*s(5132)+3*s(5133)+3*s(5134)+3*s(5143)+3*s(5144)+3*s(5145)+171*s(5148)+48*s(5149)+21*s(5152)+72*s(5154)+72*s(5155)+30*s(5156)+3*s(5157)+6*s(5158)+12*s(5161)+12*s(5162)+15*s(5163)+3*s(5164)+18*s(5165)+3*s(5166)+30*s(5175)+18*s(5176)+21*s(5177)+3*s(5178)+3*s(5179)+3*s(5180)+3*s(5181)+3*s(5182)+3*s(5191)+3*s(5192)+3*s(5193)+171*s(5196)+48*s(5197)+21*s(5200)+72*s(5202)+72*s(5203)+30*s(5204)+3*s(5205)+6*s(5206)+12*s(5209)+12*s(5210)+15*s(5211)+3*s(5212)+18*s(5213)+3*s(5214)+1 Such that:aux(271) =< V aux(272) =< 2*V aux(273) =< 2/3*V aux(274) =< 3/4*V aux(275) =< 3/5*V aux(276) =< 4/5*V aux(277) =< 4/7*V aux(278) =< 4/9*V aux(279) =< V2 aux(280) =< 2*V2 aux(281) =< 2/3*V2 aux(282) =< 3/4*V2 aux(283) =< 3/5*V2 aux(284) =< 4/5*V2 aux(285) =< 4/7*V2 aux(286) =< 4/9*V2 s(5175) =< aux(279) s(5176) =< aux(279) s(5177) =< aux(279) s(5178) =< aux(279) s(5179) =< aux(279) s(5180) =< aux(279) s(5181) =< aux(279) s(5182) =< aux(279) s(5178) =< aux(281) s(5179) =< aux(281) s(5181) =< aux(281) s(5182) =< aux(282) s(5181) =< aux(283) s(5180) =< aux(284) s(5181) =< aux(284) s(5182) =< aux(284) s(5177) =< aux(285) s(5179) =< aux(285) s(5176) =< aux(286) s(5183) =< aux(280)+3 s(5184) =< aux(280)+2 s(5185) =< aux(280)+4 s(5186) =< aux(280) s(5187) =< aux(280)+1 s(5188) =< s(5175)*s(5183) s(5189) =< s(5175)*s(5184) s(5190) =< s(5175)*s(5185) s(5191) =< s(5179)*s(5186) s(5192) =< s(5178)*s(5187) s(5193) =< s(5177)*s(5186) s(5194) =< s(5177)*s(5186) s(5195) =< s(5176)*s(5184) s(5196) =< s(5189) s(5197) =< s(5190) s(5198) =< s(5184) s(5199) =< s(5196)*s(5185) s(5200) =< s(5196)*s(5184) s(5201) =< s(5196)*s(5198) s(5202) =< s(5199) s(5203) =< s(5201) s(5204) =< s(5188) s(5205) =< s(5188) s(5204) =< s(5189) s(5206) =< s(5204)*s(5184) s(5207) =< s(5204)*s(5185) s(5208) =< s(5204)*s(5198) s(5209) =< s(5207) s(5210) =< s(5208) s(5211) =< s(5194) s(5212) =< s(5211)*aux(280) s(5213) =< s(5195) s(5214) =< s(5213)*s(5184) s(5127) =< aux(271) s(5128) =< aux(271) s(5129) =< aux(271) s(5130) =< aux(271) s(5131) =< aux(271) s(5132) =< aux(271) s(5133) =< aux(271) s(5134) =< aux(271) s(5130) =< aux(273) s(5131) =< aux(273) s(5133) =< aux(273) s(5134) =< aux(274) s(5133) =< aux(275) s(5132) =< aux(276) s(5133) =< aux(276) s(5134) =< aux(276) s(5129) =< aux(277) s(5131) =< aux(277) s(5128) =< aux(278) s(5135) =< aux(272)+3 s(5136) =< aux(272)+2 s(5137) =< aux(272)+4 s(5138) =< aux(272) s(5139) =< aux(272)+1 s(5140) =< s(5127)*s(5135) s(5141) =< s(5127)*s(5136) s(5142) =< s(5127)*s(5137) s(5143) =< s(5131)*s(5138) s(5144) =< s(5130)*s(5139) s(5145) =< s(5129)*s(5138) s(5146) =< s(5129)*s(5138) s(5147) =< s(5128)*s(5136) s(5148) =< s(5141) s(5149) =< s(5142) s(5150) =< s(5136) s(5151) =< s(5148)*s(5137) s(5152) =< s(5148)*s(5136) s(5153) =< s(5148)*s(5150) s(5154) =< s(5151) s(5155) =< s(5153) s(5156) =< s(5140) s(5157) =< s(5140) s(5156) =< s(5141) s(5158) =< s(5156)*s(5136) s(5159) =< s(5156)*s(5137) s(5160) =< s(5156)*s(5150) s(5161) =< s(5159) s(5162) =< s(5160) s(5163) =< s(5146) s(5164) =< s(5163)*aux(272) s(5165) =< s(5147) s(5166) =< s(5165)*s(5136) with precondition: [V11=2,Out=0,V>=0,V2>=0] * Chain [87]: 10*s(5415)+6*s(5416)+7*s(5417)+1*s(5418)+1*s(5419)+1*s(5420)+1*s(5421)+1*s(5422)+1*s(5431)+1*s(5432)+1*s(5433)+57*s(5436)+16*s(5437)+7*s(5440)+24*s(5442)+24*s(5443)+10*s(5444)+1*s(5445)+2*s(5446)+4*s(5449)+4*s(5450)+5*s(5451)+1*s(5452)+6*s(5453)+1*s(5454)+20*s(5463)+12*s(5464)+14*s(5465)+2*s(5466)+2*s(5467)+2*s(5468)+2*s(5469)+2*s(5470)+2*s(5479)+2*s(5480)+2*s(5481)+114*s(5484)+32*s(5485)+14*s(5488)+48*s(5490)+48*s(5491)+20*s(5492)+2*s(5493)+4*s(5494)+8*s(5497)+8*s(5498)+10*s(5499)+2*s(5500)+12*s(5501)+2*s(5502)+1 Such that:s(5407) =< V s(5408) =< 2*V s(5409) =< 2/3*V s(5410) =< 3/4*V s(5411) =< 3/5*V s(5412) =< 4/5*V s(5413) =< 4/7*V s(5414) =< 4/9*V aux(287) =< V2 aux(288) =< 2*V2 aux(289) =< 2/3*V2 aux(290) =< 3/4*V2 aux(291) =< 3/5*V2 aux(292) =< 4/5*V2 aux(293) =< 4/7*V2 aux(294) =< 4/9*V2 s(5463) =< aux(287) s(5464) =< aux(287) s(5465) =< aux(287) s(5466) =< aux(287) s(5467) =< aux(287) s(5468) =< aux(287) s(5469) =< aux(287) s(5470) =< aux(287) s(5466) =< aux(289) s(5467) =< aux(289) s(5469) =< aux(289) s(5470) =< aux(290) s(5469) =< aux(291) s(5468) =< aux(292) s(5469) =< aux(292) s(5470) =< aux(292) s(5465) =< aux(293) s(5467) =< aux(293) s(5464) =< aux(294) s(5471) =< aux(288)+3 s(5472) =< aux(288)+2 s(5473) =< aux(288)+4 s(5474) =< aux(288) s(5475) =< aux(288)+1 s(5476) =< s(5463)*s(5471) s(5477) =< s(5463)*s(5472) s(5478) =< s(5463)*s(5473) s(5479) =< s(5467)*s(5474) s(5480) =< s(5466)*s(5475) s(5481) =< s(5465)*s(5474) s(5482) =< s(5465)*s(5474) s(5483) =< s(5464)*s(5472) s(5484) =< s(5477) s(5485) =< s(5478) s(5486) =< s(5472) s(5487) =< s(5484)*s(5473) s(5488) =< s(5484)*s(5472) s(5489) =< s(5484)*s(5486) s(5490) =< s(5487) s(5491) =< s(5489) s(5492) =< s(5476) s(5493) =< s(5476) s(5492) =< s(5477) s(5494) =< s(5492)*s(5472) s(5495) =< s(5492)*s(5473) s(5496) =< s(5492)*s(5486) s(5497) =< s(5495) s(5498) =< s(5496) s(5499) =< s(5482) s(5500) =< s(5499)*aux(288) s(5501) =< s(5483) s(5502) =< s(5501)*s(5472) s(5415) =< s(5407) s(5416) =< s(5407) s(5417) =< s(5407) s(5418) =< s(5407) s(5419) =< s(5407) s(5420) =< s(5407) s(5421) =< s(5407) s(5422) =< s(5407) s(5418) =< s(5409) s(5419) =< s(5409) s(5421) =< s(5409) s(5422) =< s(5410) s(5421) =< s(5411) s(5420) =< s(5412) s(5421) =< s(5412) s(5422) =< s(5412) s(5417) =< s(5413) s(5419) =< s(5413) s(5416) =< s(5414) s(5423) =< s(5408)+3 s(5424) =< s(5408)+2 s(5425) =< s(5408)+4 s(5426) =< s(5408) s(5427) =< s(5408)+1 s(5428) =< s(5415)*s(5423) s(5429) =< s(5415)*s(5424) s(5430) =< s(5415)*s(5425) s(5431) =< s(5419)*s(5426) s(5432) =< s(5418)*s(5427) s(5433) =< s(5417)*s(5426) s(5434) =< s(5417)*s(5426) s(5435) =< s(5416)*s(5424) s(5436) =< s(5429) s(5437) =< s(5430) s(5438) =< s(5424) s(5439) =< s(5436)*s(5425) s(5440) =< s(5436)*s(5424) s(5441) =< s(5436)*s(5438) s(5442) =< s(5439) s(5443) =< s(5441) s(5444) =< s(5428) s(5445) =< s(5428) s(5444) =< s(5429) s(5446) =< s(5444)*s(5424) s(5447) =< s(5444)*s(5425) s(5448) =< s(5444)*s(5438) s(5449) =< s(5447) s(5450) =< s(5448) s(5451) =< s(5434) s(5452) =< s(5451)*s(5408) s(5453) =< s(5435) s(5454) =< s(5453)*s(5424) with precondition: [V11=2,V>=1,V2>=1,Out>=0,2*V2>=Out] * Chain [86]: 40*s(5559)+24*s(5560)+28*s(5561)+4*s(5562)+4*s(5563)+4*s(5564)+4*s(5565)+4*s(5566)+4*s(5575)+4*s(5576)+4*s(5577)+228*s(5580)+64*s(5581)+28*s(5584)+96*s(5586)+96*s(5587)+40*s(5588)+4*s(5589)+8*s(5590)+16*s(5593)+16*s(5594)+20*s(5595)+4*s(5596)+24*s(5597)+4*s(5598)+20*s(5607)+12*s(5608)+14*s(5609)+2*s(5610)+2*s(5611)+2*s(5612)+2*s(5613)+2*s(5614)+2*s(5623)+2*s(5624)+2*s(5625)+114*s(5628)+32*s(5629)+14*s(5632)+48*s(5634)+48*s(5635)+20*s(5636)+2*s(5637)+4*s(5638)+8*s(5641)+8*s(5642)+10*s(5643)+2*s(5644)+12*s(5645)+2*s(5646)+1 Such that:aux(295) =< V aux(296) =< 2*V aux(297) =< 2/3*V aux(298) =< 3/4*V aux(299) =< 3/5*V aux(300) =< 4/5*V aux(301) =< 4/7*V aux(302) =< 4/9*V aux(303) =< V11 aux(304) =< 2*V11 aux(305) =< 2/3*V11 aux(306) =< 3/4*V11 aux(307) =< 3/5*V11 aux(308) =< 4/5*V11 aux(309) =< 4/7*V11 aux(310) =< 4/9*V11 s(5607) =< aux(303) s(5608) =< aux(303) s(5609) =< aux(303) s(5610) =< aux(303) s(5611) =< aux(303) s(5612) =< aux(303) s(5613) =< aux(303) s(5614) =< aux(303) s(5610) =< aux(305) s(5611) =< aux(305) s(5613) =< aux(305) s(5614) =< aux(306) s(5613) =< aux(307) s(5612) =< aux(308) s(5613) =< aux(308) s(5614) =< aux(308) s(5609) =< aux(309) s(5611) =< aux(309) s(5608) =< aux(310) s(5615) =< aux(304)+3 s(5616) =< aux(304)+2 s(5617) =< aux(304)+4 s(5618) =< aux(304) s(5619) =< aux(304)+1 s(5620) =< s(5607)*s(5615) s(5621) =< s(5607)*s(5616) s(5622) =< s(5607)*s(5617) s(5623) =< s(5611)*s(5618) s(5624) =< s(5610)*s(5619) s(5625) =< s(5609)*s(5618) s(5626) =< s(5609)*s(5618) s(5627) =< s(5608)*s(5616) s(5628) =< s(5621) s(5629) =< s(5622) s(5630) =< s(5616) s(5631) =< s(5628)*s(5617) s(5632) =< s(5628)*s(5616) s(5633) =< s(5628)*s(5630) s(5634) =< s(5631) s(5635) =< s(5633) s(5636) =< s(5620) s(5637) =< s(5620) s(5636) =< s(5621) s(5638) =< s(5636)*s(5616) s(5639) =< s(5636)*s(5617) s(5640) =< s(5636)*s(5630) s(5641) =< s(5639) s(5642) =< s(5640) s(5643) =< s(5626) s(5644) =< s(5643)*aux(304) s(5645) =< s(5627) s(5646) =< s(5645)*s(5616) s(5559) =< aux(295) s(5560) =< aux(295) s(5561) =< aux(295) s(5562) =< aux(295) s(5563) =< aux(295) s(5564) =< aux(295) s(5565) =< aux(295) s(5566) =< aux(295) s(5562) =< aux(297) s(5563) =< aux(297) s(5565) =< aux(297) s(5566) =< aux(298) s(5565) =< aux(299) s(5564) =< aux(300) s(5565) =< aux(300) s(5566) =< aux(300) s(5561) =< aux(301) s(5563) =< aux(301) s(5560) =< aux(302) s(5567) =< aux(296)+3 s(5568) =< aux(296)+2 s(5569) =< aux(296)+4 s(5570) =< aux(296) s(5571) =< aux(296)+1 s(5572) =< s(5559)*s(5567) s(5573) =< s(5559)*s(5568) s(5574) =< s(5559)*s(5569) s(5575) =< s(5563)*s(5570) s(5576) =< s(5562)*s(5571) s(5577) =< s(5561)*s(5570) s(5578) =< s(5561)*s(5570) s(5579) =< s(5560)*s(5568) s(5580) =< s(5573) s(5581) =< s(5574) s(5582) =< s(5568) s(5583) =< s(5580)*s(5569) s(5584) =< s(5580)*s(5568) s(5585) =< s(5580)*s(5582) s(5586) =< s(5583) s(5587) =< s(5585) s(5588) =< s(5572) s(5589) =< s(5572) s(5588) =< s(5573) s(5590) =< s(5588)*s(5568) s(5591) =< s(5588)*s(5569) s(5592) =< s(5588)*s(5582) s(5593) =< s(5591) s(5594) =< s(5592) s(5595) =< s(5578) s(5596) =< s(5595)*aux(296) s(5597) =< s(5579) s(5598) =< s(5597)*s(5568) with precondition: [V2=2,Out=0,V>=0,V11>=0] * Chain [85]: 40*s(5847)+24*s(5848)+28*s(5849)+4*s(5850)+4*s(5851)+4*s(5852)+4*s(5853)+4*s(5854)+4*s(5863)+4*s(5864)+4*s(5865)+228*s(5868)+64*s(5869)+28*s(5872)+96*s(5874)+96*s(5875)+40*s(5876)+4*s(5877)+8*s(5878)+16*s(5881)+16*s(5882)+20*s(5883)+4*s(5884)+24*s(5885)+4*s(5886)+10*s(5895)+6*s(5896)+7*s(5897)+1*s(5898)+1*s(5899)+1*s(5900)+1*s(5901)+1*s(5902)+1*s(5911)+1*s(5912)+1*s(5913)+57*s(5916)+16*s(5917)+7*s(5920)+24*s(5922)+24*s(5923)+10*s(5924)+1*s(5925)+2*s(5926)+4*s(5929)+4*s(5930)+5*s(5931)+1*s(5932)+6*s(5933)+1*s(5934)+1 Such that:s(5887) =< V11 s(5888) =< 2*V11 s(5889) =< 2/3*V11 s(5890) =< 3/4*V11 s(5891) =< 3/5*V11 s(5892) =< 4/5*V11 s(5893) =< 4/7*V11 s(5894) =< 4/9*V11 aux(311) =< V aux(312) =< 2*V aux(313) =< 2/3*V aux(314) =< 3/4*V aux(315) =< 3/5*V aux(316) =< 4/5*V aux(317) =< 4/7*V aux(318) =< 4/9*V s(5895) =< s(5887) s(5896) =< s(5887) s(5897) =< s(5887) s(5898) =< s(5887) s(5899) =< s(5887) s(5900) =< s(5887) s(5901) =< s(5887) s(5902) =< s(5887) s(5898) =< s(5889) s(5899) =< s(5889) s(5901) =< s(5889) s(5902) =< s(5890) s(5901) =< s(5891) s(5900) =< s(5892) s(5901) =< s(5892) s(5902) =< s(5892) s(5897) =< s(5893) s(5899) =< s(5893) s(5896) =< s(5894) s(5903) =< s(5888)+3 s(5904) =< s(5888)+2 s(5905) =< s(5888)+4 s(5906) =< s(5888) s(5907) =< s(5888)+1 s(5908) =< s(5895)*s(5903) s(5909) =< s(5895)*s(5904) s(5910) =< s(5895)*s(5905) s(5911) =< s(5899)*s(5906) s(5912) =< s(5898)*s(5907) s(5913) =< s(5897)*s(5906) s(5914) =< s(5897)*s(5906) s(5915) =< s(5896)*s(5904) s(5916) =< s(5909) s(5917) =< s(5910) s(5918) =< s(5904) s(5919) =< s(5916)*s(5905) s(5920) =< s(5916)*s(5904) s(5921) =< s(5916)*s(5918) s(5922) =< s(5919) s(5923) =< s(5921) s(5924) =< s(5908) s(5925) =< s(5908) s(5924) =< s(5909) s(5926) =< s(5924)*s(5904) s(5927) =< s(5924)*s(5905) s(5928) =< s(5924)*s(5918) s(5929) =< s(5927) s(5930) =< s(5928) s(5931) =< s(5914) s(5932) =< s(5931)*s(5888) s(5933) =< s(5915) s(5934) =< s(5933)*s(5904) s(5847) =< aux(311) s(5848) =< aux(311) s(5849) =< aux(311) s(5850) =< aux(311) s(5851) =< aux(311) s(5852) =< aux(311) s(5853) =< aux(311) s(5854) =< aux(311) s(5850) =< aux(313) s(5851) =< aux(313) s(5853) =< aux(313) s(5854) =< aux(314) s(5853) =< aux(315) s(5852) =< aux(316) s(5853) =< aux(316) s(5854) =< aux(316) s(5849) =< aux(317) s(5851) =< aux(317) s(5848) =< aux(318) s(5855) =< aux(312)+3 s(5856) =< aux(312)+2 s(5857) =< aux(312)+4 s(5858) =< aux(312) s(5859) =< aux(312)+1 s(5860) =< s(5847)*s(5855) s(5861) =< s(5847)*s(5856) s(5862) =< s(5847)*s(5857) s(5863) =< s(5851)*s(5858) s(5864) =< s(5850)*s(5859) s(5865) =< s(5849)*s(5858) s(5866) =< s(5849)*s(5858) s(5867) =< s(5848)*s(5856) s(5868) =< s(5861) s(5869) =< s(5862) s(5870) =< s(5856) s(5871) =< s(5868)*s(5857) s(5872) =< s(5868)*s(5856) s(5873) =< s(5868)*s(5870) s(5874) =< s(5871) s(5875) =< s(5873) s(5876) =< s(5860) s(5877) =< s(5860) s(5876) =< s(5861) s(5878) =< s(5876)*s(5856) s(5879) =< s(5876)*s(5857) s(5880) =< s(5876)*s(5870) s(5881) =< s(5879) s(5882) =< s(5880) s(5883) =< s(5866) s(5884) =< s(5883)*aux(312) s(5885) =< s(5867) s(5886) =< s(5885)*s(5856) with precondition: [V2=2,Out=2,V>=1,V11>=0] * Chain [84]: 30*s(6087)+18*s(6088)+21*s(6089)+3*s(6090)+3*s(6091)+3*s(6092)+3*s(6093)+3*s(6094)+3*s(6103)+3*s(6104)+3*s(6105)+171*s(6108)+48*s(6109)+21*s(6112)+72*s(6114)+72*s(6115)+30*s(6116)+3*s(6117)+6*s(6118)+12*s(6121)+12*s(6122)+15*s(6123)+3*s(6124)+18*s(6125)+3*s(6126)+10*s(6135)+6*s(6136)+7*s(6137)+1*s(6138)+1*s(6139)+1*s(6140)+1*s(6141)+1*s(6142)+1*s(6151)+1*s(6152)+1*s(6153)+57*s(6156)+16*s(6157)+7*s(6160)+24*s(6162)+24*s(6163)+10*s(6164)+1*s(6165)+2*s(6166)+4*s(6169)+4*s(6170)+5*s(6171)+1*s(6172)+6*s(6173)+1*s(6174)+30*s(6183)+18*s(6184)+21*s(6185)+3*s(6186)+3*s(6187)+3*s(6188)+3*s(6189)+3*s(6190)+3*s(6199)+3*s(6200)+3*s(6201)+171*s(6204)+48*s(6205)+21*s(6208)+72*s(6210)+72*s(6211)+30*s(6212)+3*s(6213)+6*s(6214)+12*s(6217)+12*s(6218)+15*s(6219)+3*s(6220)+18*s(6221)+3*s(6222)+1 Such that:s(6127) =< V2 s(6128) =< 2*V2 s(6129) =< 2/3*V2 s(6130) =< 3/4*V2 s(6131) =< 3/5*V2 s(6132) =< 4/5*V2 s(6133) =< 4/7*V2 s(6134) =< 4/9*V2 aux(319) =< V aux(320) =< 2*V aux(321) =< 2/3*V aux(322) =< 3/4*V aux(323) =< 3/5*V aux(324) =< 4/5*V aux(325) =< 4/7*V aux(326) =< 4/9*V aux(327) =< V11 aux(328) =< 2*V11 aux(329) =< 2/3*V11 aux(330) =< 3/4*V11 aux(331) =< 3/5*V11 aux(332) =< 4/5*V11 aux(333) =< 4/7*V11 aux(334) =< 4/9*V11 s(6183) =< aux(327) s(6184) =< aux(327) s(6185) =< aux(327) s(6186) =< aux(327) s(6187) =< aux(327) s(6188) =< aux(327) s(6189) =< aux(327) s(6190) =< aux(327) s(6186) =< aux(329) s(6187) =< aux(329) s(6189) =< aux(329) s(6190) =< aux(330) s(6189) =< aux(331) s(6188) =< aux(332) s(6189) =< aux(332) s(6190) =< aux(332) s(6185) =< aux(333) s(6187) =< aux(333) s(6184) =< aux(334) s(6191) =< aux(328)+3 s(6192) =< aux(328)+2 s(6193) =< aux(328)+4 s(6194) =< aux(328) s(6195) =< aux(328)+1 s(6196) =< s(6183)*s(6191) s(6197) =< s(6183)*s(6192) s(6198) =< s(6183)*s(6193) s(6199) =< s(6187)*s(6194) s(6200) =< s(6186)*s(6195) s(6201) =< s(6185)*s(6194) s(6202) =< s(6185)*s(6194) s(6203) =< s(6184)*s(6192) s(6204) =< s(6197) s(6205) =< s(6198) s(6206) =< s(6192) s(6207) =< s(6204)*s(6193) s(6208) =< s(6204)*s(6192) s(6209) =< s(6204)*s(6206) s(6210) =< s(6207) s(6211) =< s(6209) s(6212) =< s(6196) s(6213) =< s(6196) s(6212) =< s(6197) s(6214) =< s(6212)*s(6192) s(6215) =< s(6212)*s(6193) s(6216) =< s(6212)*s(6206) s(6217) =< s(6215) s(6218) =< s(6216) s(6219) =< s(6202) s(6220) =< s(6219)*aux(328) s(6221) =< s(6203) s(6222) =< s(6221)*s(6192) s(6135) =< s(6127) s(6136) =< s(6127) s(6137) =< s(6127) s(6138) =< s(6127) s(6139) =< s(6127) s(6140) =< s(6127) s(6141) =< s(6127) s(6142) =< s(6127) s(6138) =< s(6129) s(6139) =< s(6129) s(6141) =< s(6129) s(6142) =< s(6130) s(6141) =< s(6131) s(6140) =< s(6132) s(6141) =< s(6132) s(6142) =< s(6132) s(6137) =< s(6133) s(6139) =< s(6133) s(6136) =< s(6134) s(6143) =< s(6128)+3 s(6144) =< s(6128)+2 s(6145) =< s(6128)+4 s(6146) =< s(6128) s(6147) =< s(6128)+1 s(6148) =< s(6135)*s(6143) s(6149) =< s(6135)*s(6144) s(6150) =< s(6135)*s(6145) s(6151) =< s(6139)*s(6146) s(6152) =< s(6138)*s(6147) s(6153) =< s(6137)*s(6146) s(6154) =< s(6137)*s(6146) s(6155) =< s(6136)*s(6144) s(6156) =< s(6149) s(6157) =< s(6150) s(6158) =< s(6144) s(6159) =< s(6156)*s(6145) s(6160) =< s(6156)*s(6144) s(6161) =< s(6156)*s(6158) s(6162) =< s(6159) s(6163) =< s(6161) s(6164) =< s(6148) s(6165) =< s(6148) s(6164) =< s(6149) s(6166) =< s(6164)*s(6144) s(6167) =< s(6164)*s(6145) s(6168) =< s(6164)*s(6158) s(6169) =< s(6167) s(6170) =< s(6168) s(6171) =< s(6154) s(6172) =< s(6171)*s(6128) s(6173) =< s(6155) s(6174) =< s(6173)*s(6144) s(6087) =< aux(319) s(6088) =< aux(319) s(6089) =< aux(319) s(6090) =< aux(319) s(6091) =< aux(319) s(6092) =< aux(319) s(6093) =< aux(319) s(6094) =< aux(319) s(6090) =< aux(321) s(6091) =< aux(321) s(6093) =< aux(321) s(6094) =< aux(322) s(6093) =< aux(323) s(6092) =< aux(324) s(6093) =< aux(324) s(6094) =< aux(324) s(6089) =< aux(325) s(6091) =< aux(325) s(6088) =< aux(326) s(6095) =< aux(320)+3 s(6096) =< aux(320)+2 s(6097) =< aux(320)+4 s(6098) =< aux(320) s(6099) =< aux(320)+1 s(6100) =< s(6087)*s(6095) s(6101) =< s(6087)*s(6096) s(6102) =< s(6087)*s(6097) s(6103) =< s(6091)*s(6098) s(6104) =< s(6090)*s(6099) s(6105) =< s(6089)*s(6098) s(6106) =< s(6089)*s(6098) s(6107) =< s(6088)*s(6096) s(6108) =< s(6101) s(6109) =< s(6102) s(6110) =< s(6096) s(6111) =< s(6108)*s(6097) s(6112) =< s(6108)*s(6096) s(6113) =< s(6108)*s(6110) s(6114) =< s(6111) s(6115) =< s(6113) s(6116) =< s(6100) s(6117) =< s(6100) s(6116) =< s(6101) s(6118) =< s(6116)*s(6096) s(6119) =< s(6116)*s(6097) s(6120) =< s(6116)*s(6110) s(6121) =< s(6119) s(6122) =< s(6120) s(6123) =< s(6106) s(6124) =< s(6123)*aux(320) s(6125) =< s(6107) s(6126) =< s(6125)*s(6096) with precondition: [V>=1,V2>=0,V11>=1,Out>=0,2*V11>=Out] * Chain [83]: 20*s(6423)+12*s(6424)+14*s(6425)+2*s(6426)+2*s(6427)+2*s(6428)+2*s(6429)+2*s(6430)+2*s(6439)+2*s(6440)+2*s(6441)+114*s(6444)+32*s(6445)+14*s(6448)+48*s(6450)+48*s(6451)+20*s(6452)+2*s(6453)+4*s(6454)+8*s(6457)+8*s(6458)+10*s(6459)+2*s(6460)+12*s(6461)+2*s(6462)+10*s(6471)+6*s(6472)+7*s(6473)+1*s(6474)+1*s(6475)+1*s(6476)+1*s(6477)+1*s(6478)+1*s(6487)+1*s(6488)+1*s(6489)+57*s(6492)+16*s(6493)+7*s(6496)+24*s(6498)+24*s(6499)+10*s(6500)+1*s(6501)+2*s(6502)+4*s(6505)+4*s(6506)+5*s(6507)+1*s(6508)+6*s(6509)+1*s(6510)+1 Such that:s(6463) =< V2 s(6464) =< 2*V2 s(6465) =< 2/3*V2 s(6466) =< 3/4*V2 s(6467) =< 3/5*V2 s(6468) =< 4/5*V2 s(6469) =< 4/7*V2 s(6470) =< 4/9*V2 aux(335) =< V aux(336) =< 2*V aux(337) =< 2/3*V aux(338) =< 3/4*V aux(339) =< 3/5*V aux(340) =< 4/5*V aux(341) =< 4/7*V aux(342) =< 4/9*V s(6471) =< s(6463) s(6472) =< s(6463) s(6473) =< s(6463) s(6474) =< s(6463) s(6475) =< s(6463) s(6476) =< s(6463) s(6477) =< s(6463) s(6478) =< s(6463) s(6474) =< s(6465) s(6475) =< s(6465) s(6477) =< s(6465) s(6478) =< s(6466) s(6477) =< s(6467) s(6476) =< s(6468) s(6477) =< s(6468) s(6478) =< s(6468) s(6473) =< s(6469) s(6475) =< s(6469) s(6472) =< s(6470) s(6479) =< s(6464)+3 s(6480) =< s(6464)+2 s(6481) =< s(6464)+4 s(6482) =< s(6464) s(6483) =< s(6464)+1 s(6484) =< s(6471)*s(6479) s(6485) =< s(6471)*s(6480) s(6486) =< s(6471)*s(6481) s(6487) =< s(6475)*s(6482) s(6488) =< s(6474)*s(6483) s(6489) =< s(6473)*s(6482) s(6490) =< s(6473)*s(6482) s(6491) =< s(6472)*s(6480) s(6492) =< s(6485) s(6493) =< s(6486) s(6494) =< s(6480) s(6495) =< s(6492)*s(6481) s(6496) =< s(6492)*s(6480) s(6497) =< s(6492)*s(6494) s(6498) =< s(6495) s(6499) =< s(6497) s(6500) =< s(6484) s(6501) =< s(6484) s(6500) =< s(6485) s(6502) =< s(6500)*s(6480) s(6503) =< s(6500)*s(6481) s(6504) =< s(6500)*s(6494) s(6505) =< s(6503) s(6506) =< s(6504) s(6507) =< s(6490) s(6508) =< s(6507)*s(6464) s(6509) =< s(6491) s(6510) =< s(6509)*s(6480) s(6423) =< aux(335) s(6424) =< aux(335) s(6425) =< aux(335) s(6426) =< aux(335) s(6427) =< aux(335) s(6428) =< aux(335) s(6429) =< aux(335) s(6430) =< aux(335) s(6426) =< aux(337) s(6427) =< aux(337) s(6429) =< aux(337) s(6430) =< aux(338) s(6429) =< aux(339) s(6428) =< aux(340) s(6429) =< aux(340) s(6430) =< aux(340) s(6425) =< aux(341) s(6427) =< aux(341) s(6424) =< aux(342) s(6431) =< aux(336)+3 s(6432) =< aux(336)+2 s(6433) =< aux(336)+4 s(6434) =< aux(336) s(6435) =< aux(336)+1 s(6436) =< s(6423)*s(6431) s(6437) =< s(6423)*s(6432) s(6438) =< s(6423)*s(6433) s(6439) =< s(6427)*s(6434) s(6440) =< s(6426)*s(6435) s(6441) =< s(6425)*s(6434) s(6442) =< s(6425)*s(6434) s(6443) =< s(6424)*s(6432) s(6444) =< s(6437) s(6445) =< s(6438) s(6446) =< s(6432) s(6447) =< s(6444)*s(6433) s(6448) =< s(6444)*s(6432) s(6449) =< s(6444)*s(6446) s(6450) =< s(6447) s(6451) =< s(6449) s(6452) =< s(6436) s(6453) =< s(6436) s(6452) =< s(6437) s(6454) =< s(6452)*s(6432) s(6455) =< s(6452)*s(6433) s(6456) =< s(6452)*s(6446) s(6457) =< s(6455) s(6458) =< s(6456) s(6459) =< s(6442) s(6460) =< s(6459)*aux(336) s(6461) =< s(6443) s(6462) =< s(6461)*s(6432) with precondition: [V11=2,Out=2,V>=1,V2>=0] #### Cost of chains of start(V,V2,V11): * Chain [91]: 464*s(7279)+557*s(7281)+8*s(7289)+24*s(7291)+24*s(7292)+15*s(7293)+2*s(7294)+3*s(7295)+4*s(7298)+4*s(7299)+324*s(7317)+378*s(7318)+54*s(7319)+54*s(7320)+54*s(7321)+54*s(7322)+54*s(7323)+54*s(7332)+54*s(7333)+54*s(7334)+3078*s(7337)+864*s(7338)+378*s(7341)+1296*s(7343)+1296*s(7344)+540*s(7345)+54*s(7346)+108*s(7347)+216*s(7350)+216*s(7351)+270*s(7352)+54*s(7353)+324*s(7354)+54*s(7355)+234*s(7517)+172*s(7518)+240*s(7520)+280*s(7521)+40*s(7522)+40*s(7523)+40*s(7524)+40*s(7525)+40*s(7526)+40*s(7535)+40*s(7536)+40*s(7537)+2280*s(7540)+640*s(7541)+280*s(7544)+960*s(7546)+960*s(7547)+400*s(7548)+40*s(7549)+80*s(7550)+160*s(7553)+160*s(7554)+200*s(7555)+40*s(7556)+240*s(7557)+40*s(7558)+11*s(7599)+55*s(7697)+1*s(7856)+1*s(7898)+4*s(7899)+35*s(7900)+7*s(7901)+21*s(7968)+24*s(7970)+72*s(7971)+4*s(7977)+12*s(7978)+23*s(8020)+24*s(8022)+72*s(8023)+30*s(8024)+3*s(8025)+6*s(8026)+4*s(8029)+12*s(8030)+24*s(8032)+4*s(8034)+24*s(8036)+4*s(8038)+180*s(8164)+108*s(8165)+126*s(8166)+18*s(8167)+18*s(8168)+18*s(8169)+18*s(8170)+18*s(8171)+18*s(8180)+18*s(8181)+18*s(8182)+1026*s(8185)+288*s(8186)+126*s(8189)+432*s(8191)+432*s(8192)+180*s(8193)+18*s(8194)+36*s(8195)+72*s(8198)+72*s(8199)+90*s(8200)+18*s(8201)+108*s(8202)+18*s(8203)+6 Such that:s(7913) =< 3 aux(392) =< 1 aux(393) =< 2 aux(394) =< V aux(395) =< 2*V aux(396) =< 2/3*V aux(397) =< 3/4*V aux(398) =< 3/5*V aux(399) =< 4/5*V aux(400) =< 4/7*V aux(401) =< 4/9*V aux(402) =< V2 aux(403) =< V2+1 aux(404) =< 2*V2 aux(405) =< 2*V2+1 aux(406) =< 2/3*V2 aux(407) =< 3/4*V2 aux(408) =< 3/5*V2 aux(409) =< 4/5*V2 aux(410) =< 4/7*V2 aux(411) =< 4/9*V2 aux(412) =< V11 aux(413) =< 2*V11 aux(414) =< 2/3*V11 aux(415) =< 3/4*V11 aux(416) =< 3/5*V11 aux(417) =< 4/5*V11 aux(418) =< 4/7*V11 aux(419) =< 4/9*V11 s(7599) =< aux(392) s(7517) =< aux(393) s(7281) =< aux(394) s(7279) =< aux(402) s(7520) =< aux(402) s(7521) =< aux(402) s(7522) =< aux(402) s(7523) =< aux(402) s(7524) =< aux(402) s(7525) =< aux(402) s(7526) =< aux(402) s(7522) =< aux(406) s(7523) =< aux(406) s(7525) =< aux(406) s(7526) =< aux(407) s(7525) =< aux(408) s(7524) =< aux(409) s(7525) =< aux(409) s(7526) =< aux(409) s(7521) =< aux(410) s(7523) =< aux(410) s(7520) =< aux(411) s(7527) =< aux(404)+3 s(7528) =< aux(404)+2 s(7529) =< aux(404)+4 s(7530) =< aux(404) s(7531) =< aux(404)+1 s(7532) =< s(7279)*s(7527) s(7533) =< s(7279)*s(7528) s(7534) =< s(7279)*s(7529) s(7535) =< s(7523)*s(7530) s(7536) =< s(7522)*s(7531) s(7537) =< s(7521)*s(7530) s(7538) =< s(7521)*s(7530) s(7539) =< s(7520)*s(7528) s(7540) =< s(7533) s(7541) =< s(7534) s(7542) =< s(7528) s(7543) =< s(7540)*s(7529) s(7544) =< s(7540)*s(7528) s(7545) =< s(7540)*s(7542) s(7546) =< s(7543) s(7547) =< s(7545) s(7548) =< s(7532) s(7549) =< s(7532) s(7548) =< s(7533) s(7550) =< s(7548)*s(7528) s(7551) =< s(7548)*s(7529) s(7552) =< s(7548)*s(7542) s(7553) =< s(7551) s(7554) =< s(7552) s(7555) =< s(7538) s(7556) =< s(7555)*aux(404) s(7557) =< s(7539) s(7558) =< s(7557)*s(7528) s(7317) =< aux(394) s(7318) =< aux(394) s(7319) =< aux(394) s(7320) =< aux(394) s(7321) =< aux(394) s(7322) =< aux(394) s(7323) =< aux(394) s(7319) =< aux(396) s(7320) =< aux(396) s(7322) =< aux(396) s(7323) =< aux(397) s(7322) =< aux(398) s(7321) =< aux(399) s(7322) =< aux(399) s(7323) =< aux(399) s(7318) =< aux(400) s(7320) =< aux(400) s(7317) =< aux(401) s(7324) =< aux(395)+3 s(7325) =< aux(395)+2 s(7326) =< aux(395)+4 s(7327) =< aux(395) s(7328) =< aux(395)+1 s(7329) =< s(7281)*s(7324) s(7330) =< s(7281)*s(7325) s(7331) =< s(7281)*s(7326) s(7332) =< s(7320)*s(7327) s(7333) =< s(7319)*s(7328) s(7334) =< s(7318)*s(7327) s(7335) =< s(7318)*s(7327) s(7336) =< s(7317)*s(7325) s(7337) =< s(7330) s(7338) =< s(7331) s(7339) =< s(7325) s(7340) =< s(7337)*s(7326) s(7341) =< s(7337)*s(7325) s(7342) =< s(7337)*s(7339) s(7343) =< s(7340) s(7344) =< s(7342) s(7345) =< s(7329) s(7346) =< s(7329) s(7345) =< s(7330) s(7347) =< s(7345)*s(7325) s(7348) =< s(7345)*s(7326) s(7349) =< s(7345)*s(7339) s(7350) =< s(7348) s(7351) =< s(7349) s(7352) =< s(7335) s(7353) =< s(7352)*aux(395) s(7354) =< s(7336) s(7355) =< s(7354)*s(7325) s(7697) =< aux(395) s(7856) =< s(7599)*aux(392) s(7898) =< s(7697)*aux(395) s(7899) =< aux(405) s(7900) =< aux(405) s(7900) =< aux(404) s(7901) =< s(7900)*aux(404) s(7518) =< aux(404) s(7967) =< s(7518)*aux(393) s(7968) =< s(7518)*aux(404) s(7969) =< s(7518)*s(7530) s(7970) =< s(7967) s(7971) =< s(7969) s(7975) =< s(7900)*aux(393) s(7976) =< s(7900)*s(7530) s(7977) =< s(7975) s(7978) =< s(7976) s(8018) =< aux(393) s(8019) =< s(7517)*aux(393) s(8020) =< s(7517)*aux(393) s(8021) =< s(7517)*s(8018) s(8022) =< s(8019) s(8023) =< s(8021) s(8024) =< s(7913) s(8025) =< s(7913) s(8024) =< aux(393) s(8026) =< s(8024)*aux(393) s(8027) =< s(8024)*aux(393) s(8028) =< s(8024)*s(8018) s(8029) =< s(8027) s(8030) =< s(8028) s(8031) =< s(7518)*aux(395) s(8032) =< s(8031) s(8033) =< s(7900)*aux(395) s(8034) =< s(8033) s(8035) =< s(7517)*aux(395) s(8036) =< s(8035) s(8037) =< s(8024)*aux(395) s(8038) =< s(8037) s(7287) =< aux(402) s(7288) =< s(7279)*aux(394) s(7289) =< s(7279)*aux(402) s(7290) =< s(7279)*s(7287) s(7291) =< s(7288) s(7292) =< s(7290) s(7293) =< aux(403) s(7294) =< aux(403) s(7293) =< aux(402) s(7295) =< s(7293)*aux(402) s(7296) =< s(7293)*aux(394) s(7297) =< s(7293)*s(7287) s(7298) =< s(7296) s(7299) =< s(7297) s(8164) =< aux(412) s(8165) =< aux(412) s(8166) =< aux(412) s(8167) =< aux(412) s(8168) =< aux(412) s(8169) =< aux(412) s(8170) =< aux(412) s(8171) =< aux(412) s(8167) =< aux(414) s(8168) =< aux(414) s(8170) =< aux(414) s(8171) =< aux(415) s(8170) =< aux(416) s(8169) =< aux(417) s(8170) =< aux(417) s(8171) =< aux(417) s(8166) =< aux(418) s(8168) =< aux(418) s(8165) =< aux(419) s(8172) =< aux(413)+3 s(8173) =< aux(413)+2 s(8174) =< aux(413)+4 s(8175) =< aux(413) s(8176) =< aux(413)+1 s(8177) =< s(8164)*s(8172) s(8178) =< s(8164)*s(8173) s(8179) =< s(8164)*s(8174) s(8180) =< s(8168)*s(8175) s(8181) =< s(8167)*s(8176) s(8182) =< s(8166)*s(8175) s(8183) =< s(8166)*s(8175) s(8184) =< s(8165)*s(8173) s(8185) =< s(8178) s(8186) =< s(8179) s(8187) =< s(8173) s(8188) =< s(8185)*s(8174) s(8189) =< s(8185)*s(8173) s(8190) =< s(8185)*s(8187) s(8191) =< s(8188) s(8192) =< s(8190) s(8193) =< s(8177) s(8194) =< s(8177) s(8193) =< s(8178) s(8195) =< s(8193)*s(8173) s(8196) =< s(8193)*s(8174) s(8197) =< s(8193)*s(8187) s(8198) =< s(8196) s(8199) =< s(8197) s(8200) =< s(8183) s(8201) =< s(8200)*aux(413) s(8202) =< s(8184) s(8203) =< s(8202)*s(8173) with precondition: [] Closed-form bounds of start(V,V2,V11): ------------------------------------- * Chain [91] with precondition: [] - Upper bound: nat(V)*35441+1193+nat(V)*24*nat(V2)+nat(V)*23112*nat(2*V)+nat(V)*3618*nat(2*V)*nat(2*V)+nat(V)*4*nat(V2+1)+nat(V2)*26304+nat(V2)*32*nat(V2)+nat(V2)*17120*nat(2*V2)+nat(V2)*2680*nat(2*V2)*nat(2*V2)+nat(V2)*7*nat(V2+1)+nat(V11)*11808+nat(V11)*7704*nat(2*V11)+nat(V11)*1206*nat(2*V11)*nat(2*V11)+nat(2*V)*115+nat(2*V)*nat(2*V)+nat(2*V)*24*nat(2*V2)+nat(2*V)*4*nat(2*V2+1)+nat(2*V2)*220+nat(2*V2)*93*nat(2*V2)+nat(2*V2)*19*nat(2*V2+1)+nat(V2+1)*17+nat(2*V2+1)*47 - Complexity: n^3 ### Maximum cost of start(V,V2,V11): nat(V)*35441+1193+nat(V)*24*nat(V2)+nat(V)*23112*nat(2*V)+nat(V)*3618*nat(2*V)*nat(2*V)+nat(V)*4*nat(V2+1)+nat(V2)*26304+nat(V2)*32*nat(V2)+nat(V2)*17120*nat(2*V2)+nat(V2)*2680*nat(2*V2)*nat(2*V2)+nat(V2)*7*nat(V2+1)+nat(V11)*11808+nat(V11)*7704*nat(2*V11)+nat(V11)*1206*nat(2*V11)*nat(2*V11)+nat(2*V)*115+nat(2*V)*nat(2*V)+nat(2*V)*24*nat(2*V2)+nat(2*V)*4*nat(2*V2+1)+nat(2*V2)*220+nat(2*V2)*93*nat(2*V2)+nat(2*V2)*19*nat(2*V2+1)+nat(V2+1)*17+nat(2*V2+1)*47 Asymptotic class: n^3 * Total analysis performed in 29295 ms. ---------------------------------------- (14) BOUNDS(1, n^3) ---------------------------------------- (15) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (16) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: p(0') -> 0' p(s(x)) -> x le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) minus(x, 0') -> x minus(x, s(y)) -> if(le(x, s(y)), 0', p(minus(x, p(s(y))))) if(true, x, y) -> x if(false, x, y) -> y The (relative) TRS S consists of the following rules: encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) Rewrite Strategy: INNERMOST ---------------------------------------- (17) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (18) Obligation: Innermost TRS: Rules: p(0') -> 0' p(s(x)) -> x le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) minus(x, 0') -> x minus(x, s(y)) -> if(le(x, s(y)), 0', p(minus(x, p(s(y))))) if(true, x, y) -> x if(false, x, y) -> y encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) Types: p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if 0' :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encArg :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_0 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if hole_0':s:true:false:cons_p:cons_le:cons_minus:cons_if1_4 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4 :: Nat -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if ---------------------------------------- (19) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: le, minus, encArg They will be analysed ascendingly in the following order: le < minus le < encArg minus < encArg ---------------------------------------- (20) Obligation: Innermost TRS: Rules: p(0') -> 0' p(s(x)) -> x le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) minus(x, 0') -> x minus(x, s(y)) -> if(le(x, s(y)), 0', p(minus(x, p(s(y))))) if(true, x, y) -> x if(false, x, y) -> y encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) Types: p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if 0' :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encArg :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_0 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if hole_0':s:true:false:cons_p:cons_le:cons_minus:cons_if1_4 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4 :: Nat -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if Generator Equations: gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(0) <=> 0' gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(+(x, 1)) <=> s(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(x)) The following defined symbols remain to be analysed: le, minus, encArg They will be analysed ascendingly in the following order: le < minus le < encArg minus < encArg ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: le(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n4_4), gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n4_4)) -> true, rt in Omega(1 + n4_4) Induction Base: le(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(0), gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(0)) ->_R^Omega(1) true Induction Step: le(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(+(n4_4, 1)), gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(+(n4_4, 1))) ->_R^Omega(1) le(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n4_4), gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n4_4)) ->_IH true We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (22) Complex Obligation (BEST) ---------------------------------------- (23) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: p(0') -> 0' p(s(x)) -> x le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) minus(x, 0') -> x minus(x, s(y)) -> if(le(x, s(y)), 0', p(minus(x, p(s(y))))) if(true, x, y) -> x if(false, x, y) -> y encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) Types: p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if 0' :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encArg :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_0 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if hole_0':s:true:false:cons_p:cons_le:cons_minus:cons_if1_4 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4 :: Nat -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if Generator Equations: gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(0) <=> 0' gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(+(x, 1)) <=> s(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(x)) The following defined symbols remain to be analysed: le, minus, encArg They will be analysed ascendingly in the following order: le < minus le < encArg minus < encArg ---------------------------------------- (24) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (25) BOUNDS(n^1, INF) ---------------------------------------- (26) Obligation: Innermost TRS: Rules: p(0') -> 0' p(s(x)) -> x le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) minus(x, 0') -> x minus(x, s(y)) -> if(le(x, s(y)), 0', p(minus(x, p(s(y))))) if(true, x, y) -> x if(false, x, y) -> y encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) Types: p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if 0' :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encArg :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if cons_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_p :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_0 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_s :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_le :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_true :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_false :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_minus :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if encode_if :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if hole_0':s:true:false:cons_p:cons_le:cons_minus:cons_if1_4 :: 0':s:true:false:cons_p:cons_le:cons_minus:cons_if gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4 :: Nat -> 0':s:true:false:cons_p:cons_le:cons_minus:cons_if Lemmas: le(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n4_4), gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n4_4)) -> true, rt in Omega(1 + n4_4) Generator Equations: gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(0) <=> 0' gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(+(x, 1)) <=> s(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(x)) The following defined symbols remain to be analysed: minus, encArg They will be analysed ascendingly in the following order: minus < encArg ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n3767_4)) -> gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n3767_4), rt in Omega(0) Induction Base: encArg(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(0)) ->_R^Omega(0) 0' Induction Step: encArg(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(+(n3767_4, 1))) ->_R^Omega(0) s(encArg(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(n3767_4))) ->_IH s(gen_0':s:true:false:cons_p:cons_le:cons_minus:cons_if2_4(c3768_4)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (28) BOUNDS(1, INF)