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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3).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), 195 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, 93.0 s] (14) BOUNDS(1, n^3) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRelTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 0 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 297 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), 28 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 13 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 351 ms] (32) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: half(0) -> 0 half(s(0)) -> 0 half(s(s(x))) -> s(half(x)) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) inc(0) -> 0 inc(s(x)) -> s(inc(x)) log(x) -> log2(x, 0) log2(x, y) -> if(le(x, s(0)), x, inc(y)) if(true, x, s(y)) -> y if(false, x, y) -> log2(half(x), y) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_half(x_1)) -> half(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_inc(x_1)) -> inc(encArg(x_1)) encArg(cons_log(x_1)) -> log(encArg(x_1)) encArg(cons_log2(x_1, x_2)) -> log2(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_half(x_1) -> half(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_inc(x_1) -> inc(encArg(x_1)) encode_log(x_1) -> log(encArg(x_1)) encode_log2(x_1, x_2) -> log2(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: half(0) -> 0 half(s(0)) -> 0 half(s(s(x))) -> s(half(x)) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) inc(0) -> 0 inc(s(x)) -> s(inc(x)) log(x) -> log2(x, 0) log2(x, y) -> if(le(x, s(0)), x, inc(y)) if(true, x, s(y)) -> y if(false, x, y) -> log2(half(x), y) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_half(x_1)) -> half(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_inc(x_1)) -> inc(encArg(x_1)) encArg(cons_log(x_1)) -> log(encArg(x_1)) encArg(cons_log2(x_1, x_2)) -> log2(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_half(x_1) -> half(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_inc(x_1) -> inc(encArg(x_1)) encode_log(x_1) -> log(encArg(x_1)) encode_log2(x_1, x_2) -> log2(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: half(0) -> 0 half(s(0)) -> 0 half(s(s(x))) -> s(half(x)) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) inc(0) -> 0 inc(s(x)) -> s(inc(x)) log(x) -> log2(x, 0) log2(x, y) -> if(le(x, s(0)), x, inc(y)) if(true, x, s(y)) -> y if(false, x, y) -> log2(half(x), y) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_half(x_1)) -> half(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_inc(x_1)) -> inc(encArg(x_1)) encArg(cons_log(x_1)) -> log(encArg(x_1)) encArg(cons_log2(x_1, x_2)) -> log2(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_half(x_1) -> half(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_inc(x_1) -> inc(encArg(x_1)) encode_log(x_1) -> log(encArg(x_1)) encode_log2(x_1, x_2) -> log2(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: half(0) -> 0 [1] half(s(0)) -> 0 [1] half(s(s(x))) -> s(half(x)) [1] le(0, y) -> true [1] le(s(x), 0) -> false [1] le(s(x), s(y)) -> le(x, y) [1] inc(0) -> 0 [1] inc(s(x)) -> s(inc(x)) [1] log(x) -> log2(x, 0) [1] log2(x, y) -> if(le(x, s(0)), x, inc(y)) [1] if(true, x, s(y)) -> y [1] if(false, x, y) -> log2(half(x), y) [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(cons_half(x_1)) -> half(encArg(x_1)) [0] encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) [0] encArg(cons_inc(x_1)) -> inc(encArg(x_1)) [0] encArg(cons_log(x_1)) -> log(encArg(x_1)) [0] encArg(cons_log2(x_1, x_2)) -> log2(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_half(x_1) -> half(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_inc(x_1) -> inc(encArg(x_1)) [0] encode_log(x_1) -> log(encArg(x_1)) [0] encode_log2(x_1, x_2) -> log2(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: half(0) -> 0 [1] half(s(0)) -> 0 [1] half(s(s(x))) -> s(half(x)) [1] le(0, y) -> true [1] le(s(x), 0) -> false [1] le(s(x), s(y)) -> le(x, y) [1] inc(0) -> 0 [1] inc(s(x)) -> s(inc(x)) [1] log(x) -> log2(x, 0) [1] log2(x, y) -> if(le(x, s(0)), x, inc(y)) [1] if(true, x, s(y)) -> y [1] if(false, x, y) -> log2(half(x), y) [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(cons_half(x_1)) -> half(encArg(x_1)) [0] encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) [0] encArg(cons_inc(x_1)) -> inc(encArg(x_1)) [0] encArg(cons_log(x_1)) -> log(encArg(x_1)) [0] encArg(cons_log2(x_1, x_2)) -> log2(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_half(x_1) -> half(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_inc(x_1) -> inc(encArg(x_1)) [0] encode_log(x_1) -> log(encArg(x_1)) [0] encode_log2(x_1, x_2) -> log2(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: half :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if 0 :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if s :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if le :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if true :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if false :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if inc :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if log :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if log2 :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if if :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encArg :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_half :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_le :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_inc :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_log :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_log2 :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_if :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_half :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_0 :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_s :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_le :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_true :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_false :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_inc :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_log :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_log2 :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_if :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2: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_half(v0) -> null_encode_half [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_inc(v0) -> null_encode_inc [0] encode_log(v0) -> null_encode_log [0] encode_log2(v0, v1) -> null_encode_log2 [0] encode_if(v0, v1, v2) -> null_encode_if [0] half(v0) -> null_half [0] le(v0, v1) -> null_le [0] inc(v0) -> null_inc [0] if(v0, v1, v2) -> null_if [0] And the following fresh constants: null_encArg, null_encode_half, null_encode_0, null_encode_s, null_encode_le, null_encode_true, null_encode_false, null_encode_inc, null_encode_log, null_encode_log2, null_encode_if, null_half, null_le, null_inc, 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: half(0) -> 0 [1] half(s(0)) -> 0 [1] half(s(s(x))) -> s(half(x)) [1] le(0, y) -> true [1] le(s(x), 0) -> false [1] le(s(x), s(y)) -> le(x, y) [1] inc(0) -> 0 [1] inc(s(x)) -> s(inc(x)) [1] log(x) -> log2(x, 0) [1] log2(x, y) -> if(le(x, s(0)), x, inc(y)) [1] if(true, x, s(y)) -> y [1] if(false, x, y) -> log2(half(x), y) [1] encArg(0) -> 0 [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(cons_half(x_1)) -> half(encArg(x_1)) [0] encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) [0] encArg(cons_inc(x_1)) -> inc(encArg(x_1)) [0] encArg(cons_log(x_1)) -> log(encArg(x_1)) [0] encArg(cons_log2(x_1, x_2)) -> log2(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_half(x_1) -> half(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_inc(x_1) -> inc(encArg(x_1)) [0] encode_log(x_1) -> log(encArg(x_1)) [0] encode_log2(x_1, x_2) -> log2(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_half(v0) -> null_encode_half [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_inc(v0) -> null_encode_inc [0] encode_log(v0) -> null_encode_log [0] encode_log2(v0, v1) -> null_encode_log2 [0] encode_if(v0, v1, v2) -> null_encode_if [0] half(v0) -> null_half [0] le(v0, v1) -> null_le [0] inc(v0) -> null_inc [0] if(v0, v1, v2) -> null_if [0] The TRS has the following type information: half :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if 0 :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if s :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if -> 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if le :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if -> 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0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if null_encode_le :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if null_encode_true :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if null_encode_false :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if null_encode_inc :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if null_encode_log :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if null_encode_log2 :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if null_encode_if :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if null_half :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if null_le :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if null_inc :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc:null_if null_if :: 0:s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if:null_encArg:null_encode_half:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_inc:null_encode_log:null_encode_log2:null_encode_if:null_half:null_le:null_inc: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_half => 0 null_encode_0 => 0 null_encode_s => 0 null_encode_le => 0 null_encode_true => 0 null_encode_false => 0 null_encode_inc => 0 null_encode_log => 0 null_encode_log2 => 0 null_encode_if => 0 null_half => 0 null_le => 0 null_inc => 0 null_if => 0 ---------------------------------------- (12) Obligation: Complexity RNTS consisting of the following rules: encArg(z) -{ 0 }-> log2(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> log(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 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 }-> inc(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 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 }-> half(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 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_half(z) -{ 0 }-> half(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_half(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 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_inc(z) -{ 0 }-> inc(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_inc(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 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_log(z) -{ 0 }-> log(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_log(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_log2(z, z') -{ 0 }-> log2(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_log2(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_s(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 encode_true -{ 0 }-> 2 :|: encode_true -{ 0 }-> 0 :|: half(z) -{ 1 }-> 0 :|: z = 0 half(z) -{ 1 }-> 0 :|: z = 1 + 0 half(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 half(z) -{ 1 }-> 1 + half(x) :|: x >= 0, z = 1 + (1 + x) if(z, z', z'') -{ 1 }-> y :|: z = 2, z' = x, x >= 0, y >= 0, z'' = 1 + y if(z, z', z'') -{ 1 }-> log2(half(x), 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 inc(z) -{ 1 }-> 0 :|: z = 0 inc(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 inc(z) -{ 1 }-> 1 + inc(x) :|: x >= 0, z = 1 + x 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 log(z) -{ 1 }-> log2(x, 0) :|: x >= 0, z = x log2(z, z') -{ 1 }-> if(le(x, 1 + 0), x, inc(y)) :|: x >= 0, y >= 0, z = x, z' = y Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (13) CompleteCoflocoProof (FINISHED) Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: eq(start(V, V2, V12),0,[half(V, Out)],[V >= 0]). eq(start(V, V2, V12),0,[le(V, V2, Out)],[V >= 0,V2 >= 0]). eq(start(V, V2, V12),0,[inc(V, Out)],[V >= 0]). eq(start(V, V2, V12),0,[log(V, Out)],[V >= 0]). eq(start(V, V2, V12),0,[log2(V, V2, Out)],[V >= 0,V2 >= 0]). eq(start(V, V2, V12),0,[if(V, V2, V12, Out)],[V >= 0,V2 >= 0,V12 >= 0]). eq(start(V, V2, V12),0,[encArg(V, Out)],[V >= 0]). eq(start(V, V2, V12),0,[fun(V, Out)],[V >= 0]). eq(start(V, V2, V12),0,[fun1(Out)],[]). eq(start(V, V2, V12),0,[fun2(V, Out)],[V >= 0]). eq(start(V, V2, V12),0,[fun3(V, V2, Out)],[V >= 0,V2 >= 0]). eq(start(V, V2, V12),0,[fun4(Out)],[]). eq(start(V, V2, V12),0,[fun5(Out)],[]). eq(start(V, V2, V12),0,[fun6(V, Out)],[V >= 0]). eq(start(V, V2, V12),0,[fun7(V, Out)],[V >= 0]). eq(start(V, V2, V12),0,[fun8(V, V2, Out)],[V >= 0,V2 >= 0]). eq(start(V, V2, V12),0,[fun9(V, V2, V12, Out)],[V >= 0,V2 >= 0,V12 >= 0]). eq(half(V, Out),1,[],[Out = 0,V = 0]). eq(half(V, Out),1,[],[Out = 0,V = 1]). eq(half(V, Out),1,[half(V1, Ret1)],[Out = 1 + Ret1,V1 >= 0,V = 2 + 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(inc(V, Out),1,[],[Out = 0,V = 0]). eq(inc(V, Out),1,[inc(V7, Ret11)],[Out = 1 + Ret11,V7 >= 0,V = 1 + V7]). eq(log(V, Out),1,[log2(V8, 0, Ret2)],[Out = Ret2,V8 >= 0,V = V8]). eq(log2(V, V2, Out),1,[le(V10, 1 + 0, Ret0),inc(V9, Ret21),if(Ret0, V10, Ret21, Ret3)],[Out = Ret3,V10 >= 0,V9 >= 0,V = V10,V2 = V9]). eq(if(V, V2, V12, Out),1,[],[Out = V11,V = 2,V2 = V13,V13 >= 0,V11 >= 0,V12 = 1 + V11]). eq(if(V, V2, V12, Out),1,[half(V15, Ret01),log2(Ret01, V14, Ret4)],[Out = Ret4,V2 = V15,V12 = V14,V = 1,V15 >= 0,V14 >= 0]). eq(encArg(V, Out),0,[],[Out = 0,V = 0]). eq(encArg(V, Out),0,[encArg(V16, Ret12)],[Out = 1 + Ret12,V = 1 + V16,V16 >= 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(V17, Ret02),half(Ret02, Ret5)],[Out = Ret5,V = 1 + V17,V17 >= 0]). eq(encArg(V, Out),0,[encArg(V18, Ret03),encArg(V19, Ret13),le(Ret03, Ret13, Ret6)],[Out = Ret6,V18 >= 0,V = 1 + V18 + V19,V19 >= 0]). eq(encArg(V, Out),0,[encArg(V20, Ret04),inc(Ret04, Ret7)],[Out = Ret7,V = 1 + V20,V20 >= 0]). eq(encArg(V, Out),0,[encArg(V21, Ret05),log(Ret05, Ret8)],[Out = Ret8,V = 1 + V21,V21 >= 0]). eq(encArg(V, Out),0,[encArg(V23, Ret06),encArg(V22, Ret14),log2(Ret06, Ret14, Ret9)],[Out = Ret9,V23 >= 0,V = 1 + V22 + V23,V22 >= 0]). eq(encArg(V, Out),0,[encArg(V26, Ret07),encArg(V25, Ret15),encArg(V24, Ret22),if(Ret07, Ret15, Ret22, Ret10)],[Out = Ret10,V26 >= 0,V = 1 + V24 + V25 + V26,V24 >= 0,V25 >= 0]). eq(fun(V, Out),0,[encArg(V27, Ret08),half(Ret08, Ret16)],[Out = Ret16,V27 >= 0,V = V27]). eq(fun1(Out),0,[],[Out = 0]). eq(fun2(V, Out),0,[encArg(V28, Ret17)],[Out = 1 + Ret17,V28 >= 0,V = V28]). eq(fun3(V, V2, Out),0,[encArg(V30, Ret09),encArg(V29, Ret18),le(Ret09, Ret18, Ret19)],[Out = Ret19,V30 >= 0,V29 >= 0,V = V30,V2 = V29]). eq(fun4(Out),0,[],[Out = 2]). eq(fun5(Out),0,[],[Out = 1]). eq(fun6(V, Out),0,[encArg(V31, Ret010),inc(Ret010, Ret20)],[Out = Ret20,V31 >= 0,V = V31]). eq(fun7(V, Out),0,[encArg(V32, Ret011),log(Ret011, Ret23)],[Out = Ret23,V32 >= 0,V = V32]). eq(fun8(V, V2, Out),0,[encArg(V34, Ret012),encArg(V33, Ret110),log2(Ret012, Ret110, Ret24)],[Out = Ret24,V34 >= 0,V33 >= 0,V = V34,V2 = V33]). eq(fun9(V, V2, V12, Out),0,[encArg(V36, Ret013),encArg(V37, Ret111),encArg(V35, Ret25),if(Ret013, Ret111, Ret25, Ret26)],[Out = Ret26,V36 >= 0,V35 >= 0,V37 >= 0,V = V36,V2 = V37,V12 = V35]). eq(encArg(V, Out),0,[],[Out = 0,V38 >= 0,V = V38]). eq(fun(V, Out),0,[],[Out = 0,V39 >= 0,V = V39]). eq(fun2(V, Out),0,[],[Out = 0,V40 >= 0,V = V40]). eq(fun3(V, V2, Out),0,[],[Out = 0,V41 >= 0,V42 >= 0,V = V41,V2 = V42]). eq(fun4(Out),0,[],[Out = 0]). eq(fun5(Out),0,[],[Out = 0]). eq(fun6(V, Out),0,[],[Out = 0,V43 >= 0,V = V43]). eq(fun7(V, Out),0,[],[Out = 0,V44 >= 0,V = V44]). eq(fun8(V, V2, Out),0,[],[Out = 0,V45 >= 0,V46 >= 0,V = V45,V2 = V46]). eq(fun9(V, V2, V12, Out),0,[],[Out = 0,V47 >= 0,V12 = V49,V48 >= 0,V = V47,V2 = V48,V49 >= 0]). eq(half(V, Out),0,[],[Out = 0,V50 >= 0,V = V50]). eq(le(V, V2, Out),0,[],[Out = 0,V51 >= 0,V52 >= 0,V = V51,V2 = V52]). eq(inc(V, Out),0,[],[Out = 0,V53 >= 0,V = V53]). eq(if(V, V2, V12, Out),0,[],[Out = 0,V56 >= 0,V12 = V55,V54 >= 0,V = V56,V2 = V54,V55 >= 0]). input_output_vars(half(V,Out),[V],[Out]). input_output_vars(le(V,V2,Out),[V,V2],[Out]). input_output_vars(inc(V,Out),[V],[Out]). input_output_vars(log(V,Out),[V],[Out]). input_output_vars(log2(V,V2,Out),[V,V2],[Out]). input_output_vars(if(V,V2,V12,Out),[V,V2,V12],[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,Out),[V],[Out]). input_output_vars(fun7(V,Out),[V],[Out]). input_output_vars(fun8(V,V2,Out),[V,V2],[Out]). input_output_vars(fun9(V,V2,V12,Out),[V,V2,V12],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [half/2] 1. recursive : [inc/2] 2. recursive : [le/3] 3. recursive : [if/4,log2/3] 4. non_recursive : [log/2] 5. recursive [non_tail,multiple] : [encArg/2] 6. non_recursive : [fun/2] 7. non_recursive : [fun1/1] 8. non_recursive : [fun2/2] 9. non_recursive : [fun3/3] 10. non_recursive : [fun4/1] 11. non_recursive : [fun5/1] 12. non_recursive : [fun6/2] 13. non_recursive : [fun7/2] 14. non_recursive : [fun8/3] 15. non_recursive : [fun9/4] 16. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into half/2 1. SCC is partially evaluated into inc/2 2. SCC is partially evaluated into le/3 3. SCC is partially evaluated into log2/3 4. SCC is completely evaluated into other SCCs 5. SCC is partially evaluated into encArg/2 6. SCC is partially evaluated into fun/2 7. SCC is completely evaluated into other SCCs 8. SCC is partially evaluated into fun2/2 9. SCC is partially evaluated into fun3/3 10. SCC is partially evaluated into fun4/1 11. SCC is partially evaluated into fun5/1 12. SCC is partially evaluated into fun6/2 13. SCC is partially evaluated into fun7/2 14. SCC is partially evaluated into fun8/3 15. SCC is partially evaluated into fun9/4 16. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations half/2 * CE 20 is refined into CE [65] * CE 19 is refined into CE [66] * CE 22 is refined into CE [67] * CE 21 is refined into CE [68] ### Cost equations --> "Loop" of half/2 * CEs [68] --> Loop 32 * CEs [65] --> Loop 33 * CEs [66,67] --> Loop 34 ### Ranking functions of CR half(V,Out) * RF of phase [32]: [V-1] #### Partial ranking functions of CR half(V,Out) * Partial RF of phase [32]: - RF of loop [32:1]: V-1 ### Specialization of cost equations inc/2 * CE 30 is refined into CE [69] * CE 32 is refined into CE [70] * CE 31 is refined into CE [71] ### Cost equations --> "Loop" of inc/2 * CEs [71] --> Loop 35 * CEs [69,70] --> Loop 36 ### Ranking functions of CR inc(V,Out) * RF of phase [35]: [V] #### Partial ranking functions of CR inc(V,Out) * Partial RF of phase [35]: - RF of loop [35:1]: V ### Specialization of cost equations le/3 * CE 29 is refined into CE [72] * CE 27 is refined into CE [73] * CE 26 is refined into CE [74] * CE 28 is refined into CE [75] ### Cost equations --> "Loop" of le/3 * CEs [75] --> Loop 37 * CEs [72] --> Loop 38 * CEs [73] --> Loop 39 * CEs [74] --> Loop 40 ### Ranking functions of CR le(V,V2,Out) * RF of phase [37]: [V,V2] #### Partial ranking functions of CR le(V,V2,Out) * Partial RF of phase [37]: - RF of loop [37:1]: V V2 ### Specialization of cost equations log2/3 * CE 23 is refined into CE [76,77,78,79,80,81,82,83] * CE 25 is refined into CE [84,85] * CE 24 is refined into CE [86,87,88,89] ### Cost equations --> "Loop" of log2/3 * CEs [89] --> Loop 41 * CEs [87] --> Loop 42 * CEs [88] --> Loop 43 * CEs [86] --> Loop 44 * CEs [85] --> Loop 45 * CEs [82,83] --> Loop 46 * CEs [84] --> Loop 47 * CEs [76,77,78,79,80,81] --> Loop 48 ### Ranking functions of CR log2(V,V2,Out) * RF of phase [41]: [V-1] * RF of phase [42]: [V-1] #### Partial ranking functions of CR log2(V,V2,Out) * Partial RF of phase [41]: - RF of loop [41:1]: V-1 * Partial RF of phase [42]: - RF of loop [42:1]: V-1 ### Specialization of cost equations encArg/2 * CE 36 is refined into CE [90] * CE 38 is refined into CE [91] * CE 39 is refined into CE [92] * CE 41 is refined into CE [93,94,95,96,97] * CE 44 is refined into CE [98,99,100,101] * CE 37 is refined into CE [102] * CE 40 is refined into CE [103,104] * CE 42 is refined into CE [105,106] * CE 43 is refined into CE [107] * CE 35 is refined into CE [108] * CE 34 is refined into CE [109,110,111,112,113] * CE 33 is refined into CE [114] ### Cost equations --> "Loop" of encArg/2 * CEs [108] --> Loop 49 * CEs [109,112,113] --> Loop 50 * CEs [110,111,114] --> Loop 51 * CEs [104,106] --> Loop 52 * CEs [102] --> Loop 53 * CEs [103,105,107] --> Loop 54 * CEs [101] --> Loop 55 * CEs [100] --> Loop 56 * CEs [98] --> Loop 57 * CEs [97] --> Loop 58 * CEs [93] --> Loop 59 * CEs [96] --> Loop 60 * CEs [94] --> Loop 61 * CEs [95,99] --> Loop 62 * CEs [90] --> Loop 63 * CEs [91] --> Loop 64 * CEs [92] --> Loop 65 ### Ranking functions of CR encArg(V,Out) * RF of phase [49,50,51,52,53,54,55,56,57,58,59,60,61,62]: [V] #### Partial ranking functions of CR encArg(V,Out) * Partial RF of phase [49,50,51,52,53,54,55,56,57,58,59,60,61,62]: - RF of loop [49:1,49:2,49:3,50:1,50:2,50:3,51:1,51:2,51:3,52:1,53:1,54:1,55:1,55:2,56:1,56:2,57:1,57:2,58:1,58:2,59:1,59:2,60:1,60:2,61:1,61:2,62:1,62:2]: V ### Specialization of cost equations fun/2 * CE 45 is refined into CE [115,116,117,118,119] * CE 46 is refined into CE [120] ### Cost equations --> "Loop" of fun/2 * CEs [116,118] --> Loop 66 * CEs [115,117,119,120] --> Loop 67 ### Ranking functions of CR fun(V,Out) #### Partial ranking functions of CR fun(V,Out) ### Specialization of cost equations fun2/2 * CE 47 is refined into CE [121,122,123] * CE 48 is refined into CE [124] ### Cost equations --> "Loop" of fun2/2 * CEs [123] --> Loop 68 * CEs [124] --> Loop 69 * CEs [121,122] --> Loop 70 ### Ranking functions of CR fun2(V,Out) #### Partial ranking functions of CR fun2(V,Out) ### Specialization of cost equations fun3/3 * CE 49 is refined into CE [125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150] * CE 50 is refined into CE [151] ### Cost equations --> "Loop" of fun3/3 * CEs [130,133,147] --> Loop 71 * CEs [132] --> Loop 72 * CEs [131,148] --> Loop 73 * CEs [126,128,135,137,139,143] --> Loop 74 * CEs [125,129,134,140,142,145,149] --> Loop 75 * CEs [127,136,138,141,144,146,150,151] --> Loop 76 ### Ranking functions of CR fun3(V,V2,Out) #### Partial ranking functions of CR fun3(V,V2,Out) ### Specialization of cost equations fun4/1 * CE 51 is refined into CE [152] * CE 52 is refined into CE [153] ### Cost equations --> "Loop" of fun4/1 * CEs [152] --> Loop 77 * CEs [153] --> Loop 78 ### Ranking functions of CR fun4(Out) #### Partial ranking functions of CR fun4(Out) ### Specialization of cost equations fun5/1 * CE 53 is refined into CE [154] * CE 54 is refined into CE [155] ### Cost equations --> "Loop" of fun5/1 * CEs [154] --> Loop 79 * CEs [155] --> Loop 80 ### Ranking functions of CR fun5(Out) #### Partial ranking functions of CR fun5(Out) ### Specialization of cost equations fun6/2 * CE 55 is refined into CE [156,157,158,159,160] * CE 56 is refined into CE [161] ### Cost equations --> "Loop" of fun6/2 * CEs [157,159] --> Loop 81 * CEs [156,158,160,161] --> Loop 82 ### Ranking functions of CR fun6(V,Out) #### Partial ranking functions of CR fun6(V,Out) ### Specialization of cost equations fun7/2 * CE 57 is refined into CE [162,163,164] * CE 58 is refined into CE [165] ### Cost equations --> "Loop" of fun7/2 * CEs [162,163,164,165] --> Loop 83 ### Ranking functions of CR fun7(V,Out) #### Partial ranking functions of CR fun7(V,Out) ### Specialization of cost equations fun8/3 * CE 59 is refined into CE [166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184] * CE 60 is refined into CE [185] ### Cost equations --> "Loop" of fun8/3 * CEs [170,171,172,173,182,183] --> Loop 84 * CEs [167,174,175,179,181,184,185] --> Loop 85 * CEs [166,168,169,176,177,178,180] --> Loop 86 ### Ranking functions of CR fun8(V,V2,Out) #### Partial ranking functions of CR fun8(V,V2,Out) ### Specialization of cost equations fun9/4 * CE 61 is refined into CE [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] * CE 62 is refined into CE [213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239] * CE 63 is refined into CE [240,241,242,243,244,245,246,247,248,249,250,251] * CE 64 is refined into CE [252] ### Cost equations --> "Loop" of fun9/4 * CEs [225,228,229,232,242,243] --> Loop 87 * CEs [189,190,191,207,208,209,226,227,230,231,233,234] --> Loop 88 * CEs [218,221,222,237,241,245,247,251] --> Loop 89 * CEs [187,193,196,202,205,211,219,220,238] --> Loop 90 * CEs [213,216,217,235,240,244,246,248,249,250] --> Loop 91 * CEs [186,188,192,194,195,197,198,199,200,201,203,204,206,210,212,214,215,223,224,236,239,252] --> Loop 92 ### Ranking functions of CR fun9(V,V2,V12,Out) #### Partial ranking functions of CR fun9(V,V2,V12,Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [253] * CE 2 is refined into CE [254,255,256,257,258] * CE 3 is refined into CE [259] * CE 4 is refined into CE [260,261] * CE 5 is refined into CE [262,263,264,265,266] * CE 6 is refined into CE [267,268] * CE 7 is refined into CE [269] * CE 8 is refined into CE [270,271,272,273] * CE 9 is refined into CE [274,275,276] * CE 10 is refined into CE [277,278] * CE 11 is refined into CE [279,280,281] * CE 12 is refined into CE [282,283,284] * CE 13 is refined into CE [285,286] * CE 14 is refined into CE [287,288] * CE 15 is refined into CE [289,290] * CE 16 is refined into CE [291] * CE 17 is refined into CE [292,293] * CE 18 is refined into CE [294,295,296,297] ### Cost equations --> "Loop" of start/3 * CEs [253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297] --> Loop 93 ### Ranking functions of CR start(V,V2,V12) #### Partial ranking functions of CR start(V,V2,V12) Computing Bounds ===================================== #### Cost of chains of half(V,Out): * Chain [[32],34]: 1*it(32)+1 Such that:it(32) =< 2*Out with precondition: [Out>=1,V>=2*Out] * Chain [[32],33]: 1*it(32)+1 Such that:it(32) =< 2*Out with precondition: [V=2*Out+1,V>=3] * Chain [34]: 1 with precondition: [Out=0,V>=0] * Chain [33]: 1 with precondition: [V=1,Out=0] #### Cost of chains of inc(V,Out): * Chain [[35],36]: 1*it(35)+1 Such that:it(35) =< Out with precondition: [Out>=1,V>=Out] * Chain [36]: 1 with precondition: [Out=0,V>=0] #### Cost of chains of le(V,V2,Out): * Chain [[37],40]: 1*it(37)+1 Such that:it(37) =< V with precondition: [Out=2,V>=1,V2>=V] * Chain [[37],39]: 1*it(37)+1 Such that:it(37) =< V2 with precondition: [Out=1,V2>=1,V>=V2+1] * Chain [[37],38]: 1*it(37)+0 Such that:it(37) =< V2 with precondition: [Out=0,V>=1,V2>=1] * Chain [40]: 1 with precondition: [V=0,Out=2,V2>=0] * Chain [39]: 1 with precondition: [V2=0,Out=1,V>=1] * Chain [38]: 0 with precondition: [Out=0,V>=0,V2>=0] #### Cost of chains of log2(V,V2,Out): * Chain [[42],48]: 6*it(42)+4*s(5)+2*s(18)+3 Such that:aux(2) =< 1 s(19) =< 2*V aux(7) =< V s(5) =< aux(2) it(42) =< aux(7) s(18) =< s(19) with precondition: [Out=0,V>=2,V2>=0] * Chain [[42],46]: 6*it(42)+2*s(18)+2*s(20)+3 Such that:aux(8) =< 1 s(19) =< 2*V aux(9) =< V s(20) =< aux(8) it(42) =< aux(9) s(18) =< s(19) with precondition: [Out=0,V>=2,V2>=0] * Chain [[42],44,48]: 6*it(42)+5*s(5)+2*s(18)+8 Such that:aux(10) =< 1 s(19) =< 2*V aux(11) =< V s(5) =< aux(10) it(42) =< aux(11) s(18) =< s(19) with precondition: [Out=0,V>=4,V2>=0] * Chain [[41],[42],48]: 6*it(41)+10*it(42)+4*s(5)+1*s(33)+3 Such that:aux(2) =< 1 aux(13) =< V2 aux(16) =< V aux(17) =< 2*V s(5) =< aux(2) it(42) =< aux(17) it(41) =< aux(16) s(33) =< it(41)*aux(13) with precondition: [Out=0,V>=4,V2>=1] * Chain [[41],[42],46]: 6*it(41)+10*it(42)+2*s(20)+1*s(33)+3 Such that:aux(8) =< 1 aux(13) =< V2 aux(18) =< V aux(19) =< 2*V s(20) =< aux(8) it(42) =< aux(19) it(41) =< aux(18) s(33) =< it(41)*aux(13) with precondition: [Out=0,V>=4,V2>=1] * Chain [[41],[42],44,48]: 6*it(41)+10*it(42)+5*s(5)+1*s(33)+8 Such that:aux(10) =< 1 aux(13) =< V2 aux(20) =< V aux(21) =< 2*V s(5) =< aux(10) it(42) =< aux(21) it(41) =< aux(20) s(33) =< it(41)*aux(13) with precondition: [Out=0,V>=8,V2>=1] * Chain [[41],48]: 6*it(41)+3*s(4)+4*s(5)+1*s(33)+2*s(34)+3 Such that:aux(2) =< 1 s(35) =< 2*V aux(22) =< V aux(23) =< V2 s(5) =< aux(2) s(4) =< aux(23) it(41) =< aux(22) s(33) =< it(41)*aux(23) s(34) =< s(35) with precondition: [Out=0,V>=2,V2>=1] * Chain [[41],46]: 6*it(41)+2*s(20)+1*s(22)+1*s(33)+2*s(34)+3 Such that:aux(8) =< 1 s(35) =< 2*V aux(24) =< V aux(25) =< V2 s(22) =< aux(25) s(20) =< aux(8) it(41) =< aux(24) s(33) =< it(41)*aux(25) s(34) =< s(35) with precondition: [Out=0,V>=2,V2>=1] * Chain [[41],45]: 6*it(41)+1*s(33)+2*s(34)+1*s(36)+1*s(37)+4 Such that:s(36) =< 1 s(35) =< 2*V aux(26) =< V aux(27) =< V2 s(37) =< aux(27) it(41) =< aux(26) s(33) =< it(41)*aux(27) s(34) =< s(35) with precondition: [V>=2,Out>=0,V2>=Out+1] * Chain [[41],44,48]: 6*it(41)+5*s(5)+1*s(33)+2*s(34)+8 Such that:aux(10) =< 1 s(35) =< 2*V aux(13) =< V2 aux(28) =< V s(5) =< aux(10) it(41) =< aux(28) s(33) =< it(41)*aux(13) s(34) =< s(35) with precondition: [Out=0,V>=4,V2>=1] * Chain [[41],43,48]: 6*it(41)+4*s(4)+5*s(5)+1*s(33)+2*s(34)+8 Such that:aux(29) =< 1 s(35) =< 2*V aux(31) =< V aux(32) =< V2 s(5) =< aux(29) s(4) =< aux(32) it(41) =< aux(31) s(33) =< it(41)*aux(32) s(34) =< s(35) with precondition: [Out=0,V>=4,V2>=1] * Chain [[41],43,47]: 6*it(41)+1*s(33)+2*s(34)+1*s(38)+2*s(39)+9 Such that:s(38) =< 1 s(35) =< 2*V aux(34) =< V aux(35) =< V2 s(39) =< aux(35) it(41) =< aux(34) s(33) =< it(41)*aux(35) s(34) =< s(35) with precondition: [V>=4,Out>=0,V2>=Out+1] * Chain [48]: 3*s(4)+4*s(5)+3 Such that:aux(2) =< 1 aux(3) =< V2 s(5) =< aux(2) s(4) =< aux(3) with precondition: [Out=0,V>=0,V2>=0] * Chain [47]: 1*s(40)+4 Such that:s(40) =< V2 with precondition: [V=0,Out>=0,V2>=Out+1] * Chain [46]: 2*s(20)+1*s(22)+3 Such that:s(22) =< V2 aux(8) =< 1 s(20) =< aux(8) with precondition: [V=1,Out=0,V2>=0] * Chain [45]: 1*s(36)+1*s(37)+4 Such that:s(36) =< 1 s(37) =< V2 with precondition: [V=1,Out>=0,V2>=Out+1] * Chain [44,48]: 5*s(5)+8 Such that:aux(10) =< 1 s(5) =< aux(10) with precondition: [Out=0,V>=2,V2>=0] * Chain [43,48]: 4*s(4)+5*s(5)+8 Such that:aux(29) =< 1 aux(30) =< V2 s(5) =< aux(29) s(4) =< aux(30) with precondition: [Out=0,V>=2,V2>=1] * Chain [43,47]: 1*s(38)+2*s(39)+9 Such that:s(38) =< 1 aux(33) =< V2 s(39) =< aux(33) with precondition: [V>=2,Out>=0,V2>=Out+1] #### Cost of chains of encArg(V,Out): * Chain [65]: 0 with precondition: [V=1,Out=1] * Chain [64]: 0 with precondition: [V=2,Out=2] * Chain [63]: 0 with precondition: [Out=0,V>=0] * Chain [multiple([49,50,51,52,53,54,55,56,57,58,59,60,61,62],[[65],[64],[63]])]: 1*it(49)+11*it(50)+10*it(51)+226*it(52)+9*it(55)+4*it(56)+5*it(57)+1*it(58)+9*it(59)+1*it(60)+7*s(274)+2*s(275)+4*s(276)+6*s(277)+12*s(278)+2*s(279)+32*s(285)+46*s(287)+60*s(288)+7*s(289)+3*s(294)+60*s(297)+44*s(298)+3*s(302)+5*s(303)+12*s(304)+2*s(305)+4*s(306)+1*s(311)+1*s(312)+1*s(313)+1*s(314)+1*s(315)+1*s(316)+16*s(317)+60*s(319)+7*s(320)+44*s(321)+0 Such that:s(238) =< 2*V aux(87) =< V aux(88) =< 2*V+1 aux(89) =< V/2 aux(90) =< 2/3*V aux(91) =< 3/5*V aux(92) =< 4/5*V aux(93) =< 4/7*V it(51) =< aux(87) it(52) =< aux(87) it(55) =< aux(87) it(56) =< aux(87) it(57) =< aux(87) it(58) =< aux(87) it(59) =< aux(87) it(60) =< aux(87) it([63]) =< aux(88) it(49) =< aux(89) aux(73) =< aux(90) it(56) =< aux(90) it(58) =< aux(90) it(60) =< aux(90) aux(54) =< aux(91) it(50) =< aux(91) it(57) =< aux(92) it(58) =< aux(92) it(60) =< aux(92) aux(68) =< aux(93) it(55) =< aux(93) it(60) =< aux(93) aux(62) =< s(238)+2 aux(65) =< s(238)+4 aux(71) =< s(238) aux(58) =< s(238)+1 aux(69) =< s(238)+3 aux(60) =< s(238)*(1/2)+1 aux(56) =< s(238)*(1/2) it(57) =< it([63])*(1/5)+aux(92) it(58) =< it([63])*(1/5)+aux(92) it(59) =< it([63])*(1/5)+aux(92) it(60) =< it([63])*(1/5)+aux(92) it(55) =< it([63])*(3/7)+aux(93) it(56) =< it([63])*(3/7)+aux(93) it(57) =< it([63])*(3/7)+aux(93) it(58) =< it([63])*(3/7)+aux(93) it(59) =< it([63])*(3/7)+aux(93) it(60) =< it([63])*(3/7)+aux(93) it(56) =< it([63])*(1/3)+aux(90) it(57) =< it([63])*(1/3)+aux(90) it(58) =< it([63])*(1/3)+aux(90) it(59) =< it([63])*(1/3)+aux(90) it(60) =< it([63])*(1/3)+aux(90) aux(73) =< it([63])*(1/3)+aux(90) aux(68) =< it([63])*(3/7)+aux(93) aux(54) =< it([63])*(1/5)+aux(91) it(51) =< it([63])*(1/5)+aux(91) it(50) =< it([63])*(1/5)+aux(91) it(49) =< it([63])*(1/4)+aux(89) it(50) =< it([63])*(1/4)+aux(89) it(51) =< it([63])*(1/4)+aux(89) s(316) =< it(59)*aux(62) aux(85) =< it(59)*aux(62) s(325) =< it(59)*aux(65) s(315) =< it(60)*aux(71) s(314) =< it(58)*aux(58) s(313) =< it(57)*aux(62) s(312) =< it(56)*aux(58) s(311) =< aux(73) s(309) =< it(55)*aux(71) aux(70) =< it(55)*aux(69) aux(66) =< it(52)*aux(65) s(295) =< it(52)*aux(62) s(293) =< it(51)*aux(62) aux(61) =< it(51)*aux(60) s(283) =< it(50)*aux(58) aux(57) =< it(50)*aux(56) s(282) =< aux(54)*2 s(322) =< aux(85)*2 s(307) =< aux(70)*2 s(299) =< aux(66)*2 s(290) =< aux(61)*2 s(280) =< aux(57)*2 s(317) =< s(325) s(319) =< aux(85) s(320) =< s(319)*aux(65) s(321) =< s(322) s(302) =< aux(68) s(303) =< s(309) s(304) =< aux(70) s(305) =< s(304)*s(238) s(306) =< s(307) s(297) =< aux(66) s(298) =< s(299) s(294) =< s(295) s(285) =< s(293) s(288) =< aux(61) s(289) =< s(288)*aux(62) s(287) =< s(290) s(276) =< aux(54) s(274) =< s(283) s(275) =< s(282) s(278) =< aux(57) s(279) =< s(278)*aux(58) s(277) =< s(280) with precondition: [V>=1,Out>=0,2*V>=Out] #### Cost of chains of fun(V,Out): * Chain [67]: 10*s(407)+226*s(408)+9*s(409)+4*s(410)+5*s(411)+1*s(412)+9*s(413)+1*s(414)+1*s(415)+11*s(418)+1*s(427)+1*s(430)+1*s(431)+1*s(432)+1*s(433)+1*s(434)+16*s(449)+60*s(450)+7*s(451)+44*s(452)+3*s(453)+5*s(454)+12*s(455)+2*s(456)+4*s(457)+60*s(458)+44*s(459)+3*s(460)+32*s(461)+60*s(462)+7*s(463)+46*s(464)+4*s(465)+7*s(466)+2*s(467)+12*s(468)+2*s(469)+6*s(470)+1 Such that:s(399) =< V s(400) =< 2*V s(401) =< 2*V+1 s(402) =< V/2 s(403) =< 2/3*V s(404) =< 3/5*V s(405) =< 4/5*V s(406) =< 4/7*V s(407) =< s(399) s(408) =< s(399) s(409) =< s(399) s(410) =< s(399) s(411) =< s(399) s(412) =< s(399) s(413) =< s(399) s(414) =< s(399) s(415) =< s(402) s(416) =< s(403) s(410) =< s(403) s(412) =< s(403) s(414) =< s(403) s(417) =< s(404) s(418) =< s(404) s(411) =< s(405) s(412) =< s(405) s(414) =< s(405) s(419) =< s(406) s(409) =< s(406) s(414) =< s(406) s(420) =< s(400)+2 s(421) =< s(400)+4 s(422) =< s(400) s(423) =< s(400)+1 s(424) =< s(400)+3 s(425) =< s(400)*(1/2)+1 s(426) =< s(400)*(1/2) s(411) =< s(401)*(1/5)+s(405) s(412) =< s(401)*(1/5)+s(405) s(413) =< s(401)*(1/5)+s(405) s(414) =< s(401)*(1/5)+s(405) s(409) =< s(401)*(3/7)+s(406) s(410) =< s(401)*(3/7)+s(406) s(411) =< s(401)*(3/7)+s(406) s(412) =< s(401)*(3/7)+s(406) s(413) =< s(401)*(3/7)+s(406) s(414) =< s(401)*(3/7)+s(406) s(410) =< s(401)*(1/3)+s(403) s(411) =< s(401)*(1/3)+s(403) s(412) =< s(401)*(1/3)+s(403) s(413) =< s(401)*(1/3)+s(403) s(414) =< s(401)*(1/3)+s(403) s(416) =< s(401)*(1/3)+s(403) s(419) =< s(401)*(3/7)+s(406) s(417) =< s(401)*(1/5)+s(404) s(407) =< s(401)*(1/5)+s(404) s(418) =< s(401)*(1/5)+s(404) s(415) =< s(401)*(1/4)+s(402) s(418) =< s(401)*(1/4)+s(402) s(407) =< s(401)*(1/4)+s(402) s(427) =< s(413)*s(420) s(428) =< s(413)*s(420) s(429) =< s(413)*s(421) s(430) =< s(414)*s(422) s(431) =< s(412)*s(423) s(432) =< s(411)*s(420) s(433) =< s(410)*s(423) s(434) =< s(416) s(435) =< s(409)*s(422) s(436) =< s(409)*s(424) s(437) =< s(408)*s(421) s(438) =< s(408)*s(420) s(439) =< s(407)*s(420) s(440) =< s(407)*s(425) s(441) =< s(418)*s(423) s(442) =< s(418)*s(426) s(443) =< s(417)*2 s(444) =< s(428)*2 s(445) =< s(436)*2 s(446) =< s(437)*2 s(447) =< s(440)*2 s(448) =< s(442)*2 s(449) =< s(429) s(450) =< s(428) s(451) =< s(450)*s(421) s(452) =< s(444) s(453) =< s(419) s(454) =< s(435) s(455) =< s(436) s(456) =< s(455)*s(400) s(457) =< s(445) s(458) =< s(437) s(459) =< s(446) s(460) =< s(438) s(461) =< s(439) s(462) =< s(440) s(463) =< s(462)*s(420) s(464) =< s(447) s(465) =< s(417) s(466) =< s(441) s(467) =< s(443) s(468) =< s(442) s(469) =< s(468)*s(423) s(470) =< s(448) with precondition: [Out=0,V>=0] * Chain [66]: 10*s(479)+226*s(480)+9*s(481)+4*s(482)+5*s(483)+1*s(484)+9*s(485)+1*s(486)+1*s(487)+11*s(490)+1*s(499)+1*s(502)+1*s(503)+1*s(504)+1*s(505)+1*s(506)+16*s(521)+60*s(522)+7*s(523)+44*s(524)+3*s(525)+5*s(526)+12*s(527)+2*s(528)+4*s(529)+60*s(530)+44*s(531)+3*s(532)+32*s(533)+60*s(534)+7*s(535)+46*s(536)+4*s(537)+7*s(538)+2*s(539)+12*s(540)+2*s(541)+6*s(542)+2*s(544)+2*s(546)+1 Such that:s(545) =< 2 s(471) =< V aux(94) =< 2*V s(473) =< 2*V+1 s(474) =< V/2 s(475) =< 2/3*V s(476) =< 3/5*V s(477) =< 4/5*V s(478) =< 4/7*V s(546) =< s(545) s(544) =< aux(94) s(479) =< s(471) s(480) =< s(471) s(481) =< s(471) s(482) =< s(471) s(483) =< s(471) s(484) =< s(471) s(485) =< s(471) s(486) =< s(471) s(487) =< s(474) s(488) =< s(475) s(482) =< s(475) s(484) =< s(475) s(486) =< s(475) s(489) =< s(476) s(490) =< s(476) s(483) =< s(477) s(484) =< s(477) s(486) =< s(477) s(491) =< s(478) s(481) =< s(478) s(486) =< s(478) s(492) =< aux(94)+2 s(493) =< aux(94)+4 s(494) =< aux(94) s(495) =< aux(94)+1 s(496) =< aux(94)+3 s(497) =< aux(94)*(1/2)+1 s(498) =< aux(94)*(1/2) s(483) =< s(473)*(1/5)+s(477) s(484) =< s(473)*(1/5)+s(477) s(485) =< s(473)*(1/5)+s(477) s(486) =< s(473)*(1/5)+s(477) s(481) =< s(473)*(3/7)+s(478) s(482) =< s(473)*(3/7)+s(478) s(483) =< s(473)*(3/7)+s(478) s(484) =< s(473)*(3/7)+s(478) s(485) =< s(473)*(3/7)+s(478) s(486) =< s(473)*(3/7)+s(478) s(482) =< s(473)*(1/3)+s(475) s(483) =< s(473)*(1/3)+s(475) s(484) =< s(473)*(1/3)+s(475) s(485) =< s(473)*(1/3)+s(475) s(486) =< s(473)*(1/3)+s(475) s(488) =< s(473)*(1/3)+s(475) s(491) =< s(473)*(3/7)+s(478) s(489) =< s(473)*(1/5)+s(476) s(479) =< s(473)*(1/5)+s(476) s(490) =< s(473)*(1/5)+s(476) s(487) =< s(473)*(1/4)+s(474) s(490) =< s(473)*(1/4)+s(474) s(479) =< s(473)*(1/4)+s(474) s(499) =< s(485)*s(492) s(500) =< s(485)*s(492) s(501) =< s(485)*s(493) s(502) =< s(486)*s(494) s(503) =< s(484)*s(495) s(504) =< s(483)*s(492) s(505) =< s(482)*s(495) s(506) =< s(488) s(507) =< s(481)*s(494) s(508) =< s(481)*s(496) s(509) =< s(480)*s(493) s(510) =< s(480)*s(492) s(511) =< s(479)*s(492) s(512) =< s(479)*s(497) s(513) =< s(490)*s(495) s(514) =< s(490)*s(498) s(515) =< s(489)*2 s(516) =< s(500)*2 s(517) =< s(508)*2 s(518) =< s(509)*2 s(519) =< s(512)*2 s(520) =< s(514)*2 s(521) =< s(501) s(522) =< s(500) s(523) =< s(522)*s(493) s(524) =< s(516) s(525) =< s(491) s(526) =< s(507) s(527) =< s(508) s(528) =< s(527)*aux(94) s(529) =< s(517) s(530) =< s(509) s(531) =< s(518) s(532) =< s(510) s(533) =< s(511) s(534) =< s(512) s(535) =< s(534)*s(492) s(536) =< s(519) s(537) =< s(489) s(538) =< s(513) s(539) =< s(515) s(540) =< s(514) s(541) =< s(540)*s(495) s(542) =< s(520) with precondition: [Out>=1,V>=Out] #### Cost of chains of fun2(V,Out): * Chain [70]: 10*s(555)+226*s(556)+9*s(557)+4*s(558)+5*s(559)+1*s(560)+9*s(561)+1*s(562)+1*s(563)+11*s(566)+1*s(575)+1*s(578)+1*s(579)+1*s(580)+1*s(581)+1*s(582)+16*s(597)+60*s(598)+7*s(599)+44*s(600)+3*s(601)+5*s(602)+12*s(603)+2*s(604)+4*s(605)+60*s(606)+44*s(607)+3*s(608)+32*s(609)+60*s(610)+7*s(611)+46*s(612)+4*s(613)+7*s(614)+2*s(615)+12*s(616)+2*s(617)+6*s(618)+0 Such that:s(547) =< V s(548) =< 2*V s(549) =< 2*V+1 s(550) =< V/2 s(551) =< 2/3*V s(552) =< 3/5*V s(553) =< 4/5*V s(554) =< 4/7*V s(555) =< s(547) s(556) =< s(547) s(557) =< s(547) s(558) =< s(547) s(559) =< s(547) s(560) =< s(547) s(561) =< s(547) s(562) =< s(547) s(563) =< s(550) s(564) =< s(551) s(558) =< s(551) s(560) =< s(551) s(562) =< s(551) s(565) =< s(552) s(566) =< s(552) s(559) =< s(553) s(560) =< s(553) s(562) =< s(553) s(567) =< s(554) s(557) =< s(554) s(562) =< s(554) s(568) =< s(548)+2 s(569) =< s(548)+4 s(570) =< s(548) s(571) =< s(548)+1 s(572) =< s(548)+3 s(573) =< s(548)*(1/2)+1 s(574) =< s(548)*(1/2) s(559) =< s(549)*(1/5)+s(553) s(560) =< s(549)*(1/5)+s(553) s(561) =< s(549)*(1/5)+s(553) s(562) =< s(549)*(1/5)+s(553) s(557) =< s(549)*(3/7)+s(554) s(558) =< s(549)*(3/7)+s(554) s(559) =< s(549)*(3/7)+s(554) s(560) =< s(549)*(3/7)+s(554) s(561) =< s(549)*(3/7)+s(554) s(562) =< s(549)*(3/7)+s(554) s(558) =< s(549)*(1/3)+s(551) s(559) =< s(549)*(1/3)+s(551) s(560) =< s(549)*(1/3)+s(551) s(561) =< s(549)*(1/3)+s(551) s(562) =< s(549)*(1/3)+s(551) s(564) =< s(549)*(1/3)+s(551) s(567) =< s(549)*(3/7)+s(554) s(565) =< s(549)*(1/5)+s(552) s(555) =< s(549)*(1/5)+s(552) s(566) =< s(549)*(1/5)+s(552) s(563) =< s(549)*(1/4)+s(550) s(566) =< s(549)*(1/4)+s(550) s(555) =< s(549)*(1/4)+s(550) s(575) =< s(561)*s(568) s(576) =< s(561)*s(568) s(577) =< s(561)*s(569) s(578) =< s(562)*s(570) s(579) =< s(560)*s(571) s(580) =< s(559)*s(568) s(581) =< s(558)*s(571) s(582) =< s(564) s(583) =< s(557)*s(570) s(584) =< s(557)*s(572) s(585) =< s(556)*s(569) s(586) =< s(556)*s(568) s(587) =< s(555)*s(568) s(588) =< s(555)*s(573) s(589) =< s(566)*s(571) s(590) =< s(566)*s(574) s(591) =< s(565)*2 s(592) =< s(576)*2 s(593) =< s(584)*2 s(594) =< s(585)*2 s(595) =< s(588)*2 s(596) =< s(590)*2 s(597) =< s(577) s(598) =< s(576) s(599) =< s(598)*s(569) s(600) =< s(592) s(601) =< s(567) s(602) =< s(583) s(603) =< s(584) s(604) =< s(603)*s(548) s(605) =< s(593) s(606) =< s(585) s(607) =< s(594) s(608) =< s(586) s(609) =< s(587) s(610) =< s(588) s(611) =< s(610)*s(568) s(612) =< s(595) s(613) =< s(565) s(614) =< s(589) s(615) =< s(591) s(616) =< s(590) s(617) =< s(616)*s(571) s(618) =< s(596) with precondition: [V>=1,Out>=1,2*V+1>=Out] * Chain [69]: 0 with precondition: [Out=0,V>=0] * Chain [68]: 0 with precondition: [Out=1,V>=0] #### Cost of chains of fun3(V,V2,Out): * Chain [76]: 20*s(627)+452*s(628)+18*s(629)+8*s(630)+10*s(631)+2*s(632)+18*s(633)+2*s(634)+2*s(635)+22*s(638)+2*s(647)+2*s(650)+2*s(651)+2*s(652)+2*s(653)+2*s(654)+32*s(669)+120*s(670)+14*s(671)+88*s(672)+6*s(673)+10*s(674)+24*s(675)+4*s(676)+8*s(677)+120*s(678)+88*s(679)+6*s(680)+64*s(681)+120*s(682)+14*s(683)+92*s(684)+8*s(685)+14*s(686)+4*s(687)+24*s(688)+4*s(689)+12*s(690)+30*s(699)+678*s(700)+27*s(701)+12*s(702)+15*s(703)+3*s(704)+27*s(705)+3*s(706)+3*s(707)+33*s(710)+3*s(719)+3*s(722)+3*s(723)+3*s(724)+3*s(725)+3*s(726)+48*s(741)+180*s(742)+21*s(743)+132*s(744)+9*s(745)+15*s(746)+36*s(747)+6*s(748)+12*s(749)+180*s(750)+132*s(751)+9*s(752)+96*s(753)+180*s(754)+21*s(755)+138*s(756)+12*s(757)+21*s(758)+6*s(759)+36*s(760)+6*s(761)+18*s(762)+3*s(763)+1*s(910)+0 Such that:s(910) =< 2 aux(98) =< V aux(99) =< 2*V aux(100) =< 2*V+1 aux(101) =< V/2 aux(102) =< 2/3*V aux(103) =< 3/5*V aux(104) =< 4/5*V aux(105) =< 4/7*V aux(106) =< V2 aux(107) =< 2*V2 aux(108) =< 2*V2+1 aux(109) =< V2/2 aux(110) =< 2/3*V2 aux(111) =< 3/5*V2 aux(112) =< 4/5*V2 aux(113) =< 4/7*V2 s(763) =< aux(107) s(699) =< aux(106) s(700) =< aux(106) s(701) =< aux(106) s(702) =< aux(106) s(703) =< aux(106) s(704) =< aux(106) s(705) =< aux(106) s(706) =< aux(106) s(707) =< aux(109) s(708) =< aux(110) s(702) =< aux(110) s(704) =< aux(110) s(706) =< aux(110) s(709) =< aux(111) s(710) =< aux(111) s(703) =< aux(112) s(704) =< aux(112) s(706) =< aux(112) s(711) =< aux(113) s(701) =< aux(113) s(706) =< aux(113) s(712) =< aux(107)+2 s(713) =< aux(107)+4 s(714) =< aux(107) s(715) =< aux(107)+1 s(716) =< aux(107)+3 s(717) =< aux(107)*(1/2)+1 s(718) =< aux(107)*(1/2) s(703) =< aux(108)*(1/5)+aux(112) s(704) =< aux(108)*(1/5)+aux(112) s(705) =< aux(108)*(1/5)+aux(112) s(706) =< aux(108)*(1/5)+aux(112) s(701) =< aux(108)*(3/7)+aux(113) s(702) =< aux(108)*(3/7)+aux(113) s(703) =< aux(108)*(3/7)+aux(113) s(704) =< aux(108)*(3/7)+aux(113) s(705) =< aux(108)*(3/7)+aux(113) s(706) =< aux(108)*(3/7)+aux(113) s(702) =< aux(108)*(1/3)+aux(110) s(703) =< aux(108)*(1/3)+aux(110) s(704) =< aux(108)*(1/3)+aux(110) s(705) =< aux(108)*(1/3)+aux(110) s(706) =< aux(108)*(1/3)+aux(110) s(708) =< aux(108)*(1/3)+aux(110) s(711) =< aux(108)*(3/7)+aux(113) s(709) =< aux(108)*(1/5)+aux(111) s(699) =< aux(108)*(1/5)+aux(111) s(710) =< aux(108)*(1/5)+aux(111) s(707) =< aux(108)*(1/4)+aux(109) s(710) =< aux(108)*(1/4)+aux(109) s(699) =< aux(108)*(1/4)+aux(109) s(719) =< s(705)*s(712) s(720) =< s(705)*s(712) s(721) =< s(705)*s(713) s(722) =< s(706)*s(714) s(723) =< s(704)*s(715) s(724) =< s(703)*s(712) s(725) =< s(702)*s(715) s(726) =< s(708) s(727) =< s(701)*s(714) s(728) =< s(701)*s(716) s(729) =< s(700)*s(713) s(730) =< s(700)*s(712) s(731) =< s(699)*s(712) s(732) =< s(699)*s(717) s(733) =< s(710)*s(715) s(734) =< s(710)*s(718) s(735) =< s(709)*2 s(736) =< s(720)*2 s(737) =< s(728)*2 s(738) =< s(729)*2 s(739) =< s(732)*2 s(740) =< s(734)*2 s(741) =< s(721) s(742) =< s(720) s(743) =< s(742)*s(713) s(744) =< s(736) s(745) =< s(711) s(746) =< s(727) s(747) =< s(728) s(748) =< s(747)*aux(107) s(749) =< s(737) s(750) =< s(729) s(751) =< s(738) s(752) =< s(730) s(753) =< s(731) s(754) =< s(732) s(755) =< s(754)*s(712) s(756) =< s(739) s(757) =< s(709) s(758) =< s(733) s(759) =< s(735) s(760) =< s(734) s(761) =< s(760)*s(715) s(762) =< s(740) s(627) =< aux(98) s(628) =< aux(98) s(629) =< aux(98) s(630) =< aux(98) s(631) =< aux(98) s(632) =< aux(98) s(633) =< aux(98) s(634) =< aux(98) s(635) =< aux(101) s(636) =< aux(102) s(630) =< aux(102) s(632) =< aux(102) s(634) =< aux(102) s(637) =< aux(103) s(638) =< aux(103) s(631) =< aux(104) s(632) =< aux(104) s(634) =< aux(104) s(639) =< aux(105) s(629) =< aux(105) s(634) =< aux(105) s(640) =< aux(99)+2 s(641) =< aux(99)+4 s(642) =< aux(99) s(643) =< aux(99)+1 s(644) =< aux(99)+3 s(645) =< aux(99)*(1/2)+1 s(646) =< aux(99)*(1/2) s(631) =< aux(100)*(1/5)+aux(104) s(632) =< aux(100)*(1/5)+aux(104) s(633) =< aux(100)*(1/5)+aux(104) s(634) =< aux(100)*(1/5)+aux(104) s(629) =< aux(100)*(3/7)+aux(105) s(630) =< aux(100)*(3/7)+aux(105) s(631) =< aux(100)*(3/7)+aux(105) s(632) =< aux(100)*(3/7)+aux(105) s(633) =< aux(100)*(3/7)+aux(105) s(634) =< aux(100)*(3/7)+aux(105) s(630) =< aux(100)*(1/3)+aux(102) s(631) =< aux(100)*(1/3)+aux(102) s(632) =< aux(100)*(1/3)+aux(102) s(633) =< aux(100)*(1/3)+aux(102) s(634) =< aux(100)*(1/3)+aux(102) s(636) =< aux(100)*(1/3)+aux(102) s(639) =< aux(100)*(3/7)+aux(105) s(637) =< aux(100)*(1/5)+aux(103) s(627) =< aux(100)*(1/5)+aux(103) s(638) =< aux(100)*(1/5)+aux(103) s(635) =< aux(100)*(1/4)+aux(101) s(638) =< aux(100)*(1/4)+aux(101) s(627) =< aux(100)*(1/4)+aux(101) s(647) =< s(633)*s(640) s(648) =< s(633)*s(640) s(649) =< s(633)*s(641) s(650) =< s(634)*s(642) s(651) =< s(632)*s(643) s(652) =< s(631)*s(640) s(653) =< s(630)*s(643) s(654) =< s(636) s(655) =< s(629)*s(642) s(656) =< s(629)*s(644) s(657) =< s(628)*s(641) s(658) =< s(628)*s(640) s(659) =< s(627)*s(640) s(660) =< s(627)*s(645) s(661) =< s(638)*s(643) s(662) =< s(638)*s(646) s(663) =< s(637)*2 s(664) =< s(648)*2 s(665) =< s(656)*2 s(666) =< s(657)*2 s(667) =< s(660)*2 s(668) =< s(662)*2 s(669) =< s(649) s(670) =< s(648) s(671) =< s(670)*s(641) s(672) =< s(664) s(673) =< s(639) s(674) =< s(655) s(675) =< s(656) s(676) =< s(675)*aux(99) s(677) =< s(665) s(678) =< s(657) s(679) =< s(666) s(680) =< s(658) s(681) =< s(659) s(682) =< s(660) s(683) =< s(682)*s(640) s(684) =< s(667) s(685) =< s(637) s(686) =< s(661) s(687) =< s(663) s(688) =< s(662) s(689) =< s(688)*s(643) s(690) =< s(668) with precondition: [Out=0,V>=0,V2>=0] * Chain [75]: 30*s(994)+678*s(995)+27*s(996)+12*s(997)+15*s(998)+3*s(999)+27*s(1000)+3*s(1001)+3*s(1002)+33*s(1005)+3*s(1014)+3*s(1017)+3*s(1018)+3*s(1019)+3*s(1020)+3*s(1021)+48*s(1036)+180*s(1037)+21*s(1038)+132*s(1039)+9*s(1040)+15*s(1041)+36*s(1042)+6*s(1043)+12*s(1044)+180*s(1045)+132*s(1046)+9*s(1047)+96*s(1048)+180*s(1049)+21*s(1050)+138*s(1051)+12*s(1052)+21*s(1053)+6*s(1054)+36*s(1055)+6*s(1056)+18*s(1057)+40*s(1066)+904*s(1067)+36*s(1068)+16*s(1069)+20*s(1070)+4*s(1071)+36*s(1072)+4*s(1073)+4*s(1074)+44*s(1077)+4*s(1086)+4*s(1089)+4*s(1090)+4*s(1091)+4*s(1092)+4*s(1093)+64*s(1108)+240*s(1109)+28*s(1110)+176*s(1111)+12*s(1112)+20*s(1113)+48*s(1114)+8*s(1115)+16*s(1116)+240*s(1117)+176*s(1118)+12*s(1119)+128*s(1120)+240*s(1121)+28*s(1122)+184*s(1123)+16*s(1124)+28*s(1125)+8*s(1126)+48*s(1127)+8*s(1128)+24*s(1129)+1*s(1274)+2*s(1419)+1 Such that:aux(115) =< 2 aux(116) =< V aux(117) =< 2*V aux(118) =< 2*V+1 aux(119) =< V/2 aux(120) =< 2/3*V aux(121) =< 3/5*V aux(122) =< 4/5*V aux(123) =< 4/7*V aux(124) =< V2 aux(125) =< 2*V2 aux(126) =< 2*V2+1 aux(127) =< V2/2 aux(128) =< 2/3*V2 aux(129) =< 3/5*V2 aux(130) =< 4/5*V2 aux(131) =< 4/7*V2 s(1419) =< aux(115) s(1066) =< aux(124) s(1067) =< aux(124) s(1068) =< aux(124) s(1069) =< aux(124) s(1070) =< aux(124) s(1071) =< aux(124) s(1072) =< aux(124) s(1073) =< aux(124) s(1074) =< aux(127) s(1075) =< aux(128) s(1069) =< aux(128) s(1071) =< aux(128) s(1073) =< aux(128) s(1076) =< aux(129) s(1077) =< aux(129) s(1070) =< aux(130) s(1071) =< aux(130) s(1073) =< aux(130) s(1078) =< aux(131) s(1068) =< aux(131) s(1073) =< aux(131) s(1079) =< aux(125)+2 s(1080) =< aux(125)+4 s(1081) =< aux(125) s(1082) =< aux(125)+1 s(1083) =< aux(125)+3 s(1084) =< aux(125)*(1/2)+1 s(1085) =< aux(125)*(1/2) s(1070) =< aux(126)*(1/5)+aux(130) s(1071) =< aux(126)*(1/5)+aux(130) s(1072) =< aux(126)*(1/5)+aux(130) s(1073) =< aux(126)*(1/5)+aux(130) s(1068) =< aux(126)*(3/7)+aux(131) s(1069) =< aux(126)*(3/7)+aux(131) s(1070) =< aux(126)*(3/7)+aux(131) s(1071) =< aux(126)*(3/7)+aux(131) s(1072) =< aux(126)*(3/7)+aux(131) s(1073) =< aux(126)*(3/7)+aux(131) s(1069) =< aux(126)*(1/3)+aux(128) s(1070) =< aux(126)*(1/3)+aux(128) s(1071) =< aux(126)*(1/3)+aux(128) s(1072) =< aux(126)*(1/3)+aux(128) s(1073) =< aux(126)*(1/3)+aux(128) s(1075) =< aux(126)*(1/3)+aux(128) s(1078) =< aux(126)*(3/7)+aux(131) s(1076) =< aux(126)*(1/5)+aux(129) s(1066) =< aux(126)*(1/5)+aux(129) s(1077) =< aux(126)*(1/5)+aux(129) s(1074) =< aux(126)*(1/4)+aux(127) s(1077) =< aux(126)*(1/4)+aux(127) s(1066) =< aux(126)*(1/4)+aux(127) s(1086) =< s(1072)*s(1079) s(1087) =< s(1072)*s(1079) s(1088) =< s(1072)*s(1080) s(1089) =< s(1073)*s(1081) s(1090) =< s(1071)*s(1082) s(1091) =< s(1070)*s(1079) s(1092) =< s(1069)*s(1082) s(1093) =< s(1075) s(1094) =< s(1068)*s(1081) s(1095) =< s(1068)*s(1083) s(1096) =< s(1067)*s(1080) s(1097) =< s(1067)*s(1079) s(1098) =< s(1066)*s(1079) s(1099) =< s(1066)*s(1084) s(1100) =< s(1077)*s(1082) s(1101) =< s(1077)*s(1085) s(1102) =< s(1076)*2 s(1103) =< s(1087)*2 s(1104) =< s(1095)*2 s(1105) =< s(1096)*2 s(1106) =< s(1099)*2 s(1107) =< s(1101)*2 s(1108) =< s(1088) s(1109) =< s(1087) s(1110) =< s(1109)*s(1080) s(1111) =< s(1103) s(1112) =< s(1078) s(1113) =< s(1094) s(1114) =< s(1095) s(1115) =< s(1114)*aux(125) s(1116) =< s(1104) s(1117) =< s(1096) s(1118) =< s(1105) s(1119) =< s(1097) s(1120) =< s(1098) s(1121) =< s(1099) s(1122) =< s(1121)*s(1079) s(1123) =< s(1106) s(1124) =< s(1076) s(1125) =< s(1100) s(1126) =< s(1102) s(1127) =< s(1101) s(1128) =< s(1127)*s(1082) s(1129) =< s(1107) s(994) =< aux(116) s(995) =< aux(116) s(996) =< aux(116) s(997) =< aux(116) s(998) =< aux(116) s(999) =< aux(116) s(1000) =< aux(116) s(1001) =< aux(116) s(1002) =< aux(119) s(1003) =< aux(120) s(997) =< aux(120) s(999) =< aux(120) s(1001) =< aux(120) s(1004) =< aux(121) s(1005) =< aux(121) s(998) =< aux(122) s(999) =< aux(122) s(1001) =< aux(122) s(1006) =< aux(123) s(996) =< aux(123) s(1001) =< aux(123) s(1007) =< aux(117)+2 s(1008) =< aux(117)+4 s(1009) =< aux(117) s(1010) =< aux(117)+1 s(1011) =< aux(117)+3 s(1012) =< aux(117)*(1/2)+1 s(1013) =< aux(117)*(1/2) s(998) =< aux(118)*(1/5)+aux(122) s(999) =< aux(118)*(1/5)+aux(122) s(1000) =< aux(118)*(1/5)+aux(122) s(1001) =< aux(118)*(1/5)+aux(122) s(996) =< aux(118)*(3/7)+aux(123) s(997) =< aux(118)*(3/7)+aux(123) s(998) =< aux(118)*(3/7)+aux(123) s(999) =< aux(118)*(3/7)+aux(123) s(1000) =< aux(118)*(3/7)+aux(123) s(1001) =< aux(118)*(3/7)+aux(123) s(997) =< aux(118)*(1/3)+aux(120) s(998) =< aux(118)*(1/3)+aux(120) s(999) =< aux(118)*(1/3)+aux(120) s(1000) =< aux(118)*(1/3)+aux(120) s(1001) =< aux(118)*(1/3)+aux(120) s(1003) =< aux(118)*(1/3)+aux(120) s(1006) =< aux(118)*(3/7)+aux(123) s(1004) =< aux(118)*(1/5)+aux(121) s(994) =< aux(118)*(1/5)+aux(121) s(1005) =< aux(118)*(1/5)+aux(121) s(1002) =< aux(118)*(1/4)+aux(119) s(1005) =< aux(118)*(1/4)+aux(119) s(994) =< aux(118)*(1/4)+aux(119) s(1014) =< s(1000)*s(1007) s(1015) =< s(1000)*s(1007) s(1016) =< s(1000)*s(1008) s(1017) =< s(1001)*s(1009) s(1018) =< s(999)*s(1010) s(1019) =< s(998)*s(1007) s(1020) =< s(997)*s(1010) s(1021) =< s(1003) s(1022) =< s(996)*s(1009) s(1023) =< s(996)*s(1011) s(1024) =< s(995)*s(1008) s(1025) =< s(995)*s(1007) s(1026) =< s(994)*s(1007) s(1027) =< s(994)*s(1012) s(1028) =< s(1005)*s(1010) s(1029) =< s(1005)*s(1013) s(1030) =< s(1004)*2 s(1031) =< s(1015)*2 s(1032) =< s(1023)*2 s(1033) =< s(1024)*2 s(1034) =< s(1027)*2 s(1035) =< s(1029)*2 s(1036) =< s(1016) s(1037) =< s(1015) s(1038) =< s(1037)*s(1008) s(1039) =< s(1031) s(1040) =< s(1006) s(1041) =< s(1022) s(1042) =< s(1023) s(1043) =< s(1042)*aux(117) s(1044) =< s(1032) s(1045) =< s(1024) s(1046) =< s(1033) s(1047) =< s(1025) s(1048) =< s(1026) s(1049) =< s(1027) s(1050) =< s(1049)*s(1007) s(1051) =< s(1034) s(1052) =< s(1004) s(1053) =< s(1028) s(1054) =< s(1030) s(1055) =< s(1029) s(1056) =< s(1055)*s(1010) s(1057) =< s(1035) s(1274) =< aux(125) with precondition: [Out=2,V>=0,V2>=0] * Chain [74]: 30*s(1501)+678*s(1502)+27*s(1503)+12*s(1504)+15*s(1505)+3*s(1506)+27*s(1507)+3*s(1508)+3*s(1509)+33*s(1512)+3*s(1521)+3*s(1524)+3*s(1525)+3*s(1526)+3*s(1527)+3*s(1528)+48*s(1543)+180*s(1544)+21*s(1545)+132*s(1546)+9*s(1547)+15*s(1548)+36*s(1549)+6*s(1550)+12*s(1551)+180*s(1552)+132*s(1553)+9*s(1554)+96*s(1555)+180*s(1556)+21*s(1557)+138*s(1558)+12*s(1559)+21*s(1560)+6*s(1561)+36*s(1562)+6*s(1563)+18*s(1564)+40*s(1573)+904*s(1574)+36*s(1575)+16*s(1576)+20*s(1577)+4*s(1578)+36*s(1579)+4*s(1580)+4*s(1581)+44*s(1584)+4*s(1593)+4*s(1596)+4*s(1597)+4*s(1598)+4*s(1599)+4*s(1600)+64*s(1615)+240*s(1616)+28*s(1617)+176*s(1618)+12*s(1619)+20*s(1620)+48*s(1621)+8*s(1622)+16*s(1623)+240*s(1624)+176*s(1625)+12*s(1626)+128*s(1627)+240*s(1628)+28*s(1629)+184*s(1630)+16*s(1631)+28*s(1632)+8*s(1633)+48*s(1634)+8*s(1635)+24*s(1636)+1*s(1781)+1*s(1998)+1 Such that:s(1998) =< 1 aux(133) =< V aux(134) =< 2*V aux(135) =< 2*V+1 aux(136) =< V/2 aux(137) =< 2/3*V aux(138) =< 3/5*V aux(139) =< 4/5*V aux(140) =< 4/7*V aux(141) =< V2 aux(142) =< 2*V2 aux(143) =< 2*V2+1 aux(144) =< V2/2 aux(145) =< 2/3*V2 aux(146) =< 3/5*V2 aux(147) =< 4/5*V2 aux(148) =< 4/7*V2 s(1573) =< aux(141) s(1574) =< aux(141) s(1575) =< aux(141) s(1576) =< aux(141) s(1577) =< aux(141) s(1578) =< aux(141) s(1579) =< aux(141) s(1580) =< aux(141) s(1581) =< aux(144) s(1582) =< aux(145) s(1576) =< aux(145) s(1578) =< aux(145) s(1580) =< aux(145) s(1583) =< aux(146) s(1584) =< aux(146) s(1577) =< aux(147) s(1578) =< aux(147) s(1580) =< aux(147) s(1585) =< aux(148) s(1575) =< aux(148) s(1580) =< aux(148) s(1586) =< aux(142)+2 s(1587) =< aux(142)+4 s(1588) =< aux(142) s(1589) =< aux(142)+1 s(1590) =< aux(142)+3 s(1591) =< aux(142)*(1/2)+1 s(1592) =< aux(142)*(1/2) s(1577) =< aux(143)*(1/5)+aux(147) s(1578) =< aux(143)*(1/5)+aux(147) s(1579) =< aux(143)*(1/5)+aux(147) s(1580) =< aux(143)*(1/5)+aux(147) s(1575) =< aux(143)*(3/7)+aux(148) s(1576) =< aux(143)*(3/7)+aux(148) s(1577) =< aux(143)*(3/7)+aux(148) s(1578) =< aux(143)*(3/7)+aux(148) s(1579) =< aux(143)*(3/7)+aux(148) s(1580) =< aux(143)*(3/7)+aux(148) s(1576) =< aux(143)*(1/3)+aux(145) s(1577) =< aux(143)*(1/3)+aux(145) s(1578) =< aux(143)*(1/3)+aux(145) s(1579) =< aux(143)*(1/3)+aux(145) s(1580) =< aux(143)*(1/3)+aux(145) s(1582) =< aux(143)*(1/3)+aux(145) s(1585) =< aux(143)*(3/7)+aux(148) s(1583) =< aux(143)*(1/5)+aux(146) s(1573) =< aux(143)*(1/5)+aux(146) s(1584) =< aux(143)*(1/5)+aux(146) s(1581) =< aux(143)*(1/4)+aux(144) s(1584) =< aux(143)*(1/4)+aux(144) s(1573) =< aux(143)*(1/4)+aux(144) s(1593) =< s(1579)*s(1586) s(1594) =< s(1579)*s(1586) s(1595) =< s(1579)*s(1587) s(1596) =< s(1580)*s(1588) s(1597) =< s(1578)*s(1589) s(1598) =< s(1577)*s(1586) s(1599) =< s(1576)*s(1589) s(1600) =< s(1582) s(1601) =< s(1575)*s(1588) s(1602) =< s(1575)*s(1590) s(1603) =< s(1574)*s(1587) s(1604) =< s(1574)*s(1586) s(1605) =< s(1573)*s(1586) s(1606) =< s(1573)*s(1591) s(1607) =< s(1584)*s(1589) s(1608) =< s(1584)*s(1592) s(1609) =< s(1583)*2 s(1610) =< s(1594)*2 s(1611) =< s(1602)*2 s(1612) =< s(1603)*2 s(1613) =< s(1606)*2 s(1614) =< s(1608)*2 s(1615) =< s(1595) s(1616) =< s(1594) s(1617) =< s(1616)*s(1587) s(1618) =< s(1610) s(1619) =< s(1585) s(1620) =< s(1601) s(1621) =< s(1602) s(1622) =< s(1621)*aux(142) s(1623) =< s(1611) s(1624) =< s(1603) s(1625) =< s(1612) s(1626) =< s(1604) s(1627) =< s(1605) s(1628) =< s(1606) s(1629) =< s(1628)*s(1586) s(1630) =< s(1613) s(1631) =< s(1583) s(1632) =< s(1607) s(1633) =< s(1609) s(1634) =< s(1608) s(1635) =< s(1634)*s(1589) s(1636) =< s(1614) s(1501) =< aux(133) s(1502) =< aux(133) s(1503) =< aux(133) s(1504) =< aux(133) s(1505) =< aux(133) s(1506) =< aux(133) s(1507) =< aux(133) s(1508) =< aux(133) s(1509) =< aux(136) s(1510) =< aux(137) s(1504) =< aux(137) s(1506) =< aux(137) s(1508) =< aux(137) s(1511) =< aux(138) s(1512) =< aux(138) s(1505) =< aux(139) s(1506) =< aux(139) s(1508) =< aux(139) s(1513) =< aux(140) s(1503) =< aux(140) s(1508) =< aux(140) s(1514) =< aux(134)+2 s(1515) =< aux(134)+4 s(1516) =< aux(134) s(1517) =< aux(134)+1 s(1518) =< aux(134)+3 s(1519) =< aux(134)*(1/2)+1 s(1520) =< aux(134)*(1/2) s(1505) =< aux(135)*(1/5)+aux(139) s(1506) =< aux(135)*(1/5)+aux(139) s(1507) =< aux(135)*(1/5)+aux(139) s(1508) =< aux(135)*(1/5)+aux(139) s(1503) =< aux(135)*(3/7)+aux(140) s(1504) =< aux(135)*(3/7)+aux(140) s(1505) =< aux(135)*(3/7)+aux(140) s(1506) =< aux(135)*(3/7)+aux(140) s(1507) =< aux(135)*(3/7)+aux(140) s(1508) =< aux(135)*(3/7)+aux(140) s(1504) =< aux(135)*(1/3)+aux(137) s(1505) =< aux(135)*(1/3)+aux(137) s(1506) =< aux(135)*(1/3)+aux(137) s(1507) =< aux(135)*(1/3)+aux(137) s(1508) =< aux(135)*(1/3)+aux(137) s(1510) =< aux(135)*(1/3)+aux(137) s(1513) =< aux(135)*(3/7)+aux(140) s(1511) =< aux(135)*(1/5)+aux(138) s(1501) =< aux(135)*(1/5)+aux(138) s(1512) =< aux(135)*(1/5)+aux(138) s(1509) =< aux(135)*(1/4)+aux(136) s(1512) =< aux(135)*(1/4)+aux(136) s(1501) =< aux(135)*(1/4)+aux(136) s(1521) =< s(1507)*s(1514) s(1522) =< s(1507)*s(1514) s(1523) =< s(1507)*s(1515) s(1524) =< s(1508)*s(1516) s(1525) =< s(1506)*s(1517) s(1526) =< s(1505)*s(1514) s(1527) =< s(1504)*s(1517) s(1528) =< s(1510) s(1529) =< s(1503)*s(1516) s(1530) =< s(1503)*s(1518) s(1531) =< s(1502)*s(1515) s(1532) =< s(1502)*s(1514) s(1533) =< s(1501)*s(1514) s(1534) =< s(1501)*s(1519) s(1535) =< s(1512)*s(1517) s(1536) =< s(1512)*s(1520) s(1537) =< s(1511)*2 s(1538) =< s(1522)*2 s(1539) =< s(1530)*2 s(1540) =< s(1531)*2 s(1541) =< s(1534)*2 s(1542) =< s(1536)*2 s(1543) =< s(1523) s(1544) =< s(1522) s(1545) =< s(1544)*s(1515) s(1546) =< s(1538) s(1547) =< s(1513) s(1548) =< s(1529) s(1549) =< s(1530) s(1550) =< s(1549)*aux(134) s(1551) =< s(1539) s(1552) =< s(1531) s(1553) =< s(1540) s(1554) =< s(1532) s(1555) =< s(1533) s(1556) =< s(1534) s(1557) =< s(1556)*s(1514) s(1558) =< s(1541) s(1559) =< s(1511) s(1560) =< s(1535) s(1561) =< s(1537) s(1562) =< s(1536) s(1563) =< s(1562)*s(1517) s(1564) =< s(1542) s(1781) =< aux(134) with precondition: [Out=1,V>=1,V2>=0] * Chain [73]: 10*s(2007)+226*s(2008)+9*s(2009)+4*s(2010)+5*s(2011)+1*s(2012)+9*s(2013)+1*s(2014)+1*s(2015)+11*s(2018)+1*s(2027)+1*s(2030)+1*s(2031)+1*s(2032)+1*s(2033)+1*s(2034)+16*s(2049)+60*s(2050)+7*s(2051)+44*s(2052)+3*s(2053)+5*s(2054)+12*s(2055)+2*s(2056)+4*s(2057)+60*s(2058)+44*s(2059)+3*s(2060)+32*s(2061)+60*s(2062)+7*s(2063)+46*s(2064)+4*s(2065)+7*s(2066)+2*s(2067)+12*s(2068)+2*s(2069)+6*s(2070)+2*s(2071)+0 Such that:s(1999) =< V s(2000) =< 2*V s(2001) =< 2*V+1 s(2002) =< V/2 s(2003) =< 2/3*V s(2004) =< 3/5*V s(2005) =< 4/5*V s(2006) =< 4/7*V aux(149) =< 2 s(2071) =< aux(149) s(2007) =< s(1999) s(2008) =< s(1999) s(2009) =< s(1999) s(2010) =< s(1999) s(2011) =< s(1999) s(2012) =< s(1999) s(2013) =< s(1999) s(2014) =< s(1999) s(2015) =< s(2002) s(2016) =< s(2003) s(2010) =< s(2003) s(2012) =< s(2003) s(2014) =< s(2003) s(2017) =< s(2004) s(2018) =< s(2004) s(2011) =< s(2005) s(2012) =< s(2005) s(2014) =< s(2005) s(2019) =< s(2006) s(2009) =< s(2006) s(2014) =< s(2006) s(2020) =< s(2000)+2 s(2021) =< s(2000)+4 s(2022) =< s(2000) s(2023) =< s(2000)+1 s(2024) =< s(2000)+3 s(2025) =< s(2000)*(1/2)+1 s(2026) =< s(2000)*(1/2) s(2011) =< s(2001)*(1/5)+s(2005) s(2012) =< s(2001)*(1/5)+s(2005) s(2013) =< s(2001)*(1/5)+s(2005) s(2014) =< s(2001)*(1/5)+s(2005) s(2009) =< s(2001)*(3/7)+s(2006) s(2010) =< s(2001)*(3/7)+s(2006) s(2011) =< s(2001)*(3/7)+s(2006) s(2012) =< s(2001)*(3/7)+s(2006) s(2013) =< s(2001)*(3/7)+s(2006) s(2014) =< s(2001)*(3/7)+s(2006) s(2010) =< s(2001)*(1/3)+s(2003) s(2011) =< s(2001)*(1/3)+s(2003) s(2012) =< s(2001)*(1/3)+s(2003) s(2013) =< s(2001)*(1/3)+s(2003) s(2014) =< s(2001)*(1/3)+s(2003) s(2016) =< s(2001)*(1/3)+s(2003) s(2019) =< s(2001)*(3/7)+s(2006) s(2017) =< s(2001)*(1/5)+s(2004) s(2007) =< s(2001)*(1/5)+s(2004) s(2018) =< s(2001)*(1/5)+s(2004) s(2015) =< s(2001)*(1/4)+s(2002) s(2018) =< s(2001)*(1/4)+s(2002) s(2007) =< s(2001)*(1/4)+s(2002) s(2027) =< s(2013)*s(2020) s(2028) =< s(2013)*s(2020) s(2029) =< s(2013)*s(2021) s(2030) =< s(2014)*s(2022) s(2031) =< s(2012)*s(2023) s(2032) =< s(2011)*s(2020) s(2033) =< s(2010)*s(2023) s(2034) =< s(2016) s(2035) =< s(2009)*s(2022) s(2036) =< s(2009)*s(2024) s(2037) =< s(2008)*s(2021) s(2038) =< s(2008)*s(2020) s(2039) =< s(2007)*s(2020) s(2040) =< s(2007)*s(2025) s(2041) =< s(2018)*s(2023) s(2042) =< s(2018)*s(2026) s(2043) =< s(2017)*2 s(2044) =< s(2028)*2 s(2045) =< s(2036)*2 s(2046) =< s(2037)*2 s(2047) =< s(2040)*2 s(2048) =< s(2042)*2 s(2049) =< s(2029) s(2050) =< s(2028) s(2051) =< s(2050)*s(2021) s(2052) =< s(2044) s(2053) =< s(2019) s(2054) =< s(2035) s(2055) =< s(2036) s(2056) =< s(2055)*s(2000) s(2057) =< s(2045) s(2058) =< s(2037) s(2059) =< s(2046) s(2060) =< s(2038) s(2061) =< s(2039) s(2062) =< s(2040) s(2063) =< s(2062)*s(2020) s(2064) =< s(2047) s(2065) =< s(2017) s(2066) =< s(2041) s(2067) =< s(2043) s(2068) =< s(2042) s(2069) =< s(2068)*s(2023) s(2070) =< s(2048) with precondition: [V2=2,Out=0,V>=0] * Chain [72]: 10*s(2081)+226*s(2082)+9*s(2083)+4*s(2084)+5*s(2085)+1*s(2086)+9*s(2087)+1*s(2088)+1*s(2089)+11*s(2092)+1*s(2101)+1*s(2104)+1*s(2105)+1*s(2106)+1*s(2107)+1*s(2108)+16*s(2123)+60*s(2124)+7*s(2125)+44*s(2126)+3*s(2127)+5*s(2128)+12*s(2129)+2*s(2130)+4*s(2131)+60*s(2132)+44*s(2133)+3*s(2134)+32*s(2135)+60*s(2136)+7*s(2137)+46*s(2138)+4*s(2139)+7*s(2140)+2*s(2141)+12*s(2142)+2*s(2143)+6*s(2144)+1*s(2145)+1 Such that:s(2145) =< 2 s(2073) =< V s(2074) =< 2*V s(2075) =< 2*V+1 s(2076) =< V/2 s(2077) =< 2/3*V s(2078) =< 3/5*V s(2079) =< 4/5*V s(2080) =< 4/7*V s(2081) =< s(2073) s(2082) =< s(2073) s(2083) =< s(2073) s(2084) =< s(2073) s(2085) =< s(2073) s(2086) =< s(2073) s(2087) =< s(2073) s(2088) =< s(2073) s(2089) =< s(2076) s(2090) =< s(2077) s(2084) =< s(2077) s(2086) =< s(2077) s(2088) =< s(2077) s(2091) =< s(2078) s(2092) =< s(2078) s(2085) =< s(2079) s(2086) =< s(2079) s(2088) =< s(2079) s(2093) =< s(2080) s(2083) =< s(2080) s(2088) =< s(2080) s(2094) =< s(2074)+2 s(2095) =< s(2074)+4 s(2096) =< s(2074) s(2097) =< s(2074)+1 s(2098) =< s(2074)+3 s(2099) =< s(2074)*(1/2)+1 s(2100) =< s(2074)*(1/2) s(2085) =< s(2075)*(1/5)+s(2079) s(2086) =< s(2075)*(1/5)+s(2079) s(2087) =< s(2075)*(1/5)+s(2079) s(2088) =< s(2075)*(1/5)+s(2079) s(2083) =< s(2075)*(3/7)+s(2080) s(2084) =< s(2075)*(3/7)+s(2080) s(2085) =< s(2075)*(3/7)+s(2080) s(2086) =< s(2075)*(3/7)+s(2080) s(2087) =< s(2075)*(3/7)+s(2080) s(2088) =< s(2075)*(3/7)+s(2080) s(2084) =< s(2075)*(1/3)+s(2077) s(2085) =< s(2075)*(1/3)+s(2077) s(2086) =< s(2075)*(1/3)+s(2077) s(2087) =< s(2075)*(1/3)+s(2077) s(2088) =< s(2075)*(1/3)+s(2077) s(2090) =< s(2075)*(1/3)+s(2077) s(2093) =< s(2075)*(3/7)+s(2080) s(2091) =< s(2075)*(1/5)+s(2078) s(2081) =< s(2075)*(1/5)+s(2078) s(2092) =< s(2075)*(1/5)+s(2078) s(2089) =< s(2075)*(1/4)+s(2076) s(2092) =< s(2075)*(1/4)+s(2076) s(2081) =< s(2075)*(1/4)+s(2076) s(2101) =< s(2087)*s(2094) s(2102) =< s(2087)*s(2094) s(2103) =< s(2087)*s(2095) s(2104) =< s(2088)*s(2096) s(2105) =< s(2086)*s(2097) s(2106) =< s(2085)*s(2094) s(2107) =< s(2084)*s(2097) s(2108) =< s(2090) s(2109) =< s(2083)*s(2096) s(2110) =< s(2083)*s(2098) s(2111) =< s(2082)*s(2095) s(2112) =< s(2082)*s(2094) s(2113) =< s(2081)*s(2094) s(2114) =< s(2081)*s(2099) s(2115) =< s(2092)*s(2097) s(2116) =< s(2092)*s(2100) s(2117) =< s(2091)*2 s(2118) =< s(2102)*2 s(2119) =< s(2110)*2 s(2120) =< s(2111)*2 s(2121) =< s(2114)*2 s(2122) =< s(2116)*2 s(2123) =< s(2103) s(2124) =< s(2102) s(2125) =< s(2124)*s(2095) s(2126) =< s(2118) s(2127) =< s(2093) s(2128) =< s(2109) s(2129) =< s(2110) s(2130) =< s(2129)*s(2074) s(2131) =< s(2119) s(2132) =< s(2111) s(2133) =< s(2120) s(2134) =< s(2112) s(2135) =< s(2113) s(2136) =< s(2114) s(2137) =< s(2136)*s(2094) s(2138) =< s(2121) s(2139) =< s(2091) s(2140) =< s(2115) s(2141) =< s(2117) s(2142) =< s(2116) s(2143) =< s(2142)*s(2097) s(2144) =< s(2122) with precondition: [V2=2,Out=1,2*V>=3] * Chain [71]: 20*s(2154)+452*s(2155)+18*s(2156)+8*s(2157)+10*s(2158)+2*s(2159)+18*s(2160)+2*s(2161)+2*s(2162)+22*s(2165)+2*s(2174)+2*s(2177)+2*s(2178)+2*s(2179)+2*s(2180)+2*s(2181)+32*s(2196)+120*s(2197)+14*s(2198)+88*s(2199)+6*s(2200)+10*s(2201)+24*s(2202)+4*s(2203)+8*s(2204)+120*s(2205)+88*s(2206)+6*s(2207)+64*s(2208)+120*s(2209)+14*s(2210)+92*s(2211)+8*s(2212)+14*s(2213)+4*s(2214)+24*s(2215)+4*s(2216)+12*s(2217)+1*s(2290)+1 Such that:s(2290) =< 2 aux(150) =< V aux(151) =< 2*V aux(152) =< 2*V+1 aux(153) =< V/2 aux(154) =< 2/3*V aux(155) =< 3/5*V aux(156) =< 4/5*V aux(157) =< 4/7*V s(2154) =< aux(150) s(2155) =< aux(150) s(2156) =< aux(150) s(2157) =< aux(150) s(2158) =< aux(150) s(2159) =< aux(150) s(2160) =< aux(150) s(2161) =< aux(150) s(2162) =< aux(153) s(2163) =< aux(154) s(2157) =< aux(154) s(2159) =< aux(154) s(2161) =< aux(154) s(2164) =< aux(155) s(2165) =< aux(155) s(2158) =< aux(156) s(2159) =< aux(156) s(2161) =< aux(156) s(2166) =< aux(157) s(2156) =< aux(157) s(2161) =< aux(157) s(2167) =< aux(151)+2 s(2168) =< aux(151)+4 s(2169) =< aux(151) s(2170) =< aux(151)+1 s(2171) =< aux(151)+3 s(2172) =< aux(151)*(1/2)+1 s(2173) =< aux(151)*(1/2) s(2158) =< aux(152)*(1/5)+aux(156) s(2159) =< aux(152)*(1/5)+aux(156) s(2160) =< aux(152)*(1/5)+aux(156) s(2161) =< aux(152)*(1/5)+aux(156) s(2156) =< aux(152)*(3/7)+aux(157) s(2157) =< aux(152)*(3/7)+aux(157) s(2158) =< aux(152)*(3/7)+aux(157) s(2159) =< aux(152)*(3/7)+aux(157) s(2160) =< aux(152)*(3/7)+aux(157) s(2161) =< aux(152)*(3/7)+aux(157) s(2157) =< aux(152)*(1/3)+aux(154) s(2158) =< aux(152)*(1/3)+aux(154) s(2159) =< aux(152)*(1/3)+aux(154) s(2160) =< aux(152)*(1/3)+aux(154) s(2161) =< aux(152)*(1/3)+aux(154) s(2163) =< aux(152)*(1/3)+aux(154) s(2166) =< aux(152)*(3/7)+aux(157) s(2164) =< aux(152)*(1/5)+aux(155) s(2154) =< aux(152)*(1/5)+aux(155) s(2165) =< aux(152)*(1/5)+aux(155) s(2162) =< aux(152)*(1/4)+aux(153) s(2165) =< aux(152)*(1/4)+aux(153) s(2154) =< aux(152)*(1/4)+aux(153) s(2174) =< s(2160)*s(2167) s(2175) =< s(2160)*s(2167) s(2176) =< s(2160)*s(2168) s(2177) =< s(2161)*s(2169) s(2178) =< s(2159)*s(2170) s(2179) =< s(2158)*s(2167) s(2180) =< s(2157)*s(2170) s(2181) =< s(2163) s(2182) =< s(2156)*s(2169) s(2183) =< s(2156)*s(2171) s(2184) =< s(2155)*s(2168) s(2185) =< s(2155)*s(2167) s(2186) =< s(2154)*s(2167) s(2187) =< s(2154)*s(2172) s(2188) =< s(2165)*s(2170) s(2189) =< s(2165)*s(2173) s(2190) =< s(2164)*2 s(2191) =< s(2175)*2 s(2192) =< s(2183)*2 s(2193) =< s(2184)*2 s(2194) =< s(2187)*2 s(2195) =< s(2189)*2 s(2196) =< s(2176) s(2197) =< s(2175) s(2198) =< s(2197)*s(2168) s(2199) =< s(2191) s(2200) =< s(2166) s(2201) =< s(2182) s(2202) =< s(2183) s(2203) =< s(2202)*aux(151) s(2204) =< s(2192) s(2205) =< s(2184) s(2206) =< s(2193) s(2207) =< s(2185) s(2208) =< s(2186) s(2209) =< s(2187) s(2210) =< s(2209)*s(2167) s(2211) =< s(2194) s(2212) =< s(2164) s(2213) =< s(2188) s(2214) =< s(2190) s(2215) =< s(2189) s(2216) =< s(2215)*s(2170) s(2217) =< s(2195) with precondition: [V2=2,Out=2,V>=0] #### Cost of chains of fun4(Out): * Chain [78]: 0 with precondition: [Out=0] * Chain [77]: 0 with precondition: [Out=2] #### Cost of chains of fun5(Out): * Chain [80]: 0 with precondition: [Out=0] * Chain [79]: 0 with precondition: [Out=1] #### Cost of chains of fun6(V,Out): * Chain [82]: 10*s(2958)+226*s(2959)+9*s(2960)+4*s(2961)+5*s(2962)+1*s(2963)+9*s(2964)+1*s(2965)+1*s(2966)+11*s(2969)+1*s(2978)+1*s(2981)+1*s(2982)+1*s(2983)+1*s(2984)+1*s(2985)+16*s(3000)+60*s(3001)+7*s(3002)+44*s(3003)+3*s(3004)+5*s(3005)+12*s(3006)+2*s(3007)+4*s(3008)+60*s(3009)+44*s(3010)+3*s(3011)+32*s(3012)+60*s(3013)+7*s(3014)+46*s(3015)+4*s(3016)+7*s(3017)+2*s(3018)+12*s(3019)+2*s(3020)+6*s(3021)+1 Such that:s(2950) =< V s(2951) =< 2*V s(2952) =< 2*V+1 s(2953) =< V/2 s(2954) =< 2/3*V s(2955) =< 3/5*V s(2956) =< 4/5*V s(2957) =< 4/7*V s(2958) =< s(2950) s(2959) =< s(2950) s(2960) =< s(2950) s(2961) =< s(2950) s(2962) =< s(2950) s(2963) =< s(2950) s(2964) =< s(2950) s(2965) =< s(2950) s(2966) =< s(2953) s(2967) =< s(2954) s(2961) =< s(2954) s(2963) =< s(2954) s(2965) =< s(2954) s(2968) =< s(2955) s(2969) =< s(2955) s(2962) =< s(2956) s(2963) =< s(2956) s(2965) =< s(2956) s(2970) =< s(2957) s(2960) =< s(2957) s(2965) =< s(2957) s(2971) =< s(2951)+2 s(2972) =< s(2951)+4 s(2973) =< s(2951) s(2974) =< s(2951)+1 s(2975) =< s(2951)+3 s(2976) =< s(2951)*(1/2)+1 s(2977) =< s(2951)*(1/2) s(2962) =< s(2952)*(1/5)+s(2956) s(2963) =< s(2952)*(1/5)+s(2956) s(2964) =< s(2952)*(1/5)+s(2956) s(2965) =< s(2952)*(1/5)+s(2956) s(2960) =< s(2952)*(3/7)+s(2957) s(2961) =< s(2952)*(3/7)+s(2957) s(2962) =< s(2952)*(3/7)+s(2957) s(2963) =< s(2952)*(3/7)+s(2957) s(2964) =< s(2952)*(3/7)+s(2957) s(2965) =< s(2952)*(3/7)+s(2957) s(2961) =< s(2952)*(1/3)+s(2954) s(2962) =< s(2952)*(1/3)+s(2954) s(2963) =< s(2952)*(1/3)+s(2954) s(2964) =< s(2952)*(1/3)+s(2954) s(2965) =< s(2952)*(1/3)+s(2954) s(2967) =< s(2952)*(1/3)+s(2954) s(2970) =< s(2952)*(3/7)+s(2957) s(2968) =< s(2952)*(1/5)+s(2955) s(2958) =< s(2952)*(1/5)+s(2955) s(2969) =< s(2952)*(1/5)+s(2955) s(2966) =< s(2952)*(1/4)+s(2953) s(2969) =< s(2952)*(1/4)+s(2953) s(2958) =< s(2952)*(1/4)+s(2953) s(2978) =< s(2964)*s(2971) s(2979) =< s(2964)*s(2971) s(2980) =< s(2964)*s(2972) s(2981) =< s(2965)*s(2973) s(2982) =< s(2963)*s(2974) s(2983) =< s(2962)*s(2971) s(2984) =< s(2961)*s(2974) s(2985) =< s(2967) s(2986) =< s(2960)*s(2973) s(2987) =< s(2960)*s(2975) s(2988) =< s(2959)*s(2972) s(2989) =< s(2959)*s(2971) s(2990) =< s(2958)*s(2971) s(2991) =< s(2958)*s(2976) s(2992) =< s(2969)*s(2974) s(2993) =< s(2969)*s(2977) s(2994) =< s(2968)*2 s(2995) =< s(2979)*2 s(2996) =< s(2987)*2 s(2997) =< s(2988)*2 s(2998) =< s(2991)*2 s(2999) =< s(2993)*2 s(3000) =< s(2980) s(3001) =< s(2979) s(3002) =< s(3001)*s(2972) s(3003) =< s(2995) s(3004) =< s(2970) s(3005) =< s(2986) s(3006) =< s(2987) s(3007) =< s(3006)*s(2951) s(3008) =< s(2996) s(3009) =< s(2988) s(3010) =< s(2997) s(3011) =< s(2989) s(3012) =< s(2990) s(3013) =< s(2991) s(3014) =< s(3013)*s(2971) s(3015) =< s(2998) s(3016) =< s(2968) s(3017) =< s(2992) s(3018) =< s(2994) s(3019) =< s(2993) s(3020) =< s(3019)*s(2974) s(3021) =< s(2999) with precondition: [Out=0,V>=0] * Chain [81]: 10*s(3030)+226*s(3031)+9*s(3032)+4*s(3033)+5*s(3034)+1*s(3035)+9*s(3036)+1*s(3037)+1*s(3038)+11*s(3041)+1*s(3050)+1*s(3053)+1*s(3054)+1*s(3055)+1*s(3056)+1*s(3057)+16*s(3072)+60*s(3073)+7*s(3074)+44*s(3075)+3*s(3076)+5*s(3077)+12*s(3078)+2*s(3079)+4*s(3080)+60*s(3081)+44*s(3082)+3*s(3083)+32*s(3084)+60*s(3085)+7*s(3086)+46*s(3087)+4*s(3088)+7*s(3089)+2*s(3090)+12*s(3091)+2*s(3092)+6*s(3093)+1*s(3094)+1*s(3095)+1 Such that:s(3095) =< 2 s(3022) =< V aux(184) =< 2*V s(3024) =< 2*V+1 s(3025) =< V/2 s(3026) =< 2/3*V s(3027) =< 3/5*V s(3028) =< 4/5*V s(3029) =< 4/7*V s(3094) =< aux(184) s(3030) =< s(3022) s(3031) =< s(3022) s(3032) =< s(3022) s(3033) =< s(3022) s(3034) =< s(3022) s(3035) =< s(3022) s(3036) =< s(3022) s(3037) =< s(3022) s(3038) =< s(3025) s(3039) =< s(3026) s(3033) =< s(3026) s(3035) =< s(3026) s(3037) =< s(3026) s(3040) =< s(3027) s(3041) =< s(3027) s(3034) =< s(3028) s(3035) =< s(3028) s(3037) =< s(3028) s(3042) =< s(3029) s(3032) =< s(3029) s(3037) =< s(3029) s(3043) =< aux(184)+2 s(3044) =< aux(184)+4 s(3045) =< aux(184) s(3046) =< aux(184)+1 s(3047) =< aux(184)+3 s(3048) =< aux(184)*(1/2)+1 s(3049) =< aux(184)*(1/2) s(3034) =< s(3024)*(1/5)+s(3028) s(3035) =< s(3024)*(1/5)+s(3028) s(3036) =< s(3024)*(1/5)+s(3028) s(3037) =< s(3024)*(1/5)+s(3028) s(3032) =< s(3024)*(3/7)+s(3029) s(3033) =< s(3024)*(3/7)+s(3029) s(3034) =< s(3024)*(3/7)+s(3029) s(3035) =< s(3024)*(3/7)+s(3029) s(3036) =< s(3024)*(3/7)+s(3029) s(3037) =< s(3024)*(3/7)+s(3029) s(3033) =< s(3024)*(1/3)+s(3026) s(3034) =< s(3024)*(1/3)+s(3026) s(3035) =< s(3024)*(1/3)+s(3026) s(3036) =< s(3024)*(1/3)+s(3026) s(3037) =< s(3024)*(1/3)+s(3026) s(3039) =< s(3024)*(1/3)+s(3026) s(3042) =< s(3024)*(3/7)+s(3029) s(3040) =< s(3024)*(1/5)+s(3027) s(3030) =< s(3024)*(1/5)+s(3027) s(3041) =< s(3024)*(1/5)+s(3027) s(3038) =< s(3024)*(1/4)+s(3025) s(3041) =< s(3024)*(1/4)+s(3025) s(3030) =< s(3024)*(1/4)+s(3025) s(3050) =< s(3036)*s(3043) s(3051) =< s(3036)*s(3043) s(3052) =< s(3036)*s(3044) s(3053) =< s(3037)*s(3045) s(3054) =< s(3035)*s(3046) s(3055) =< s(3034)*s(3043) s(3056) =< s(3033)*s(3046) s(3057) =< s(3039) s(3058) =< s(3032)*s(3045) s(3059) =< s(3032)*s(3047) s(3060) =< s(3031)*s(3044) s(3061) =< s(3031)*s(3043) s(3062) =< s(3030)*s(3043) s(3063) =< s(3030)*s(3048) s(3064) =< s(3041)*s(3046) s(3065) =< s(3041)*s(3049) s(3066) =< s(3040)*2 s(3067) =< s(3051)*2 s(3068) =< s(3059)*2 s(3069) =< s(3060)*2 s(3070) =< s(3063)*2 s(3071) =< s(3065)*2 s(3072) =< s(3052) s(3073) =< s(3051) s(3074) =< s(3073)*s(3044) s(3075) =< s(3067) s(3076) =< s(3042) s(3077) =< s(3058) s(3078) =< s(3059) s(3079) =< s(3078)*aux(184) s(3080) =< s(3068) s(3081) =< s(3060) s(3082) =< s(3069) s(3083) =< s(3061) s(3084) =< s(3062) s(3085) =< s(3063) s(3086) =< s(3085)*s(3043) s(3087) =< s(3070) s(3088) =< s(3040) s(3089) =< s(3064) s(3090) =< s(3066) s(3091) =< s(3065) s(3092) =< s(3091)*s(3046) s(3093) =< s(3071) with precondition: [V>=1,Out>=1,2*V>=Out] #### Cost of chains of fun7(V,Out): * Chain [83]: 10*s(3104)+226*s(3105)+9*s(3106)+4*s(3107)+5*s(3108)+1*s(3109)+9*s(3110)+1*s(3111)+1*s(3112)+11*s(3115)+1*s(3124)+1*s(3127)+1*s(3128)+1*s(3129)+1*s(3130)+1*s(3131)+16*s(3146)+60*s(3147)+7*s(3148)+44*s(3149)+3*s(3150)+5*s(3151)+12*s(3152)+2*s(3153)+4*s(3154)+60*s(3155)+44*s(3156)+3*s(3157)+32*s(3158)+60*s(3159)+7*s(3160)+46*s(3161)+4*s(3162)+7*s(3163)+2*s(3164)+12*s(3165)+2*s(3166)+6*s(3167)+162*s(3173)+60*s(3174)+44*s(3176)+60*s(3183)+44*s(3185)+9 Such that:s(3178) =< 2 s(3179) =< 4 s(3096) =< V aux(185) =< 2*V s(3098) =< 2*V+1 s(3170) =< 4*V s(3099) =< V/2 s(3100) =< 2/3*V s(3101) =< 3/5*V s(3102) =< 4/5*V s(3103) =< 4/7*V aux(187) =< 1 s(3173) =< aux(187) s(3174) =< aux(185) s(3176) =< s(3170) s(3104) =< s(3096) s(3105) =< s(3096) s(3106) =< s(3096) s(3107) =< s(3096) s(3108) =< s(3096) s(3109) =< s(3096) s(3110) =< s(3096) s(3111) =< s(3096) s(3112) =< s(3099) s(3113) =< s(3100) s(3107) =< s(3100) s(3109) =< s(3100) s(3111) =< s(3100) s(3114) =< s(3101) s(3115) =< s(3101) s(3108) =< s(3102) s(3109) =< s(3102) s(3111) =< s(3102) s(3116) =< s(3103) s(3106) =< s(3103) s(3111) =< s(3103) s(3117) =< aux(185)+2 s(3118) =< aux(185)+4 s(3119) =< aux(185) s(3120) =< aux(185)+1 s(3121) =< aux(185)+3 s(3122) =< aux(185)*(1/2)+1 s(3123) =< aux(185)*(1/2) s(3108) =< s(3098)*(1/5)+s(3102) s(3109) =< s(3098)*(1/5)+s(3102) s(3110) =< s(3098)*(1/5)+s(3102) s(3111) =< s(3098)*(1/5)+s(3102) s(3106) =< s(3098)*(3/7)+s(3103) s(3107) =< s(3098)*(3/7)+s(3103) s(3108) =< s(3098)*(3/7)+s(3103) s(3109) =< s(3098)*(3/7)+s(3103) s(3110) =< s(3098)*(3/7)+s(3103) s(3111) =< s(3098)*(3/7)+s(3103) s(3107) =< s(3098)*(1/3)+s(3100) s(3108) =< s(3098)*(1/3)+s(3100) s(3109) =< s(3098)*(1/3)+s(3100) s(3110) =< s(3098)*(1/3)+s(3100) s(3111) =< s(3098)*(1/3)+s(3100) s(3113) =< s(3098)*(1/3)+s(3100) s(3116) =< s(3098)*(3/7)+s(3103) s(3114) =< s(3098)*(1/5)+s(3101) s(3104) =< s(3098)*(1/5)+s(3101) s(3115) =< s(3098)*(1/5)+s(3101) s(3112) =< s(3098)*(1/4)+s(3099) s(3115) =< s(3098)*(1/4)+s(3099) s(3104) =< s(3098)*(1/4)+s(3099) s(3124) =< s(3110)*s(3117) s(3125) =< s(3110)*s(3117) s(3126) =< s(3110)*s(3118) s(3127) =< s(3111)*s(3119) s(3128) =< s(3109)*s(3120) s(3129) =< s(3108)*s(3117) s(3130) =< s(3107)*s(3120) s(3131) =< s(3113) s(3132) =< s(3106)*s(3119) s(3133) =< s(3106)*s(3121) s(3134) =< s(3105)*s(3118) s(3135) =< s(3105)*s(3117) s(3136) =< s(3104)*s(3117) s(3137) =< s(3104)*s(3122) s(3138) =< s(3115)*s(3120) s(3139) =< s(3115)*s(3123) s(3140) =< s(3114)*2 s(3141) =< s(3125)*2 s(3142) =< s(3133)*2 s(3143) =< s(3134)*2 s(3144) =< s(3137)*2 s(3145) =< s(3139)*2 s(3146) =< s(3126) s(3147) =< s(3125) s(3148) =< s(3147)*s(3118) s(3149) =< s(3141) s(3150) =< s(3116) s(3151) =< s(3132) s(3152) =< s(3133) s(3153) =< s(3152)*aux(185) s(3154) =< s(3142) s(3155) =< s(3134) s(3156) =< s(3143) s(3157) =< s(3135) s(3158) =< s(3136) s(3159) =< s(3137) s(3160) =< s(3159)*s(3117) s(3161) =< s(3144) s(3162) =< s(3114) s(3163) =< s(3138) s(3164) =< s(3140) s(3165) =< s(3139) s(3166) =< s(3165)*s(3120) s(3167) =< s(3145) s(3183) =< s(3178) s(3185) =< s(3179) with precondition: [Out=0,V>=0] #### Cost of chains of fun8(V,V2,Out): * Chain [86]: 30*s(3203)+678*s(3204)+27*s(3205)+12*s(3206)+15*s(3207)+3*s(3208)+27*s(3209)+3*s(3210)+3*s(3211)+33*s(3214)+3*s(3223)+3*s(3226)+3*s(3227)+3*s(3228)+3*s(3229)+3*s(3230)+48*s(3245)+180*s(3246)+21*s(3247)+132*s(3248)+9*s(3249)+15*s(3250)+36*s(3251)+6*s(3252)+12*s(3253)+180*s(3254)+132*s(3255)+9*s(3256)+96*s(3257)+180*s(3258)+21*s(3259)+138*s(3260)+12*s(3261)+21*s(3262)+6*s(3263)+36*s(3264)+6*s(3265)+18*s(3266)+50*s(3275)+1130*s(3276)+45*s(3277)+20*s(3278)+25*s(3279)+5*s(3280)+45*s(3281)+5*s(3282)+5*s(3283)+55*s(3286)+5*s(3295)+5*s(3298)+5*s(3299)+5*s(3300)+5*s(3301)+5*s(3302)+80*s(3317)+300*s(3318)+35*s(3319)+220*s(3320)+15*s(3321)+25*s(3322)+60*s(3323)+10*s(3324)+20*s(3325)+300*s(3326)+220*s(3327)+15*s(3328)+160*s(3329)+300*s(3330)+35*s(3331)+230*s(3332)+20*s(3333)+35*s(3334)+10*s(3335)+60*s(3336)+10*s(3337)+30*s(3338)+13*s(3339)+64*s(3484)+12*s(3636)+2*s(3637)+4*s(3638)+105*s(3717)+2*s(3718)+52*s(3719)+9*s(3727)+9 Such that:s(3632) =< 4*V aux(196) =< 1 aux(197) =< 2 aux(198) =< 4 aux(199) =< V aux(200) =< 2*V aux(201) =< 2*V+1 aux(202) =< V/2 aux(203) =< 2/3*V aux(204) =< 3/5*V aux(205) =< 4/5*V aux(206) =< 4/7*V aux(207) =< V2 aux(208) =< 2*V2 aux(209) =< 2*V2+1 aux(210) =< V2/2 aux(211) =< 2/3*V2 aux(212) =< 3/5*V2 aux(213) =< 4/5*V2 aux(214) =< 4/7*V2 s(3484) =< aux(196) s(3339) =< aux(208) s(3275) =< aux(207) s(3276) =< aux(207) s(3277) =< aux(207) s(3278) =< aux(207) s(3279) =< aux(207) s(3280) =< aux(207) s(3281) =< aux(207) s(3282) =< aux(207) s(3283) =< aux(210) s(3284) =< aux(211) s(3278) =< aux(211) s(3280) =< aux(211) s(3282) =< aux(211) s(3285) =< aux(212) s(3286) =< aux(212) s(3279) =< aux(213) s(3280) =< aux(213) s(3282) =< aux(213) s(3287) =< aux(214) s(3277) =< aux(214) s(3282) =< aux(214) s(3288) =< aux(208)+2 s(3289) =< aux(208)+4 s(3290) =< aux(208) s(3291) =< aux(208)+1 s(3292) =< aux(208)+3 s(3293) =< aux(208)*(1/2)+1 s(3294) =< aux(208)*(1/2) s(3279) =< aux(209)*(1/5)+aux(213) s(3280) =< aux(209)*(1/5)+aux(213) s(3281) =< aux(209)*(1/5)+aux(213) s(3282) =< aux(209)*(1/5)+aux(213) s(3277) =< aux(209)*(3/7)+aux(214) s(3278) =< aux(209)*(3/7)+aux(214) s(3279) =< aux(209)*(3/7)+aux(214) s(3280) =< aux(209)*(3/7)+aux(214) s(3281) =< aux(209)*(3/7)+aux(214) s(3282) =< aux(209)*(3/7)+aux(214) s(3278) =< aux(209)*(1/3)+aux(211) s(3279) =< aux(209)*(1/3)+aux(211) s(3280) =< aux(209)*(1/3)+aux(211) s(3281) =< aux(209)*(1/3)+aux(211) s(3282) =< aux(209)*(1/3)+aux(211) s(3284) =< aux(209)*(1/3)+aux(211) s(3287) =< aux(209)*(3/7)+aux(214) s(3285) =< aux(209)*(1/5)+aux(212) s(3275) =< aux(209)*(1/5)+aux(212) s(3286) =< aux(209)*(1/5)+aux(212) s(3283) =< aux(209)*(1/4)+aux(210) s(3286) =< aux(209)*(1/4)+aux(210) s(3275) =< aux(209)*(1/4)+aux(210) s(3295) =< s(3281)*s(3288) s(3296) =< s(3281)*s(3288) s(3297) =< s(3281)*s(3289) s(3298) =< s(3282)*s(3290) s(3299) =< s(3280)*s(3291) s(3300) =< s(3279)*s(3288) s(3301) =< s(3278)*s(3291) s(3302) =< s(3284) s(3303) =< s(3277)*s(3290) s(3304) =< s(3277)*s(3292) s(3305) =< s(3276)*s(3289) s(3306) =< s(3276)*s(3288) s(3307) =< s(3275)*s(3288) s(3308) =< s(3275)*s(3293) s(3309) =< s(3286)*s(3291) s(3310) =< s(3286)*s(3294) s(3311) =< s(3285)*2 s(3312) =< s(3296)*2 s(3313) =< s(3304)*2 s(3314) =< s(3305)*2 s(3315) =< s(3308)*2 s(3316) =< s(3310)*2 s(3317) =< s(3297) s(3318) =< s(3296) s(3319) =< s(3318)*s(3289) s(3320) =< s(3312) s(3321) =< s(3287) s(3322) =< s(3303) s(3323) =< s(3304) s(3324) =< s(3323)*aux(208) s(3325) =< s(3313) s(3326) =< s(3305) s(3327) =< s(3314) s(3328) =< s(3306) s(3329) =< s(3307) s(3330) =< s(3308) s(3331) =< s(3330)*s(3288) s(3332) =< s(3315) s(3333) =< s(3285) s(3334) =< s(3309) s(3335) =< s(3311) s(3336) =< s(3310) s(3337) =< s(3336)*s(3291) s(3338) =< s(3316) s(3203) =< aux(199) s(3204) =< aux(199) s(3205) =< aux(199) s(3206) =< aux(199) s(3207) =< aux(199) s(3208) =< aux(199) s(3209) =< aux(199) s(3210) =< aux(199) s(3211) =< aux(202) s(3212) =< aux(203) s(3206) =< aux(203) s(3208) =< aux(203) s(3210) =< aux(203) s(3213) =< aux(204) s(3214) =< aux(204) s(3207) =< aux(205) s(3208) =< aux(205) s(3210) =< aux(205) s(3215) =< aux(206) s(3205) =< aux(206) s(3210) =< aux(206) s(3216) =< aux(200)+2 s(3217) =< aux(200)+4 s(3218) =< aux(200) s(3219) =< aux(200)+1 s(3220) =< aux(200)+3 s(3221) =< aux(200)*(1/2)+1 s(3222) =< aux(200)*(1/2) s(3207) =< aux(201)*(1/5)+aux(205) s(3208) =< aux(201)*(1/5)+aux(205) s(3209) =< aux(201)*(1/5)+aux(205) s(3210) =< aux(201)*(1/5)+aux(205) s(3205) =< aux(201)*(3/7)+aux(206) s(3206) =< aux(201)*(3/7)+aux(206) s(3207) =< aux(201)*(3/7)+aux(206) s(3208) =< aux(201)*(3/7)+aux(206) s(3209) =< aux(201)*(3/7)+aux(206) s(3210) =< aux(201)*(3/7)+aux(206) s(3206) =< aux(201)*(1/3)+aux(203) s(3207) =< aux(201)*(1/3)+aux(203) s(3208) =< aux(201)*(1/3)+aux(203) s(3209) =< aux(201)*(1/3)+aux(203) s(3210) =< aux(201)*(1/3)+aux(203) s(3212) =< aux(201)*(1/3)+aux(203) s(3215) =< aux(201)*(3/7)+aux(206) s(3213) =< aux(201)*(1/5)+aux(204) s(3203) =< aux(201)*(1/5)+aux(204) s(3214) =< aux(201)*(1/5)+aux(204) s(3211) =< aux(201)*(1/4)+aux(202) s(3214) =< aux(201)*(1/4)+aux(202) s(3203) =< aux(201)*(1/4)+aux(202) s(3223) =< s(3209)*s(3216) s(3224) =< s(3209)*s(3216) s(3225) =< s(3209)*s(3217) s(3226) =< s(3210)*s(3218) s(3227) =< s(3208)*s(3219) s(3228) =< s(3207)*s(3216) s(3229) =< s(3206)*s(3219) s(3230) =< s(3212) s(3231) =< s(3205)*s(3218) s(3232) =< s(3205)*s(3220) s(3233) =< s(3204)*s(3217) s(3234) =< s(3204)*s(3216) s(3235) =< s(3203)*s(3216) s(3236) =< s(3203)*s(3221) s(3237) =< s(3214)*s(3219) s(3238) =< s(3214)*s(3222) s(3239) =< s(3213)*2 s(3240) =< s(3224)*2 s(3241) =< s(3232)*2 s(3242) =< s(3233)*2 s(3243) =< s(3236)*2 s(3244) =< s(3238)*2 s(3245) =< s(3225) s(3246) =< s(3224) s(3247) =< s(3246)*s(3217) s(3248) =< s(3240) s(3249) =< s(3215) s(3250) =< s(3231) s(3251) =< s(3232) s(3252) =< s(3251)*aux(200) s(3253) =< s(3241) s(3254) =< s(3233) s(3255) =< s(3242) s(3256) =< s(3234) s(3257) =< s(3235) s(3258) =< s(3236) s(3259) =< s(3258)*s(3216) s(3260) =< s(3243) s(3261) =< s(3213) s(3262) =< s(3237) s(3263) =< s(3239) s(3264) =< s(3238) s(3265) =< s(3264)*s(3219) s(3266) =< s(3244) s(3636) =< aux(200) s(3637) =< s(3636)*aux(208) s(3638) =< s(3632) s(3717) =< aux(197) s(3718) =< s(3717)*aux(208) s(3719) =< aux(198) s(3727) =< s(3717)*aux(197) with precondition: [V>=0,V2>=1,Out>=0,2*V2>=Out+1] * Chain [85]: 20*s(3819)+452*s(3820)+18*s(3821)+8*s(3822)+10*s(3823)+2*s(3824)+18*s(3825)+2*s(3826)+2*s(3827)+22*s(3830)+2*s(3839)+2*s(3842)+2*s(3843)+2*s(3844)+2*s(3845)+2*s(3846)+32*s(3861)+120*s(3862)+14*s(3863)+88*s(3864)+6*s(3865)+10*s(3866)+24*s(3867)+4*s(3868)+8*s(3869)+120*s(3870)+88*s(3871)+6*s(3872)+64*s(3873)+120*s(3874)+14*s(3875)+92*s(3876)+8*s(3877)+14*s(3878)+4*s(3879)+24*s(3880)+4*s(3881)+12*s(3882)+30*s(3891)+678*s(3892)+27*s(3893)+12*s(3894)+15*s(3895)+3*s(3896)+27*s(3897)+3*s(3898)+3*s(3899)+33*s(3902)+3*s(3911)+3*s(3914)+3*s(3915)+3*s(3916)+3*s(3917)+3*s(3918)+48*s(3933)+180*s(3934)+21*s(3935)+132*s(3936)+9*s(3937)+15*s(3938)+36*s(3939)+6*s(3940)+12*s(3941)+180*s(3942)+132*s(3943)+9*s(3944)+96*s(3945)+180*s(3946)+21*s(3947)+138*s(3948)+12*s(3949)+21*s(3950)+6*s(3951)+36*s(3952)+6*s(3953)+18*s(3954)+48*s(3959)+324*s(3960)+120*s(3961)+7*s(3962)+88*s(3963)+120*s(4123)+7*s(4124)+88*s(4125)+8 Such that:aux(222) =< 1 aux(223) =< 2 aux(224) =< 4 aux(225) =< V aux(226) =< 2*V aux(227) =< 2*V+1 aux(228) =< 4*V aux(229) =< V/2 aux(230) =< 2/3*V aux(231) =< 3/5*V aux(232) =< 4/5*V aux(233) =< 4/7*V aux(234) =< V2 aux(235) =< 2*V2 aux(236) =< 2*V2+1 aux(237) =< V2/2 aux(238) =< 2/3*V2 aux(239) =< 3/5*V2 aux(240) =< 4/5*V2 aux(241) =< 4/7*V2 s(3959) =< aux(235) s(3960) =< aux(222) s(3961) =< aux(226) s(3962) =< s(3961)*aux(235) s(3963) =< aux(228) s(3891) =< aux(234) s(3892) =< aux(234) s(3893) =< aux(234) s(3894) =< aux(234) s(3895) =< aux(234) s(3896) =< aux(234) s(3897) =< aux(234) s(3898) =< aux(234) s(3899) =< aux(237) s(3900) =< aux(238) s(3894) =< aux(238) s(3896) =< aux(238) s(3898) =< aux(238) s(3901) =< aux(239) s(3902) =< aux(239) s(3895) =< aux(240) s(3896) =< aux(240) s(3898) =< aux(240) s(3903) =< aux(241) s(3893) =< aux(241) s(3898) =< aux(241) s(3904) =< aux(235)+2 s(3905) =< aux(235)+4 s(3906) =< aux(235) s(3907) =< aux(235)+1 s(3908) =< aux(235)+3 s(3909) =< aux(235)*(1/2)+1 s(3910) =< aux(235)*(1/2) s(3895) =< aux(236)*(1/5)+aux(240) s(3896) =< aux(236)*(1/5)+aux(240) s(3897) =< aux(236)*(1/5)+aux(240) s(3898) =< aux(236)*(1/5)+aux(240) s(3893) =< aux(236)*(3/7)+aux(241) s(3894) =< aux(236)*(3/7)+aux(241) s(3895) =< aux(236)*(3/7)+aux(241) s(3896) =< aux(236)*(3/7)+aux(241) s(3897) =< aux(236)*(3/7)+aux(241) s(3898) =< aux(236)*(3/7)+aux(241) s(3894) =< aux(236)*(1/3)+aux(238) s(3895) =< aux(236)*(1/3)+aux(238) s(3896) =< aux(236)*(1/3)+aux(238) s(3897) =< aux(236)*(1/3)+aux(238) s(3898) =< aux(236)*(1/3)+aux(238) s(3900) =< aux(236)*(1/3)+aux(238) s(3903) =< aux(236)*(3/7)+aux(241) s(3901) =< aux(236)*(1/5)+aux(239) s(3891) =< aux(236)*(1/5)+aux(239) s(3902) =< aux(236)*(1/5)+aux(239) s(3899) =< aux(236)*(1/4)+aux(237) s(3902) =< aux(236)*(1/4)+aux(237) s(3891) =< aux(236)*(1/4)+aux(237) s(3911) =< s(3897)*s(3904) s(3912) =< s(3897)*s(3904) s(3913) =< s(3897)*s(3905) s(3914) =< s(3898)*s(3906) s(3915) =< s(3896)*s(3907) s(3916) =< s(3895)*s(3904) s(3917) =< s(3894)*s(3907) s(3918) =< s(3900) s(3919) =< s(3893)*s(3906) s(3920) =< s(3893)*s(3908) s(3921) =< s(3892)*s(3905) s(3922) =< s(3892)*s(3904) s(3923) =< s(3891)*s(3904) s(3924) =< s(3891)*s(3909) s(3925) =< s(3902)*s(3907) s(3926) =< s(3902)*s(3910) s(3927) =< s(3901)*2 s(3928) =< s(3912)*2 s(3929) =< s(3920)*2 s(3930) =< s(3921)*2 s(3931) =< s(3924)*2 s(3932) =< s(3926)*2 s(3933) =< s(3913) s(3934) =< s(3912) s(3935) =< s(3934)*s(3905) s(3936) =< s(3928) s(3937) =< s(3903) s(3938) =< s(3919) s(3939) =< s(3920) s(3940) =< s(3939)*aux(235) s(3941) =< s(3929) s(3942) =< s(3921) s(3943) =< s(3930) s(3944) =< s(3922) s(3945) =< s(3923) s(3946) =< s(3924) s(3947) =< s(3946)*s(3904) s(3948) =< s(3931) s(3949) =< s(3901) s(3950) =< s(3925) s(3951) =< s(3927) s(3952) =< s(3926) s(3953) =< s(3952)*s(3907) s(3954) =< s(3932) s(3819) =< aux(225) s(3820) =< aux(225) s(3821) =< aux(225) s(3822) =< aux(225) s(3823) =< aux(225) s(3824) =< aux(225) s(3825) =< aux(225) s(3826) =< aux(225) s(3827) =< aux(229) s(3828) =< aux(230) s(3822) =< aux(230) s(3824) =< aux(230) s(3826) =< aux(230) s(3829) =< aux(231) s(3830) =< aux(231) s(3823) =< aux(232) s(3824) =< aux(232) s(3826) =< aux(232) s(3831) =< aux(233) s(3821) =< aux(233) s(3826) =< aux(233) s(3832) =< aux(226)+2 s(3833) =< aux(226)+4 s(3834) =< aux(226) s(3835) =< aux(226)+1 s(3836) =< aux(226)+3 s(3837) =< aux(226)*(1/2)+1 s(3838) =< aux(226)*(1/2) s(3823) =< aux(227)*(1/5)+aux(232) s(3824) =< aux(227)*(1/5)+aux(232) s(3825) =< aux(227)*(1/5)+aux(232) s(3826) =< aux(227)*(1/5)+aux(232) s(3821) =< aux(227)*(3/7)+aux(233) s(3822) =< aux(227)*(3/7)+aux(233) s(3823) =< aux(227)*(3/7)+aux(233) s(3824) =< aux(227)*(3/7)+aux(233) s(3825) =< aux(227)*(3/7)+aux(233) s(3826) =< aux(227)*(3/7)+aux(233) s(3822) =< aux(227)*(1/3)+aux(230) s(3823) =< aux(227)*(1/3)+aux(230) s(3824) =< aux(227)*(1/3)+aux(230) s(3825) =< aux(227)*(1/3)+aux(230) s(3826) =< aux(227)*(1/3)+aux(230) s(3828) =< aux(227)*(1/3)+aux(230) s(3831) =< aux(227)*(3/7)+aux(233) s(3829) =< aux(227)*(1/5)+aux(231) s(3819) =< aux(227)*(1/5)+aux(231) s(3830) =< aux(227)*(1/5)+aux(231) s(3827) =< aux(227)*(1/4)+aux(229) s(3830) =< aux(227)*(1/4)+aux(229) s(3819) =< aux(227)*(1/4)+aux(229) s(3839) =< s(3825)*s(3832) s(3840) =< s(3825)*s(3832) s(3841) =< s(3825)*s(3833) s(3842) =< s(3826)*s(3834) s(3843) =< s(3824)*s(3835) s(3844) =< s(3823)*s(3832) s(3845) =< s(3822)*s(3835) s(3846) =< s(3828) s(3847) =< s(3821)*s(3834) s(3848) =< s(3821)*s(3836) s(3849) =< s(3820)*s(3833) s(3850) =< s(3820)*s(3832) s(3851) =< s(3819)*s(3832) s(3852) =< s(3819)*s(3837) s(3853) =< s(3830)*s(3835) s(3854) =< s(3830)*s(3838) s(3855) =< s(3829)*2 s(3856) =< s(3840)*2 s(3857) =< s(3848)*2 s(3858) =< s(3849)*2 s(3859) =< s(3852)*2 s(3860) =< s(3854)*2 s(3861) =< s(3841) s(3862) =< s(3840) s(3863) =< s(3862)*s(3833) s(3864) =< s(3856) s(3865) =< s(3831) s(3866) =< s(3847) s(3867) =< s(3848) s(3868) =< s(3867)*aux(226) s(3869) =< s(3857) s(3870) =< s(3849) s(3871) =< s(3858) s(3872) =< s(3850) s(3873) =< s(3851) s(3874) =< s(3852) s(3875) =< s(3874)*s(3832) s(3876) =< s(3859) s(3877) =< s(3829) s(3878) =< s(3853) s(3879) =< s(3855) s(3880) =< s(3854) s(3881) =< s(3880)*s(3835) s(3882) =< s(3860) s(4123) =< aux(223) s(4124) =< s(4123)*aux(235) s(4125) =< aux(224) with precondition: [Out=0,V>=0,V2>=0] * Chain [84]: 40*s(4233)+904*s(4234)+36*s(4235)+16*s(4236)+20*s(4237)+4*s(4238)+36*s(4239)+4*s(4240)+4*s(4241)+44*s(4244)+4*s(4253)+4*s(4256)+4*s(4257)+4*s(4258)+4*s(4259)+4*s(4260)+64*s(4275)+240*s(4276)+28*s(4277)+176*s(4278)+12*s(4279)+20*s(4280)+48*s(4281)+8*s(4282)+16*s(4283)+240*s(4284)+176*s(4285)+12*s(4286)+128*s(4287)+240*s(4288)+28*s(4289)+184*s(4290)+16*s(4291)+28*s(4292)+8*s(4293)+48*s(4294)+8*s(4295)+24*s(4296)+40*s(4297)+112*s(4375)+72*s(4376)+9*s(4377)+48*s(4378)+9 Such that:aux(245) =< 1 aux(246) =< 2 aux(247) =< V aux(248) =< 2*V aux(249) =< 2*V+1 aux(250) =< 4*V aux(251) =< V/2 aux(252) =< 2/3*V aux(253) =< 3/5*V aux(254) =< 4/5*V aux(255) =< 4/7*V s(4375) =< aux(245) s(4297) =< aux(246) s(4376) =< aux(248) s(4377) =< s(4376)*aux(246) s(4378) =< aux(250) s(4233) =< aux(247) s(4234) =< aux(247) s(4235) =< aux(247) s(4236) =< aux(247) s(4237) =< aux(247) s(4238) =< aux(247) s(4239) =< aux(247) s(4240) =< aux(247) s(4241) =< aux(251) s(4242) =< aux(252) s(4236) =< aux(252) s(4238) =< aux(252) s(4240) =< aux(252) s(4243) =< aux(253) s(4244) =< aux(253) s(4237) =< aux(254) s(4238) =< aux(254) s(4240) =< aux(254) s(4245) =< aux(255) s(4235) =< aux(255) s(4240) =< aux(255) s(4246) =< aux(248)+2 s(4247) =< aux(248)+4 s(4248) =< aux(248) s(4249) =< aux(248)+1 s(4250) =< aux(248)+3 s(4251) =< aux(248)*(1/2)+1 s(4252) =< aux(248)*(1/2) s(4237) =< aux(249)*(1/5)+aux(254) s(4238) =< aux(249)*(1/5)+aux(254) s(4239) =< aux(249)*(1/5)+aux(254) s(4240) =< aux(249)*(1/5)+aux(254) s(4235) =< aux(249)*(3/7)+aux(255) s(4236) =< aux(249)*(3/7)+aux(255) s(4237) =< aux(249)*(3/7)+aux(255) s(4238) =< aux(249)*(3/7)+aux(255) s(4239) =< aux(249)*(3/7)+aux(255) s(4240) =< aux(249)*(3/7)+aux(255) s(4236) =< aux(249)*(1/3)+aux(252) s(4237) =< aux(249)*(1/3)+aux(252) s(4238) =< aux(249)*(1/3)+aux(252) s(4239) =< aux(249)*(1/3)+aux(252) s(4240) =< aux(249)*(1/3)+aux(252) s(4242) =< aux(249)*(1/3)+aux(252) s(4245) =< aux(249)*(3/7)+aux(255) s(4243) =< aux(249)*(1/5)+aux(253) s(4233) =< aux(249)*(1/5)+aux(253) s(4244) =< aux(249)*(1/5)+aux(253) s(4241) =< aux(249)*(1/4)+aux(251) s(4244) =< aux(249)*(1/4)+aux(251) s(4233) =< aux(249)*(1/4)+aux(251) s(4253) =< s(4239)*s(4246) s(4254) =< s(4239)*s(4246) s(4255) =< s(4239)*s(4247) s(4256) =< s(4240)*s(4248) s(4257) =< s(4238)*s(4249) s(4258) =< s(4237)*s(4246) s(4259) =< s(4236)*s(4249) s(4260) =< s(4242) s(4261) =< s(4235)*s(4248) s(4262) =< s(4235)*s(4250) s(4263) =< s(4234)*s(4247) s(4264) =< s(4234)*s(4246) s(4265) =< s(4233)*s(4246) s(4266) =< s(4233)*s(4251) s(4267) =< s(4244)*s(4249) s(4268) =< s(4244)*s(4252) s(4269) =< s(4243)*2 s(4270) =< s(4254)*2 s(4271) =< s(4262)*2 s(4272) =< s(4263)*2 s(4273) =< s(4266)*2 s(4274) =< s(4268)*2 s(4275) =< s(4255) s(4276) =< s(4254) s(4277) =< s(4276)*s(4247) s(4278) =< s(4270) s(4279) =< s(4245) s(4280) =< s(4261) s(4281) =< s(4262) s(4282) =< s(4281)*aux(248) s(4283) =< s(4271) s(4284) =< s(4263) s(4285) =< s(4272) s(4286) =< s(4264) s(4287) =< s(4265) s(4288) =< s(4266) s(4289) =< s(4288)*s(4246) s(4290) =< s(4273) s(4291) =< s(4243) s(4292) =< s(4267) s(4293) =< s(4269) s(4294) =< s(4268) s(4295) =< s(4294)*s(4249) s(4296) =< s(4274) with precondition: [V2=2,1>=Out,V>=0,Out>=0] #### Cost of chains of fun9(V,V2,V12,Out): * Chain [92]: 100*s(4789)+2260*s(4790)+90*s(4791)+40*s(4792)+50*s(4793)+10*s(4794)+90*s(4795)+10*s(4796)+10*s(4797)+110*s(4800)+10*s(4809)+10*s(4812)+10*s(4813)+10*s(4814)+10*s(4815)+10*s(4816)+160*s(4831)+600*s(4832)+70*s(4833)+440*s(4834)+30*s(4835)+50*s(4836)+120*s(4837)+20*s(4838)+40*s(4839)+600*s(4840)+440*s(4841)+30*s(4842)+320*s(4843)+600*s(4844)+70*s(4845)+460*s(4846)+40*s(4847)+70*s(4848)+20*s(4849)+120*s(4850)+20*s(4851)+60*s(4852)+100*s(4861)+2380*s(4862)+90*s(4863)+40*s(4864)+50*s(4865)+10*s(4866)+90*s(4867)+10*s(4868)+10*s(4869)+110*s(4872)+10*s(4881)+10*s(4884)+10*s(4885)+10*s(4886)+10*s(4887)+10*s(4888)+160*s(4903)+600*s(4904)+70*s(4905)+440*s(4906)+30*s(4907)+50*s(4908)+120*s(4909)+20*s(4910)+40*s(4911)+600*s(4912)+440*s(4913)+30*s(4914)+320*s(4915)+600*s(4916)+70*s(4917)+460*s(4918)+40*s(4919)+70*s(4920)+20*s(4921)+120*s(4922)+20*s(4923)+60*s(4924)+100*s(4933)+2260*s(4934)+90*s(4935)+40*s(4936)+50*s(4937)+10*s(4938)+90*s(4939)+10*s(4940)+10*s(4941)+110*s(4944)+10*s(4953)+10*s(4956)+10*s(4957)+10*s(4958)+10*s(4959)+10*s(4960)+160*s(4975)+600*s(4976)+70*s(4977)+440*s(4978)+30*s(4979)+50*s(4980)+120*s(4981)+20*s(4982)+40*s(4983)+600*s(4984)+440*s(4985)+30*s(4986)+320*s(4987)+600*s(4988)+70*s(4989)+460*s(4990)+40*s(4991)+70*s(4992)+20*s(4993)+120*s(4994)+20*s(4995)+60*s(4996)+48*s(6225)+324*s(6226)+92*s(6447)+7*s(6455)+10 Such that:aux(278) =< 1 aux(279) =< V aux(280) =< 2*V aux(281) =< 2*V+1 aux(282) =< V/2 aux(283) =< 2/3*V aux(284) =< 3/5*V aux(285) =< 4/5*V aux(286) =< 4/7*V aux(287) =< V2 aux(288) =< 2*V2 aux(289) =< 2*V2+1 aux(290) =< V2/2 aux(291) =< 2/3*V2 aux(292) =< 3/5*V2 aux(293) =< 4/5*V2 aux(294) =< 4/7*V2 aux(295) =< V12 aux(296) =< 2*V12 aux(297) =< 2*V12+1 aux(298) =< V12/2 aux(299) =< 2/3*V12 aux(300) =< 3/5*V12 aux(301) =< 4/5*V12 aux(302) =< 4/7*V12 s(6225) =< aux(296) s(6226) =< aux(278) s(4933) =< aux(295) s(4934) =< aux(295) s(4935) =< aux(295) s(4936) =< aux(295) s(4937) =< aux(295) s(4938) =< aux(295) s(4939) =< aux(295) s(4940) =< aux(295) s(4941) =< aux(298) s(4942) =< aux(299) s(4936) =< aux(299) s(4938) =< aux(299) s(4940) =< aux(299) s(4943) =< aux(300) s(4944) =< aux(300) s(4937) =< aux(301) s(4938) =< aux(301) s(4940) =< aux(301) s(4945) =< aux(302) s(4935) =< aux(302) s(4940) =< aux(302) s(4946) =< aux(296)+2 s(4947) =< aux(296)+4 s(4948) =< aux(296) s(4949) =< aux(296)+1 s(4950) =< aux(296)+3 s(4951) =< aux(296)*(1/2)+1 s(4952) =< aux(296)*(1/2) s(4937) =< aux(297)*(1/5)+aux(301) s(4938) =< aux(297)*(1/5)+aux(301) s(4939) =< aux(297)*(1/5)+aux(301) s(4940) =< aux(297)*(1/5)+aux(301) s(4935) =< aux(297)*(3/7)+aux(302) s(4936) =< aux(297)*(3/7)+aux(302) s(4937) =< aux(297)*(3/7)+aux(302) s(4938) =< aux(297)*(3/7)+aux(302) s(4939) =< aux(297)*(3/7)+aux(302) s(4940) =< aux(297)*(3/7)+aux(302) s(4936) =< aux(297)*(1/3)+aux(299) s(4937) =< aux(297)*(1/3)+aux(299) s(4938) =< aux(297)*(1/3)+aux(299) s(4939) =< aux(297)*(1/3)+aux(299) s(4940) =< aux(297)*(1/3)+aux(299) s(4942) =< aux(297)*(1/3)+aux(299) s(4945) =< aux(297)*(3/7)+aux(302) s(4943) =< aux(297)*(1/5)+aux(300) s(4933) =< aux(297)*(1/5)+aux(300) s(4944) =< aux(297)*(1/5)+aux(300) s(4941) =< aux(297)*(1/4)+aux(298) s(4944) =< aux(297)*(1/4)+aux(298) s(4933) =< aux(297)*(1/4)+aux(298) s(4953) =< s(4939)*s(4946) s(4954) =< s(4939)*s(4946) s(4955) =< s(4939)*s(4947) s(4956) =< s(4940)*s(4948) s(4957) =< s(4938)*s(4949) s(4958) =< s(4937)*s(4946) s(4959) =< s(4936)*s(4949) s(4960) =< s(4942) s(4961) =< s(4935)*s(4948) s(4962) =< s(4935)*s(4950) s(4963) =< s(4934)*s(4947) s(4964) =< s(4934)*s(4946) s(4965) =< s(4933)*s(4946) s(4966) =< s(4933)*s(4951) s(4967) =< s(4944)*s(4949) s(4968) =< s(4944)*s(4952) s(4969) =< s(4943)*2 s(4970) =< s(4954)*2 s(4971) =< s(4962)*2 s(4972) =< s(4963)*2 s(4973) =< s(4966)*2 s(4974) =< s(4968)*2 s(4975) =< s(4955) s(4976) =< s(4954) s(4977) =< s(4976)*s(4947) s(4978) =< s(4970) s(4979) =< s(4945) s(4980) =< s(4961) s(4981) =< s(4962) s(4982) =< s(4981)*aux(296) s(4983) =< s(4971) s(4984) =< s(4963) s(4985) =< s(4972) s(4986) =< s(4964) s(4987) =< s(4965) s(4988) =< s(4966) s(4989) =< s(4988)*s(4946) s(4990) =< s(4973) s(4991) =< s(4943) s(4992) =< s(4967) s(4993) =< s(4969) s(4994) =< s(4968) s(4995) =< s(4994)*s(4949) s(4996) =< s(4974) s(4861) =< aux(287) s(4862) =< aux(287) s(4863) =< aux(287) s(4864) =< aux(287) s(4865) =< aux(287) s(4866) =< aux(287) s(4867) =< aux(287) s(4868) =< aux(287) s(4869) =< aux(290) s(4870) =< aux(291) s(4864) =< aux(291) s(4866) =< aux(291) s(4868) =< aux(291) s(4871) =< aux(292) s(4872) =< aux(292) s(4865) =< aux(293) s(4866) =< aux(293) s(4868) =< aux(293) s(4873) =< aux(294) s(4863) =< aux(294) s(4868) =< aux(294) s(4874) =< aux(288)+2 s(4875) =< aux(288)+4 s(4876) =< aux(288) s(4877) =< aux(288)+1 s(4878) =< aux(288)+3 s(4879) =< aux(288)*(1/2)+1 s(4880) =< aux(288)*(1/2) s(4865) =< aux(289)*(1/5)+aux(293) s(4866) =< aux(289)*(1/5)+aux(293) s(4867) =< aux(289)*(1/5)+aux(293) s(4868) =< aux(289)*(1/5)+aux(293) s(4863) =< aux(289)*(3/7)+aux(294) s(4864) =< aux(289)*(3/7)+aux(294) s(4865) =< aux(289)*(3/7)+aux(294) s(4866) =< aux(289)*(3/7)+aux(294) s(4867) =< aux(289)*(3/7)+aux(294) s(4868) =< aux(289)*(3/7)+aux(294) s(4864) =< aux(289)*(1/3)+aux(291) s(4865) =< aux(289)*(1/3)+aux(291) s(4866) =< aux(289)*(1/3)+aux(291) s(4867) =< aux(289)*(1/3)+aux(291) s(4868) =< aux(289)*(1/3)+aux(291) s(4870) =< aux(289)*(1/3)+aux(291) s(4873) =< aux(289)*(3/7)+aux(294) s(4871) =< aux(289)*(1/5)+aux(292) s(4861) =< aux(289)*(1/5)+aux(292) s(4872) =< aux(289)*(1/5)+aux(292) s(4869) =< aux(289)*(1/4)+aux(290) s(4872) =< aux(289)*(1/4)+aux(290) s(4861) =< aux(289)*(1/4)+aux(290) s(4881) =< s(4867)*s(4874) s(4882) =< s(4867)*s(4874) s(4883) =< s(4867)*s(4875) s(4884) =< s(4868)*s(4876) s(4885) =< s(4866)*s(4877) s(4886) =< s(4865)*s(4874) s(4887) =< s(4864)*s(4877) s(4888) =< s(4870) s(4889) =< s(4863)*s(4876) s(4890) =< s(4863)*s(4878) s(4891) =< s(4862)*s(4875) s(4892) =< s(4862)*s(4874) s(4893) =< s(4861)*s(4874) s(4894) =< s(4861)*s(4879) s(4895) =< s(4872)*s(4877) s(4896) =< s(4872)*s(4880) s(4897) =< s(4871)*2 s(4898) =< s(4882)*2 s(4899) =< s(4890)*2 s(4900) =< s(4891)*2 s(4901) =< s(4894)*2 s(4902) =< s(4896)*2 s(4903) =< s(4883) s(4904) =< s(4882) s(4905) =< s(4904)*s(4875) s(4906) =< s(4898) s(4907) =< s(4873) s(4908) =< s(4889) s(4909) =< s(4890) s(4910) =< s(4909)*aux(288) s(4911) =< s(4899) s(4912) =< s(4891) s(4913) =< s(4900) s(4914) =< s(4892) s(4915) =< s(4893) s(4916) =< s(4894) s(4917) =< s(4916)*s(4874) s(4918) =< s(4901) s(4919) =< s(4871) s(4920) =< s(4895) s(4921) =< s(4897) s(4922) =< s(4896) s(4923) =< s(4922)*s(4877) s(4924) =< s(4902) s(4789) =< aux(279) s(4790) =< aux(279) s(4791) =< aux(279) s(4792) =< aux(279) s(4793) =< aux(279) s(4794) =< aux(279) s(4795) =< aux(279) s(4796) =< aux(279) s(4797) =< aux(282) s(4798) =< aux(283) s(4792) =< aux(283) s(4794) =< aux(283) s(4796) =< aux(283) s(4799) =< aux(284) s(4800) =< aux(284) s(4793) =< aux(285) s(4794) =< aux(285) s(4796) =< aux(285) s(4801) =< aux(286) s(4791) =< aux(286) s(4796) =< aux(286) s(4802) =< aux(280)+2 s(4803) =< aux(280)+4 s(4804) =< aux(280) s(4805) =< aux(280)+1 s(4806) =< aux(280)+3 s(4807) =< aux(280)*(1/2)+1 s(4808) =< aux(280)*(1/2) s(4793) =< aux(281)*(1/5)+aux(285) s(4794) =< aux(281)*(1/5)+aux(285) s(4795) =< aux(281)*(1/5)+aux(285) s(4796) =< aux(281)*(1/5)+aux(285) s(4791) =< aux(281)*(3/7)+aux(286) s(4792) =< aux(281)*(3/7)+aux(286) s(4793) =< aux(281)*(3/7)+aux(286) s(4794) =< aux(281)*(3/7)+aux(286) s(4795) =< aux(281)*(3/7)+aux(286) s(4796) =< aux(281)*(3/7)+aux(286) s(4792) =< aux(281)*(1/3)+aux(283) s(4793) =< aux(281)*(1/3)+aux(283) s(4794) =< aux(281)*(1/3)+aux(283) s(4795) =< aux(281)*(1/3)+aux(283) s(4796) =< aux(281)*(1/3)+aux(283) s(4798) =< aux(281)*(1/3)+aux(283) s(4801) =< aux(281)*(3/7)+aux(286) s(4799) =< aux(281)*(1/5)+aux(284) s(4789) =< aux(281)*(1/5)+aux(284) s(4800) =< aux(281)*(1/5)+aux(284) s(4797) =< aux(281)*(1/4)+aux(282) s(4800) =< aux(281)*(1/4)+aux(282) s(4789) =< aux(281)*(1/4)+aux(282) s(4809) =< s(4795)*s(4802) s(4810) =< s(4795)*s(4802) s(4811) =< s(4795)*s(4803) s(4812) =< s(4796)*s(4804) s(4813) =< s(4794)*s(4805) s(4814) =< s(4793)*s(4802) s(4815) =< s(4792)*s(4805) s(4816) =< s(4798) s(4817) =< s(4791)*s(4804) s(4818) =< s(4791)*s(4806) s(4819) =< s(4790)*s(4803) s(4820) =< s(4790)*s(4802) s(4821) =< s(4789)*s(4802) s(4822) =< s(4789)*s(4807) s(4823) =< s(4800)*s(4805) s(4824) =< s(4800)*s(4808) s(4825) =< s(4799)*2 s(4826) =< s(4810)*2 s(4827) =< s(4818)*2 s(4828) =< s(4819)*2 s(4829) =< s(4822)*2 s(4830) =< s(4824)*2 s(4831) =< s(4811) s(4832) =< s(4810) s(4833) =< s(4832)*s(4803) s(4834) =< s(4826) s(4835) =< s(4801) s(4836) =< s(4817) s(4837) =< s(4818) s(4838) =< s(4837)*aux(280) s(4839) =< s(4827) s(4840) =< s(4819) s(4841) =< s(4828) s(4842) =< s(4820) s(4843) =< s(4821) s(4844) =< s(4822) s(4845) =< s(4844)*s(4802) s(4846) =< s(4829) s(4847) =< s(4799) s(4848) =< s(4823) s(4849) =< s(4825) s(4850) =< s(4824) s(4851) =< s(4850)*s(4805) s(4852) =< s(4830) s(6455) =< s(4862)*aux(296) s(6447) =< aux(288) with precondition: [Out=0,V>=0,V2>=0,V12>=0] * Chain [91]: 60*s(7007)+1356*s(7008)+54*s(7009)+24*s(7010)+30*s(7011)+6*s(7012)+54*s(7013)+6*s(7014)+6*s(7015)+66*s(7018)+6*s(7027)+6*s(7030)+6*s(7031)+6*s(7032)+6*s(7033)+6*s(7034)+96*s(7049)+360*s(7050)+42*s(7051)+264*s(7052)+18*s(7053)+30*s(7054)+72*s(7055)+12*s(7056)+24*s(7057)+360*s(7058)+264*s(7059)+18*s(7060)+192*s(7061)+360*s(7062)+42*s(7063)+276*s(7064)+24*s(7065)+42*s(7066)+12*s(7067)+72*s(7068)+12*s(7069)+36*s(7070)+50*s(7079)+1142*s(7080)+45*s(7081)+20*s(7082)+25*s(7083)+5*s(7084)+45*s(7085)+5*s(7086)+5*s(7087)+55*s(7090)+5*s(7099)+5*s(7102)+5*s(7103)+5*s(7104)+5*s(7105)+5*s(7106)+80*s(7121)+300*s(7122)+35*s(7123)+220*s(7124)+15*s(7125)+25*s(7126)+60*s(7127)+10*s(7128)+20*s(7129)+300*s(7130)+220*s(7131)+15*s(7132)+160*s(7133)+300*s(7134)+35*s(7135)+230*s(7136)+20*s(7137)+35*s(7138)+10*s(7139)+60*s(7140)+10*s(7141)+30*s(7142)+90*s(7151)+2034*s(7152)+81*s(7153)+36*s(7154)+45*s(7155)+9*s(7156)+81*s(7157)+9*s(7158)+9*s(7159)+99*s(7162)+9*s(7171)+9*s(7174)+9*s(7175)+9*s(7176)+9*s(7177)+9*s(7178)+144*s(7193)+540*s(7194)+63*s(7195)+396*s(7196)+27*s(7197)+45*s(7198)+108*s(7199)+18*s(7200)+36*s(7201)+540*s(7202)+396*s(7203)+27*s(7204)+288*s(7205)+540*s(7206)+63*s(7207)+414*s(7208)+36*s(7209)+63*s(7210)+18*s(7211)+108*s(7212)+18*s(7213)+54*s(7214)+8*s(7215)+2*s(7433)+4*s(7434)+6*s(7653)+2*s(7661)+11 Such that:s(7432) =< 2 aux(309) =< 1 aux(310) =< V aux(311) =< 2*V aux(312) =< 2*V+1 aux(313) =< V/2 aux(314) =< 2/3*V aux(315) =< 3/5*V aux(316) =< 4/5*V aux(317) =< 4/7*V aux(318) =< V2 aux(319) =< 2*V2 aux(320) =< 2*V2+1 aux(321) =< V2/2 aux(322) =< 2/3*V2 aux(323) =< 3/5*V2 aux(324) =< 4/5*V2 aux(325) =< 4/7*V2 aux(326) =< V12 aux(327) =< 2*V12 aux(328) =< 2*V12+1 aux(329) =< V12/2 aux(330) =< 2/3*V12 aux(331) =< 3/5*V12 aux(332) =< 4/5*V12 aux(333) =< 4/7*V12 s(7434) =< aux(309) s(7215) =< aux(327) s(7433) =< s(7432) s(7151) =< aux(326) s(7152) =< aux(326) s(7153) =< aux(326) s(7154) =< aux(326) s(7155) =< aux(326) s(7156) =< aux(326) s(7157) =< aux(326) s(7158) =< aux(326) s(7159) =< aux(329) s(7160) =< aux(330) s(7154) =< aux(330) s(7156) =< aux(330) s(7158) =< aux(330) s(7161) =< aux(331) s(7162) =< aux(331) s(7155) =< aux(332) s(7156) =< aux(332) s(7158) =< aux(332) s(7163) =< aux(333) s(7153) =< aux(333) s(7158) =< aux(333) s(7164) =< aux(327)+2 s(7165) =< aux(327)+4 s(7166) =< aux(327) s(7167) =< aux(327)+1 s(7168) =< aux(327)+3 s(7169) =< aux(327)*(1/2)+1 s(7170) =< aux(327)*(1/2) s(7155) =< aux(328)*(1/5)+aux(332) s(7156) =< aux(328)*(1/5)+aux(332) s(7157) =< aux(328)*(1/5)+aux(332) s(7158) =< aux(328)*(1/5)+aux(332) s(7153) =< aux(328)*(3/7)+aux(333) s(7154) =< aux(328)*(3/7)+aux(333) s(7155) =< aux(328)*(3/7)+aux(333) s(7156) =< aux(328)*(3/7)+aux(333) s(7157) =< aux(328)*(3/7)+aux(333) s(7158) =< aux(328)*(3/7)+aux(333) s(7154) =< aux(328)*(1/3)+aux(330) s(7155) =< aux(328)*(1/3)+aux(330) s(7156) =< aux(328)*(1/3)+aux(330) s(7157) =< aux(328)*(1/3)+aux(330) s(7158) =< aux(328)*(1/3)+aux(330) s(7160) =< aux(328)*(1/3)+aux(330) s(7163) =< aux(328)*(3/7)+aux(333) s(7161) =< aux(328)*(1/5)+aux(331) s(7151) =< aux(328)*(1/5)+aux(331) s(7162) =< aux(328)*(1/5)+aux(331) s(7159) =< aux(328)*(1/4)+aux(329) s(7162) =< aux(328)*(1/4)+aux(329) s(7151) =< aux(328)*(1/4)+aux(329) s(7171) =< s(7157)*s(7164) s(7172) =< s(7157)*s(7164) s(7173) =< s(7157)*s(7165) s(7174) =< s(7158)*s(7166) s(7175) =< s(7156)*s(7167) s(7176) =< s(7155)*s(7164) s(7177) =< s(7154)*s(7167) s(7178) =< s(7160) s(7179) =< s(7153)*s(7166) s(7180) =< s(7153)*s(7168) s(7181) =< s(7152)*s(7165) s(7182) =< s(7152)*s(7164) s(7183) =< s(7151)*s(7164) s(7184) =< s(7151)*s(7169) s(7185) =< s(7162)*s(7167) s(7186) =< s(7162)*s(7170) s(7187) =< s(7161)*2 s(7188) =< s(7172)*2 s(7189) =< s(7180)*2 s(7190) =< s(7181)*2 s(7191) =< s(7184)*2 s(7192) =< s(7186)*2 s(7193) =< s(7173) s(7194) =< s(7172) s(7195) =< s(7194)*s(7165) s(7196) =< s(7188) s(7197) =< s(7163) s(7198) =< s(7179) s(7199) =< s(7180) s(7200) =< s(7199)*aux(327) s(7201) =< s(7189) s(7202) =< s(7181) s(7203) =< s(7190) s(7204) =< s(7182) s(7205) =< s(7183) s(7206) =< s(7184) s(7207) =< s(7206)*s(7164) s(7208) =< s(7191) s(7209) =< s(7161) s(7210) =< s(7185) s(7211) =< s(7187) s(7212) =< s(7186) s(7213) =< s(7212)*s(7167) s(7214) =< s(7192) s(7079) =< aux(318) s(7080) =< aux(318) s(7081) =< aux(318) s(7082) =< aux(318) s(7083) =< aux(318) s(7084) =< aux(318) s(7085) =< aux(318) s(7086) =< aux(318) s(7087) =< aux(321) s(7088) =< aux(322) s(7082) =< aux(322) s(7084) =< aux(322) s(7086) =< aux(322) s(7089) =< aux(323) s(7090) =< aux(323) s(7083) =< aux(324) s(7084) =< aux(324) s(7086) =< aux(324) s(7091) =< aux(325) s(7081) =< aux(325) s(7086) =< aux(325) s(7092) =< aux(319)+2 s(7093) =< aux(319)+4 s(7094) =< aux(319) s(7095) =< aux(319)+1 s(7096) =< aux(319)+3 s(7097) =< aux(319)*(1/2)+1 s(7098) =< aux(319)*(1/2) s(7083) =< aux(320)*(1/5)+aux(324) s(7084) =< aux(320)*(1/5)+aux(324) s(7085) =< aux(320)*(1/5)+aux(324) s(7086) =< aux(320)*(1/5)+aux(324) s(7081) =< aux(320)*(3/7)+aux(325) s(7082) =< aux(320)*(3/7)+aux(325) s(7083) =< aux(320)*(3/7)+aux(325) s(7084) =< aux(320)*(3/7)+aux(325) s(7085) =< aux(320)*(3/7)+aux(325) s(7086) =< aux(320)*(3/7)+aux(325) s(7082) =< aux(320)*(1/3)+aux(322) s(7083) =< aux(320)*(1/3)+aux(322) s(7084) =< aux(320)*(1/3)+aux(322) s(7085) =< aux(320)*(1/3)+aux(322) s(7086) =< aux(320)*(1/3)+aux(322) s(7088) =< aux(320)*(1/3)+aux(322) s(7091) =< aux(320)*(3/7)+aux(325) s(7089) =< aux(320)*(1/5)+aux(323) s(7079) =< aux(320)*(1/5)+aux(323) s(7090) =< aux(320)*(1/5)+aux(323) s(7087) =< aux(320)*(1/4)+aux(321) s(7090) =< aux(320)*(1/4)+aux(321) s(7079) =< aux(320)*(1/4)+aux(321) s(7099) =< s(7085)*s(7092) s(7100) =< s(7085)*s(7092) s(7101) =< s(7085)*s(7093) s(7102) =< s(7086)*s(7094) s(7103) =< s(7084)*s(7095) s(7104) =< s(7083)*s(7092) s(7105) =< s(7082)*s(7095) s(7106) =< s(7088) s(7107) =< s(7081)*s(7094) s(7108) =< s(7081)*s(7096) s(7109) =< s(7080)*s(7093) s(7110) =< s(7080)*s(7092) s(7111) =< s(7079)*s(7092) s(7112) =< s(7079)*s(7097) s(7113) =< s(7090)*s(7095) s(7114) =< s(7090)*s(7098) s(7115) =< s(7089)*2 s(7116) =< s(7100)*2 s(7117) =< s(7108)*2 s(7118) =< s(7109)*2 s(7119) =< s(7112)*2 s(7120) =< s(7114)*2 s(7121) =< s(7101) s(7122) =< s(7100) s(7123) =< s(7122)*s(7093) s(7124) =< s(7116) s(7125) =< s(7091) s(7126) =< s(7107) s(7127) =< s(7108) s(7128) =< s(7127)*aux(319) s(7129) =< s(7117) s(7130) =< s(7109) s(7131) =< s(7118) s(7132) =< s(7110) s(7133) =< s(7111) s(7134) =< s(7112) s(7135) =< s(7134)*s(7092) s(7136) =< s(7119) s(7137) =< s(7089) s(7138) =< s(7113) s(7139) =< s(7115) s(7140) =< s(7114) s(7141) =< s(7140)*s(7095) s(7142) =< s(7120) s(7007) =< aux(310) s(7008) =< aux(310) s(7009) =< aux(310) s(7010) =< aux(310) s(7011) =< aux(310) s(7012) =< aux(310) s(7013) =< aux(310) s(7014) =< aux(310) s(7015) =< aux(313) s(7016) =< aux(314) s(7010) =< aux(314) s(7012) =< aux(314) s(7014) =< aux(314) s(7017) =< aux(315) s(7018) =< aux(315) s(7011) =< aux(316) s(7012) =< aux(316) s(7014) =< aux(316) s(7019) =< aux(317) s(7009) =< aux(317) s(7014) =< aux(317) s(7020) =< aux(311)+2 s(7021) =< aux(311)+4 s(7022) =< aux(311) s(7023) =< aux(311)+1 s(7024) =< aux(311)+3 s(7025) =< aux(311)*(1/2)+1 s(7026) =< aux(311)*(1/2) s(7011) =< aux(312)*(1/5)+aux(316) s(7012) =< aux(312)*(1/5)+aux(316) s(7013) =< aux(312)*(1/5)+aux(316) s(7014) =< aux(312)*(1/5)+aux(316) s(7009) =< aux(312)*(3/7)+aux(317) s(7010) =< aux(312)*(3/7)+aux(317) s(7011) =< aux(312)*(3/7)+aux(317) s(7012) =< aux(312)*(3/7)+aux(317) s(7013) =< aux(312)*(3/7)+aux(317) s(7014) =< aux(312)*(3/7)+aux(317) s(7010) =< aux(312)*(1/3)+aux(314) s(7011) =< aux(312)*(1/3)+aux(314) s(7012) =< aux(312)*(1/3)+aux(314) s(7013) =< aux(312)*(1/3)+aux(314) s(7014) =< aux(312)*(1/3)+aux(314) s(7016) =< aux(312)*(1/3)+aux(314) s(7019) =< aux(312)*(3/7)+aux(317) s(7017) =< aux(312)*(1/5)+aux(315) s(7007) =< aux(312)*(1/5)+aux(315) s(7018) =< aux(312)*(1/5)+aux(315) s(7015) =< aux(312)*(1/4)+aux(313) s(7018) =< aux(312)*(1/4)+aux(313) s(7007) =< aux(312)*(1/4)+aux(313) s(7027) =< s(7013)*s(7020) s(7028) =< s(7013)*s(7020) s(7029) =< s(7013)*s(7021) s(7030) =< s(7014)*s(7022) s(7031) =< s(7012)*s(7023) s(7032) =< s(7011)*s(7020) s(7033) =< s(7010)*s(7023) s(7034) =< s(7016) s(7035) =< s(7009)*s(7022) s(7036) =< s(7009)*s(7024) s(7037) =< s(7008)*s(7021) s(7038) =< s(7008)*s(7020) s(7039) =< s(7007)*s(7020) s(7040) =< s(7007)*s(7025) s(7041) =< s(7018)*s(7023) s(7042) =< s(7018)*s(7026) s(7043) =< s(7017)*2 s(7044) =< s(7028)*2 s(7045) =< s(7036)*2 s(7046) =< s(7037)*2 s(7047) =< s(7040)*2 s(7048) =< s(7042)*2 s(7049) =< s(7029) s(7050) =< s(7028) s(7051) =< s(7050)*s(7021) s(7052) =< s(7044) s(7053) =< s(7019) s(7054) =< s(7035) s(7055) =< s(7036) s(7056) =< s(7055)*aux(311) s(7057) =< s(7045) s(7058) =< s(7037) s(7059) =< s(7046) s(7060) =< s(7038) s(7061) =< s(7039) s(7062) =< s(7040) s(7063) =< s(7062)*s(7020) s(7064) =< s(7047) s(7065) =< s(7017) s(7066) =< s(7041) s(7067) =< s(7043) s(7068) =< s(7042) s(7069) =< s(7068)*s(7023) s(7070) =< s(7048) s(7661) =< s(7080)*aux(327) s(7653) =< aux(319) with precondition: [V>=1,V2>=0,V12>=1,Out>=0,2*V12>=Out+1] * Chain [90]: 50*s(8464)+1130*s(8465)+45*s(8466)+20*s(8467)+25*s(8468)+5*s(8469)+45*s(8470)+5*s(8471)+5*s(8472)+55*s(8475)+5*s(8484)+5*s(8487)+5*s(8488)+5*s(8489)+5*s(8490)+5*s(8491)+80*s(8506)+300*s(8507)+35*s(8508)+220*s(8509)+15*s(8510)+25*s(8511)+60*s(8512)+10*s(8513)+20*s(8514)+300*s(8515)+220*s(8516)+15*s(8517)+160*s(8518)+300*s(8519)+35*s(8520)+230*s(8521)+20*s(8522)+35*s(8523)+10*s(8524)+60*s(8525)+10*s(8526)+30*s(8527)+50*s(8536)+1190*s(8537)+45*s(8538)+20*s(8539)+25*s(8540)+5*s(8541)+45*s(8542)+5*s(8543)+5*s(8544)+55*s(8547)+5*s(8556)+5*s(8559)+5*s(8560)+5*s(8561)+5*s(8562)+5*s(8563)+80*s(8578)+300*s(8579)+35*s(8580)+220*s(8581)+15*s(8582)+25*s(8583)+60*s(8584)+10*s(8585)+20*s(8586)+300*s(8587)+220*s(8588)+15*s(8589)+160*s(8590)+300*s(8591)+35*s(8592)+230*s(8593)+20*s(8594)+35*s(8595)+10*s(8596)+60*s(8597)+10*s(8598)+30*s(8599)+48*s(8964)+162*s(8965)+46*s(9114)+7*s(9122)+10 Such that:aux(338) =< 1 aux(339) =< 2 aux(340) =< V aux(341) =< 2*V aux(342) =< 2*V+1 aux(343) =< V/2 aux(344) =< 2/3*V aux(345) =< 3/5*V aux(346) =< 4/5*V aux(347) =< 4/7*V aux(348) =< V2 aux(349) =< 2*V2 aux(350) =< 2*V2+1 aux(351) =< V2/2 aux(352) =< 2/3*V2 aux(353) =< 3/5*V2 aux(354) =< 4/5*V2 aux(355) =< 4/7*V2 s(8964) =< aux(339) s(8965) =< aux(338) s(8536) =< aux(348) s(8537) =< aux(348) s(8538) =< aux(348) s(8539) =< aux(348) s(8540) =< aux(348) s(8541) =< aux(348) s(8542) =< aux(348) s(8543) =< aux(348) s(8544) =< aux(351) s(8545) =< aux(352) s(8539) =< aux(352) s(8541) =< aux(352) s(8543) =< aux(352) s(8546) =< aux(353) s(8547) =< aux(353) s(8540) =< aux(354) s(8541) =< aux(354) s(8543) =< aux(354) s(8548) =< aux(355) s(8538) =< aux(355) s(8543) =< aux(355) s(8549) =< aux(349)+2 s(8550) =< aux(349)+4 s(8551) =< aux(349) s(8552) =< aux(349)+1 s(8553) =< aux(349)+3 s(8554) =< aux(349)*(1/2)+1 s(8555) =< aux(349)*(1/2) s(8540) =< aux(350)*(1/5)+aux(354) s(8541) =< aux(350)*(1/5)+aux(354) s(8542) =< aux(350)*(1/5)+aux(354) s(8543) =< aux(350)*(1/5)+aux(354) s(8538) =< aux(350)*(3/7)+aux(355) s(8539) =< aux(350)*(3/7)+aux(355) s(8540) =< aux(350)*(3/7)+aux(355) s(8541) =< aux(350)*(3/7)+aux(355) s(8542) =< aux(350)*(3/7)+aux(355) s(8543) =< aux(350)*(3/7)+aux(355) s(8539) =< aux(350)*(1/3)+aux(352) s(8540) =< aux(350)*(1/3)+aux(352) s(8541) =< aux(350)*(1/3)+aux(352) s(8542) =< aux(350)*(1/3)+aux(352) s(8543) =< aux(350)*(1/3)+aux(352) s(8545) =< aux(350)*(1/3)+aux(352) s(8548) =< aux(350)*(3/7)+aux(355) s(8546) =< aux(350)*(1/5)+aux(353) s(8536) =< aux(350)*(1/5)+aux(353) s(8547) =< aux(350)*(1/5)+aux(353) s(8544) =< aux(350)*(1/4)+aux(351) s(8547) =< aux(350)*(1/4)+aux(351) s(8536) =< aux(350)*(1/4)+aux(351) s(8556) =< s(8542)*s(8549) s(8557) =< s(8542)*s(8549) s(8558) =< s(8542)*s(8550) s(8559) =< s(8543)*s(8551) s(8560) =< s(8541)*s(8552) s(8561) =< s(8540)*s(8549) s(8562) =< s(8539)*s(8552) s(8563) =< s(8545) s(8564) =< s(8538)*s(8551) s(8565) =< s(8538)*s(8553) s(8566) =< s(8537)*s(8550) s(8567) =< s(8537)*s(8549) s(8568) =< s(8536)*s(8549) s(8569) =< s(8536)*s(8554) s(8570) =< s(8547)*s(8552) s(8571) =< s(8547)*s(8555) s(8572) =< s(8546)*2 s(8573) =< s(8557)*2 s(8574) =< s(8565)*2 s(8575) =< s(8566)*2 s(8576) =< s(8569)*2 s(8577) =< s(8571)*2 s(8578) =< s(8558) s(8579) =< s(8557) s(8580) =< s(8579)*s(8550) s(8581) =< s(8573) s(8582) =< s(8548) s(8583) =< s(8564) s(8584) =< s(8565) s(8585) =< s(8584)*aux(349) s(8586) =< s(8574) s(8587) =< s(8566) s(8588) =< s(8575) s(8589) =< s(8567) s(8590) =< s(8568) s(8591) =< s(8569) s(8592) =< s(8591)*s(8549) s(8593) =< s(8576) s(8594) =< s(8546) s(8595) =< s(8570) s(8596) =< s(8572) s(8597) =< s(8571) s(8598) =< s(8597)*s(8552) s(8599) =< s(8577) s(8464) =< aux(340) s(8465) =< aux(340) s(8466) =< aux(340) s(8467) =< aux(340) s(8468) =< aux(340) s(8469) =< aux(340) s(8470) =< aux(340) s(8471) =< aux(340) s(8472) =< aux(343) s(8473) =< aux(344) s(8467) =< aux(344) s(8469) =< aux(344) s(8471) =< aux(344) s(8474) =< aux(345) s(8475) =< aux(345) s(8468) =< aux(346) s(8469) =< aux(346) s(8471) =< aux(346) s(8476) =< aux(347) s(8466) =< aux(347) s(8471) =< aux(347) s(8477) =< aux(341)+2 s(8478) =< aux(341)+4 s(8479) =< aux(341) s(8480) =< aux(341)+1 s(8481) =< aux(341)+3 s(8482) =< aux(341)*(1/2)+1 s(8483) =< aux(341)*(1/2) s(8468) =< aux(342)*(1/5)+aux(346) s(8469) =< aux(342)*(1/5)+aux(346) s(8470) =< aux(342)*(1/5)+aux(346) s(8471) =< aux(342)*(1/5)+aux(346) s(8466) =< aux(342)*(3/7)+aux(347) s(8467) =< aux(342)*(3/7)+aux(347) s(8468) =< aux(342)*(3/7)+aux(347) s(8469) =< aux(342)*(3/7)+aux(347) s(8470) =< aux(342)*(3/7)+aux(347) s(8471) =< aux(342)*(3/7)+aux(347) s(8467) =< aux(342)*(1/3)+aux(344) s(8468) =< aux(342)*(1/3)+aux(344) s(8469) =< aux(342)*(1/3)+aux(344) s(8470) =< aux(342)*(1/3)+aux(344) s(8471) =< aux(342)*(1/3)+aux(344) s(8473) =< aux(342)*(1/3)+aux(344) s(8476) =< aux(342)*(3/7)+aux(347) s(8474) =< aux(342)*(1/5)+aux(345) s(8464) =< aux(342)*(1/5)+aux(345) s(8475) =< aux(342)*(1/5)+aux(345) s(8472) =< aux(342)*(1/4)+aux(343) s(8475) =< aux(342)*(1/4)+aux(343) s(8464) =< aux(342)*(1/4)+aux(343) s(8484) =< s(8470)*s(8477) s(8485) =< s(8470)*s(8477) s(8486) =< s(8470)*s(8478) s(8487) =< s(8471)*s(8479) s(8488) =< s(8469)*s(8480) s(8489) =< s(8468)*s(8477) s(8490) =< s(8467)*s(8480) s(8491) =< s(8473) s(8492) =< s(8466)*s(8479) s(8493) =< s(8466)*s(8481) s(8494) =< s(8465)*s(8478) s(8495) =< s(8465)*s(8477) s(8496) =< s(8464)*s(8477) s(8497) =< s(8464)*s(8482) s(8498) =< s(8475)*s(8480) s(8499) =< s(8475)*s(8483) s(8500) =< s(8474)*2 s(8501) =< s(8485)*2 s(8502) =< s(8493)*2 s(8503) =< s(8494)*2 s(8504) =< s(8497)*2 s(8505) =< s(8499)*2 s(8506) =< s(8486) s(8507) =< s(8485) s(8508) =< s(8507)*s(8478) s(8509) =< s(8501) s(8510) =< s(8476) s(8511) =< s(8492) s(8512) =< s(8493) s(8513) =< s(8512)*aux(341) s(8514) =< s(8502) s(8515) =< s(8494) s(8516) =< s(8503) s(8517) =< s(8495) s(8518) =< s(8496) s(8519) =< s(8497) s(8520) =< s(8519)*s(8477) s(8521) =< s(8504) s(8522) =< s(8474) s(8523) =< s(8498) s(8524) =< s(8500) s(8525) =< s(8499) s(8526) =< s(8525)*s(8480) s(8527) =< s(8505) s(9122) =< s(8537)*aux(339) s(9114) =< aux(349) with precondition: [V12=2,Out=0,V>=0,V2>=0] * Chain [89]: 60*s(9213)+1356*s(9214)+54*s(9215)+24*s(9216)+30*s(9217)+6*s(9218)+54*s(9219)+6*s(9220)+6*s(9221)+66*s(9224)+6*s(9233)+6*s(9236)+6*s(9237)+6*s(9238)+6*s(9239)+6*s(9240)+96*s(9255)+360*s(9256)+42*s(9257)+264*s(9258)+18*s(9259)+30*s(9260)+72*s(9261)+12*s(9262)+24*s(9263)+360*s(9264)+264*s(9265)+18*s(9266)+192*s(9267)+360*s(9268)+42*s(9269)+276*s(9270)+24*s(9271)+42*s(9272)+12*s(9273)+72*s(9274)+12*s(9275)+36*s(9276)+50*s(9285)+1142*s(9286)+45*s(9287)+20*s(9288)+25*s(9289)+5*s(9290)+45*s(9291)+5*s(9292)+5*s(9293)+55*s(9296)+5*s(9305)+5*s(9308)+5*s(9309)+5*s(9310)+5*s(9311)+5*s(9312)+80*s(9327)+300*s(9328)+35*s(9329)+220*s(9330)+15*s(9331)+25*s(9332)+60*s(9333)+10*s(9334)+20*s(9335)+300*s(9336)+220*s(9337)+15*s(9338)+160*s(9339)+300*s(9340)+35*s(9341)+230*s(9342)+20*s(9343)+35*s(9344)+10*s(9345)+60*s(9346)+10*s(9347)+30*s(9348)+10*s(9349)+4*s(9496)+6*s(9643)+2*s(9651)+11 Such that:aux(359) =< 1 aux(360) =< 2 aux(361) =< V aux(362) =< 2*V aux(363) =< 2*V+1 aux(364) =< V/2 aux(365) =< 2/3*V aux(366) =< 3/5*V aux(367) =< 4/5*V aux(368) =< 4/7*V aux(369) =< V2 aux(370) =< 2*V2 aux(371) =< 2*V2+1 aux(372) =< V2/2 aux(373) =< 2/3*V2 aux(374) =< 3/5*V2 aux(375) =< 4/5*V2 aux(376) =< 4/7*V2 s(9496) =< aux(359) s(9349) =< aux(360) s(9285) =< aux(369) s(9286) =< aux(369) s(9287) =< aux(369) s(9288) =< aux(369) s(9289) =< aux(369) s(9290) =< aux(369) s(9291) =< aux(369) s(9292) =< aux(369) s(9293) =< aux(372) s(9294) =< aux(373) s(9288) =< aux(373) s(9290) =< aux(373) s(9292) =< aux(373) s(9295) =< aux(374) s(9296) =< aux(374) s(9289) =< aux(375) s(9290) =< aux(375) s(9292) =< aux(375) s(9297) =< aux(376) s(9287) =< aux(376) s(9292) =< aux(376) s(9298) =< aux(370)+2 s(9299) =< aux(370)+4 s(9300) =< aux(370) s(9301) =< aux(370)+1 s(9302) =< aux(370)+3 s(9303) =< aux(370)*(1/2)+1 s(9304) =< aux(370)*(1/2) s(9289) =< aux(371)*(1/5)+aux(375) s(9290) =< aux(371)*(1/5)+aux(375) s(9291) =< aux(371)*(1/5)+aux(375) s(9292) =< aux(371)*(1/5)+aux(375) s(9287) =< aux(371)*(3/7)+aux(376) s(9288) =< aux(371)*(3/7)+aux(376) s(9289) =< aux(371)*(3/7)+aux(376) s(9290) =< aux(371)*(3/7)+aux(376) s(9291) =< aux(371)*(3/7)+aux(376) s(9292) =< aux(371)*(3/7)+aux(376) s(9288) =< aux(371)*(1/3)+aux(373) s(9289) =< aux(371)*(1/3)+aux(373) s(9290) =< aux(371)*(1/3)+aux(373) s(9291) =< aux(371)*(1/3)+aux(373) s(9292) =< aux(371)*(1/3)+aux(373) s(9294) =< aux(371)*(1/3)+aux(373) s(9297) =< aux(371)*(3/7)+aux(376) s(9295) =< aux(371)*(1/5)+aux(374) s(9285) =< aux(371)*(1/5)+aux(374) s(9296) =< aux(371)*(1/5)+aux(374) s(9293) =< aux(371)*(1/4)+aux(372) s(9296) =< aux(371)*(1/4)+aux(372) s(9285) =< aux(371)*(1/4)+aux(372) s(9305) =< s(9291)*s(9298) s(9306) =< s(9291)*s(9298) s(9307) =< s(9291)*s(9299) s(9308) =< s(9292)*s(9300) s(9309) =< s(9290)*s(9301) s(9310) =< s(9289)*s(9298) s(9311) =< s(9288)*s(9301) s(9312) =< s(9294) s(9313) =< s(9287)*s(9300) s(9314) =< s(9287)*s(9302) s(9315) =< s(9286)*s(9299) s(9316) =< s(9286)*s(9298) s(9317) =< s(9285)*s(9298) s(9318) =< s(9285)*s(9303) s(9319) =< s(9296)*s(9301) s(9320) =< s(9296)*s(9304) s(9321) =< s(9295)*2 s(9322) =< s(9306)*2 s(9323) =< s(9314)*2 s(9324) =< s(9315)*2 s(9325) =< s(9318)*2 s(9326) =< s(9320)*2 s(9327) =< s(9307) s(9328) =< s(9306) s(9329) =< s(9328)*s(9299) s(9330) =< s(9322) s(9331) =< s(9297) s(9332) =< s(9313) s(9333) =< s(9314) s(9334) =< s(9333)*aux(370) s(9335) =< s(9323) s(9336) =< s(9315) s(9337) =< s(9324) s(9338) =< s(9316) s(9339) =< s(9317) s(9340) =< s(9318) s(9341) =< s(9340)*s(9298) s(9342) =< s(9325) s(9343) =< s(9295) s(9344) =< s(9319) s(9345) =< s(9321) s(9346) =< s(9320) s(9347) =< s(9346)*s(9301) s(9348) =< s(9326) s(9213) =< aux(361) s(9214) =< aux(361) s(9215) =< aux(361) s(9216) =< aux(361) s(9217) =< aux(361) s(9218) =< aux(361) s(9219) =< aux(361) s(9220) =< aux(361) s(9221) =< aux(364) s(9222) =< aux(365) s(9216) =< aux(365) s(9218) =< aux(365) s(9220) =< aux(365) s(9223) =< aux(366) s(9224) =< aux(366) s(9217) =< aux(367) s(9218) =< aux(367) s(9220) =< aux(367) s(9225) =< aux(368) s(9215) =< aux(368) s(9220) =< aux(368) s(9226) =< aux(362)+2 s(9227) =< aux(362)+4 s(9228) =< aux(362) s(9229) =< aux(362)+1 s(9230) =< aux(362)+3 s(9231) =< aux(362)*(1/2)+1 s(9232) =< aux(362)*(1/2) s(9217) =< aux(363)*(1/5)+aux(367) s(9218) =< aux(363)*(1/5)+aux(367) s(9219) =< aux(363)*(1/5)+aux(367) s(9220) =< aux(363)*(1/5)+aux(367) s(9215) =< aux(363)*(3/7)+aux(368) s(9216) =< aux(363)*(3/7)+aux(368) s(9217) =< aux(363)*(3/7)+aux(368) s(9218) =< aux(363)*(3/7)+aux(368) s(9219) =< aux(363)*(3/7)+aux(368) s(9220) =< aux(363)*(3/7)+aux(368) s(9216) =< aux(363)*(1/3)+aux(365) s(9217) =< aux(363)*(1/3)+aux(365) s(9218) =< aux(363)*(1/3)+aux(365) s(9219) =< aux(363)*(1/3)+aux(365) s(9220) =< aux(363)*(1/3)+aux(365) s(9222) =< aux(363)*(1/3)+aux(365) s(9225) =< aux(363)*(3/7)+aux(368) s(9223) =< aux(363)*(1/5)+aux(366) s(9213) =< aux(363)*(1/5)+aux(366) s(9224) =< aux(363)*(1/5)+aux(366) s(9221) =< aux(363)*(1/4)+aux(364) s(9224) =< aux(363)*(1/4)+aux(364) s(9213) =< aux(363)*(1/4)+aux(364) s(9233) =< s(9219)*s(9226) s(9234) =< s(9219)*s(9226) s(9235) =< s(9219)*s(9227) s(9236) =< s(9220)*s(9228) s(9237) =< s(9218)*s(9229) s(9238) =< s(9217)*s(9226) s(9239) =< s(9216)*s(9229) s(9240) =< s(9222) s(9241) =< s(9215)*s(9228) s(9242) =< s(9215)*s(9230) s(9243) =< s(9214)*s(9227) s(9244) =< s(9214)*s(9226) s(9245) =< s(9213)*s(9226) s(9246) =< s(9213)*s(9231) s(9247) =< s(9224)*s(9229) s(9248) =< s(9224)*s(9232) s(9249) =< s(9223)*2 s(9250) =< s(9234)*2 s(9251) =< s(9242)*2 s(9252) =< s(9243)*2 s(9253) =< s(9246)*2 s(9254) =< s(9248)*2 s(9255) =< s(9235) s(9256) =< s(9234) s(9257) =< s(9256)*s(9227) s(9258) =< s(9250) s(9259) =< s(9225) s(9260) =< s(9241) s(9261) =< s(9242) s(9262) =< s(9261)*aux(362) s(9263) =< s(9251) s(9264) =< s(9243) s(9265) =< s(9252) s(9266) =< s(9244) s(9267) =< s(9245) s(9268) =< s(9246) s(9269) =< s(9268)*s(9226) s(9270) =< s(9253) s(9271) =< s(9223) s(9272) =< s(9247) s(9273) =< s(9249) s(9274) =< s(9248) s(9275) =< s(9274)*s(9229) s(9276) =< s(9254) s(9651) =< s(9286)*aux(360) s(9643) =< aux(370) with precondition: [V12=2,1>=Out,V>=1,V2>=0,Out>=0] * Chain [88]: 90*s(10022)+2034*s(10023)+81*s(10024)+36*s(10025)+45*s(10026)+9*s(10027)+81*s(10028)+9*s(10029)+9*s(10030)+99*s(10033)+9*s(10042)+9*s(10045)+9*s(10046)+9*s(10047)+9*s(10048)+9*s(10049)+144*s(10064)+540*s(10065)+63*s(10066)+396*s(10067)+27*s(10068)+45*s(10069)+108*s(10070)+18*s(10071)+36*s(10072)+540*s(10073)+396*s(10074)+27*s(10075)+288*s(10076)+540*s(10077)+63*s(10078)+414*s(10079)+36*s(10080)+63*s(10081)+18*s(10082)+108*s(10083)+18*s(10084)+54*s(10085)+40*s(10094)+904*s(10095)+36*s(10096)+16*s(10097)+20*s(10098)+4*s(10099)+36*s(10100)+4*s(10101)+4*s(10102)+44*s(10105)+4*s(10114)+4*s(10117)+4*s(10118)+4*s(10119)+4*s(10120)+4*s(10121)+64*s(10136)+240*s(10137)+28*s(10138)+176*s(10139)+12*s(10140)+20*s(10141)+48*s(10142)+8*s(10143)+16*s(10144)+240*s(10145)+176*s(10146)+12*s(10147)+128*s(10148)+240*s(10149)+28*s(10150)+184*s(10151)+16*s(10152)+28*s(10153)+8*s(10154)+48*s(10155)+8*s(10156)+24*s(10157)+32*s(10522)+504*s(10523)+170*s(10672)+7*s(10680)+7*s(10844)+10 Such that:aux(388) =< 1 aux(389) =< 2 aux(390) =< V aux(391) =< 2*V aux(392) =< 2*V+1 aux(393) =< V/2 aux(394) =< 2/3*V aux(395) =< 3/5*V aux(396) =< 4/5*V aux(397) =< 4/7*V aux(398) =< V12 aux(399) =< 2*V12 aux(400) =< 2*V12+1 aux(401) =< V12/2 aux(402) =< 2/3*V12 aux(403) =< 3/5*V12 aux(404) =< 4/5*V12 aux(405) =< 4/7*V12 s(10522) =< aux(399) s(10523) =< aux(388) s(10094) =< aux(398) s(10095) =< aux(398) s(10096) =< aux(398) s(10097) =< aux(398) s(10098) =< aux(398) s(10099) =< aux(398) s(10100) =< aux(398) s(10101) =< aux(398) s(10102) =< aux(401) s(10103) =< aux(402) s(10097) =< aux(402) s(10099) =< aux(402) s(10101) =< aux(402) s(10104) =< aux(403) s(10105) =< aux(403) s(10098) =< aux(404) s(10099) =< aux(404) s(10101) =< aux(404) s(10106) =< aux(405) s(10096) =< aux(405) s(10101) =< aux(405) s(10107) =< aux(399)+2 s(10108) =< aux(399)+4 s(10109) =< aux(399) s(10110) =< aux(399)+1 s(10111) =< aux(399)+3 s(10112) =< aux(399)*(1/2)+1 s(10113) =< aux(399)*(1/2) s(10098) =< aux(400)*(1/5)+aux(404) s(10099) =< aux(400)*(1/5)+aux(404) s(10100) =< aux(400)*(1/5)+aux(404) s(10101) =< aux(400)*(1/5)+aux(404) s(10096) =< aux(400)*(3/7)+aux(405) s(10097) =< aux(400)*(3/7)+aux(405) s(10098) =< aux(400)*(3/7)+aux(405) s(10099) =< aux(400)*(3/7)+aux(405) s(10100) =< aux(400)*(3/7)+aux(405) s(10101) =< aux(400)*(3/7)+aux(405) s(10097) =< aux(400)*(1/3)+aux(402) s(10098) =< aux(400)*(1/3)+aux(402) s(10099) =< aux(400)*(1/3)+aux(402) s(10100) =< aux(400)*(1/3)+aux(402) s(10101) =< aux(400)*(1/3)+aux(402) s(10103) =< aux(400)*(1/3)+aux(402) s(10106) =< aux(400)*(3/7)+aux(405) s(10104) =< aux(400)*(1/5)+aux(403) s(10094) =< aux(400)*(1/5)+aux(403) s(10105) =< aux(400)*(1/5)+aux(403) s(10102) =< aux(400)*(1/4)+aux(401) s(10105) =< aux(400)*(1/4)+aux(401) s(10094) =< aux(400)*(1/4)+aux(401) s(10114) =< s(10100)*s(10107) s(10115) =< s(10100)*s(10107) s(10116) =< s(10100)*s(10108) s(10117) =< s(10101)*s(10109) s(10118) =< s(10099)*s(10110) s(10119) =< s(10098)*s(10107) s(10120) =< s(10097)*s(10110) s(10121) =< s(10103) s(10122) =< s(10096)*s(10109) s(10123) =< s(10096)*s(10111) s(10124) =< s(10095)*s(10108) s(10125) =< s(10095)*s(10107) s(10126) =< s(10094)*s(10107) s(10127) =< s(10094)*s(10112) s(10128) =< s(10105)*s(10110) s(10129) =< s(10105)*s(10113) s(10130) =< s(10104)*2 s(10131) =< s(10115)*2 s(10132) =< s(10123)*2 s(10133) =< s(10124)*2 s(10134) =< s(10127)*2 s(10135) =< s(10129)*2 s(10136) =< s(10116) s(10137) =< s(10115) s(10138) =< s(10137)*s(10108) s(10139) =< s(10131) s(10140) =< s(10106) s(10141) =< s(10122) s(10142) =< s(10123) s(10143) =< s(10142)*aux(399) s(10144) =< s(10132) s(10145) =< s(10124) s(10146) =< s(10133) s(10147) =< s(10125) s(10148) =< s(10126) s(10149) =< s(10127) s(10150) =< s(10149)*s(10107) s(10151) =< s(10134) s(10152) =< s(10104) s(10153) =< s(10128) s(10154) =< s(10130) s(10155) =< s(10129) s(10156) =< s(10155)*s(10110) s(10157) =< s(10135) s(10022) =< aux(390) s(10023) =< aux(390) s(10024) =< aux(390) s(10025) =< aux(390) s(10026) =< aux(390) s(10027) =< aux(390) s(10028) =< aux(390) s(10029) =< aux(390) s(10030) =< aux(393) s(10031) =< aux(394) s(10025) =< aux(394) s(10027) =< aux(394) s(10029) =< aux(394) s(10032) =< aux(395) s(10033) =< aux(395) s(10026) =< aux(396) s(10027) =< aux(396) s(10029) =< aux(396) s(10034) =< aux(397) s(10024) =< aux(397) s(10029) =< aux(397) s(10035) =< aux(391)+2 s(10036) =< aux(391)+4 s(10037) =< aux(391) s(10038) =< aux(391)+1 s(10039) =< aux(391)+3 s(10040) =< aux(391)*(1/2)+1 s(10041) =< aux(391)*(1/2) s(10026) =< aux(392)*(1/5)+aux(396) s(10027) =< aux(392)*(1/5)+aux(396) s(10028) =< aux(392)*(1/5)+aux(396) s(10029) =< aux(392)*(1/5)+aux(396) s(10024) =< aux(392)*(3/7)+aux(397) s(10025) =< aux(392)*(3/7)+aux(397) s(10026) =< aux(392)*(3/7)+aux(397) s(10027) =< aux(392)*(3/7)+aux(397) s(10028) =< aux(392)*(3/7)+aux(397) s(10029) =< aux(392)*(3/7)+aux(397) s(10025) =< aux(392)*(1/3)+aux(394) s(10026) =< aux(392)*(1/3)+aux(394) s(10027) =< aux(392)*(1/3)+aux(394) s(10028) =< aux(392)*(1/3)+aux(394) s(10029) =< aux(392)*(1/3)+aux(394) s(10031) =< aux(392)*(1/3)+aux(394) s(10034) =< aux(392)*(3/7)+aux(397) s(10032) =< aux(392)*(1/5)+aux(395) s(10022) =< aux(392)*(1/5)+aux(395) s(10033) =< aux(392)*(1/5)+aux(395) s(10030) =< aux(392)*(1/4)+aux(393) s(10033) =< aux(392)*(1/4)+aux(393) s(10022) =< aux(392)*(1/4)+aux(393) s(10042) =< s(10028)*s(10035) s(10043) =< s(10028)*s(10035) s(10044) =< s(10028)*s(10036) s(10045) =< s(10029)*s(10037) s(10046) =< s(10027)*s(10038) s(10047) =< s(10026)*s(10035) s(10048) =< s(10025)*s(10038) s(10049) =< s(10031) s(10050) =< s(10024)*s(10037) s(10051) =< s(10024)*s(10039) s(10052) =< s(10023)*s(10036) s(10053) =< s(10023)*s(10035) s(10054) =< s(10022)*s(10035) s(10055) =< s(10022)*s(10040) s(10056) =< s(10033)*s(10038) s(10057) =< s(10033)*s(10041) s(10058) =< s(10032)*2 s(10059) =< s(10043)*2 s(10060) =< s(10051)*2 s(10061) =< s(10052)*2 s(10062) =< s(10055)*2 s(10063) =< s(10057)*2 s(10064) =< s(10044) s(10065) =< s(10043) s(10066) =< s(10065)*s(10036) s(10067) =< s(10059) s(10068) =< s(10034) s(10069) =< s(10050) s(10070) =< s(10051) s(10071) =< s(10070)*aux(391) s(10072) =< s(10060) s(10073) =< s(10052) s(10074) =< s(10061) s(10075) =< s(10053) s(10076) =< s(10054) s(10077) =< s(10055) s(10078) =< s(10077)*s(10035) s(10079) =< s(10062) s(10080) =< s(10032) s(10081) =< s(10056) s(10082) =< s(10058) s(10083) =< s(10057) s(10084) =< s(10083)*s(10038) s(10085) =< s(10063) s(10672) =< aux(389) s(10680) =< s(10523)*aux(399) s(10844) =< s(10523)*aux(389) with precondition: [V2=2,Out=0,V>=0,V12>=0] * Chain [87]: 60*s(11018)+1356*s(11019)+54*s(11020)+24*s(11021)+30*s(11022)+6*s(11023)+54*s(11024)+6*s(11025)+6*s(11026)+66*s(11029)+6*s(11038)+6*s(11041)+6*s(11042)+6*s(11043)+6*s(11044)+6*s(11045)+96*s(11060)+360*s(11061)+42*s(11062)+264*s(11063)+18*s(11064)+30*s(11065)+72*s(11066)+12*s(11067)+24*s(11068)+360*s(11069)+264*s(11070)+18*s(11071)+192*s(11072)+360*s(11073)+42*s(11074)+276*s(11075)+24*s(11076)+42*s(11077)+12*s(11078)+72*s(11079)+12*s(11080)+36*s(11081)+30*s(11090)+678*s(11091)+27*s(11092)+12*s(11093)+15*s(11094)+3*s(11095)+27*s(11096)+3*s(11097)+3*s(11098)+33*s(11101)+3*s(11110)+3*s(11113)+3*s(11114)+3*s(11115)+3*s(11116)+3*s(11117)+48*s(11132)+180*s(11133)+21*s(11134)+132*s(11135)+9*s(11136)+15*s(11137)+36*s(11138)+6*s(11139)+12*s(11140)+180*s(11141)+132*s(11142)+9*s(11143)+96*s(11144)+180*s(11145)+21*s(11146)+138*s(11147)+12*s(11148)+21*s(11149)+6*s(11150)+36*s(11151)+6*s(11152)+18*s(11153)+2*s(11154)+6*s(11300)+2*s(11301)+6 Such that:aux(409) =< 1 aux(410) =< 2 aux(411) =< V aux(412) =< 2*V aux(413) =< 2*V+1 aux(414) =< V/2 aux(415) =< 2/3*V aux(416) =< 3/5*V aux(417) =< 4/5*V aux(418) =< 4/7*V aux(419) =< V12 aux(420) =< 2*V12 aux(421) =< 2*V12+1 aux(422) =< V12/2 aux(423) =< 2/3*V12 aux(424) =< 3/5*V12 aux(425) =< 4/5*V12 aux(426) =< 4/7*V12 s(11301) =< aux(409) s(11300) =< aux(410) s(11154) =< aux(420) s(11090) =< aux(419) s(11091) =< aux(419) s(11092) =< aux(419) s(11093) =< aux(419) s(11094) =< aux(419) s(11095) =< aux(419) s(11096) =< aux(419) s(11097) =< aux(419) s(11098) =< aux(422) s(11099) =< aux(423) s(11093) =< aux(423) s(11095) =< aux(423) s(11097) =< aux(423) s(11100) =< aux(424) s(11101) =< aux(424) s(11094) =< aux(425) s(11095) =< aux(425) s(11097) =< aux(425) s(11102) =< aux(426) s(11092) =< aux(426) s(11097) =< aux(426) s(11103) =< aux(420)+2 s(11104) =< aux(420)+4 s(11105) =< aux(420) s(11106) =< aux(420)+1 s(11107) =< aux(420)+3 s(11108) =< aux(420)*(1/2)+1 s(11109) =< aux(420)*(1/2) s(11094) =< aux(421)*(1/5)+aux(425) s(11095) =< aux(421)*(1/5)+aux(425) s(11096) =< aux(421)*(1/5)+aux(425) s(11097) =< aux(421)*(1/5)+aux(425) s(11092) =< aux(421)*(3/7)+aux(426) s(11093) =< aux(421)*(3/7)+aux(426) s(11094) =< aux(421)*(3/7)+aux(426) s(11095) =< aux(421)*(3/7)+aux(426) s(11096) =< aux(421)*(3/7)+aux(426) s(11097) =< aux(421)*(3/7)+aux(426) s(11093) =< aux(421)*(1/3)+aux(423) s(11094) =< aux(421)*(1/3)+aux(423) s(11095) =< aux(421)*(1/3)+aux(423) s(11096) =< aux(421)*(1/3)+aux(423) s(11097) =< aux(421)*(1/3)+aux(423) s(11099) =< aux(421)*(1/3)+aux(423) s(11102) =< aux(421)*(3/7)+aux(426) s(11100) =< aux(421)*(1/5)+aux(424) s(11090) =< aux(421)*(1/5)+aux(424) s(11101) =< aux(421)*(1/5)+aux(424) s(11098) =< aux(421)*(1/4)+aux(422) s(11101) =< aux(421)*(1/4)+aux(422) s(11090) =< aux(421)*(1/4)+aux(422) s(11110) =< s(11096)*s(11103) s(11111) =< s(11096)*s(11103) s(11112) =< s(11096)*s(11104) s(11113) =< s(11097)*s(11105) s(11114) =< s(11095)*s(11106) s(11115) =< s(11094)*s(11103) s(11116) =< s(11093)*s(11106) s(11117) =< s(11099) s(11118) =< s(11092)*s(11105) s(11119) =< s(11092)*s(11107) s(11120) =< s(11091)*s(11104) s(11121) =< s(11091)*s(11103) s(11122) =< s(11090)*s(11103) s(11123) =< s(11090)*s(11108) s(11124) =< s(11101)*s(11106) s(11125) =< s(11101)*s(11109) s(11126) =< s(11100)*2 s(11127) =< s(11111)*2 s(11128) =< s(11119)*2 s(11129) =< s(11120)*2 s(11130) =< s(11123)*2 s(11131) =< s(11125)*2 s(11132) =< s(11112) s(11133) =< s(11111) s(11134) =< s(11133)*s(11104) s(11135) =< s(11127) s(11136) =< s(11102) s(11137) =< s(11118) s(11138) =< s(11119) s(11139) =< s(11138)*aux(420) s(11140) =< s(11128) s(11141) =< s(11120) s(11142) =< s(11129) s(11143) =< s(11121) s(11144) =< s(11122) s(11145) =< s(11123) s(11146) =< s(11145)*s(11103) s(11147) =< s(11130) s(11148) =< s(11100) s(11149) =< s(11124) s(11150) =< s(11126) s(11151) =< s(11125) s(11152) =< s(11151)*s(11106) s(11153) =< s(11131) s(11018) =< aux(411) s(11019) =< aux(411) s(11020) =< aux(411) s(11021) =< aux(411) s(11022) =< aux(411) s(11023) =< aux(411) s(11024) =< aux(411) s(11025) =< aux(411) s(11026) =< aux(414) s(11027) =< aux(415) s(11021) =< aux(415) s(11023) =< aux(415) s(11025) =< aux(415) s(11028) =< aux(416) s(11029) =< aux(416) s(11022) =< aux(417) s(11023) =< aux(417) s(11025) =< aux(417) s(11030) =< aux(418) s(11020) =< aux(418) s(11025) =< aux(418) s(11031) =< aux(412)+2 s(11032) =< aux(412)+4 s(11033) =< aux(412) s(11034) =< aux(412)+1 s(11035) =< aux(412)+3 s(11036) =< aux(412)*(1/2)+1 s(11037) =< aux(412)*(1/2) s(11022) =< aux(413)*(1/5)+aux(417) s(11023) =< aux(413)*(1/5)+aux(417) s(11024) =< aux(413)*(1/5)+aux(417) s(11025) =< aux(413)*(1/5)+aux(417) s(11020) =< aux(413)*(3/7)+aux(418) s(11021) =< aux(413)*(3/7)+aux(418) s(11022) =< aux(413)*(3/7)+aux(418) s(11023) =< aux(413)*(3/7)+aux(418) s(11024) =< aux(413)*(3/7)+aux(418) s(11025) =< aux(413)*(3/7)+aux(418) s(11021) =< aux(413)*(1/3)+aux(415) s(11022) =< aux(413)*(1/3)+aux(415) s(11023) =< aux(413)*(1/3)+aux(415) s(11024) =< aux(413)*(1/3)+aux(415) s(11025) =< aux(413)*(1/3)+aux(415) s(11027) =< aux(413)*(1/3)+aux(415) s(11030) =< aux(413)*(3/7)+aux(418) s(11028) =< aux(413)*(1/5)+aux(416) s(11018) =< aux(413)*(1/5)+aux(416) s(11029) =< aux(413)*(1/5)+aux(416) s(11026) =< aux(413)*(1/4)+aux(414) s(11029) =< aux(413)*(1/4)+aux(414) s(11018) =< aux(413)*(1/4)+aux(414) s(11038) =< s(11024)*s(11031) s(11039) =< s(11024)*s(11031) s(11040) =< s(11024)*s(11032) s(11041) =< s(11025)*s(11033) s(11042) =< s(11023)*s(11034) s(11043) =< s(11022)*s(11031) s(11044) =< s(11021)*s(11034) s(11045) =< s(11027) s(11046) =< s(11020)*s(11033) s(11047) =< s(11020)*s(11035) s(11048) =< s(11019)*s(11032) s(11049) =< s(11019)*s(11031) s(11050) =< s(11018)*s(11031) s(11051) =< s(11018)*s(11036) s(11052) =< s(11029)*s(11034) s(11053) =< s(11029)*s(11037) s(11054) =< s(11028)*2 s(11055) =< s(11039)*2 s(11056) =< s(11047)*2 s(11057) =< s(11048)*2 s(11058) =< s(11051)*2 s(11059) =< s(11053)*2 s(11060) =< s(11040) s(11061) =< s(11039) s(11062) =< s(11061)*s(11032) s(11063) =< s(11055) s(11064) =< s(11030) s(11065) =< s(11046) s(11066) =< s(11047) s(11067) =< s(11066)*aux(412) s(11068) =< s(11056) s(11069) =< s(11048) s(11070) =< s(11057) s(11071) =< s(11049) s(11072) =< s(11050) s(11073) =< s(11051) s(11074) =< s(11073)*s(11031) s(11075) =< s(11058) s(11076) =< s(11028) s(11077) =< s(11052) s(11078) =< s(11054) s(11079) =< s(11053) s(11080) =< s(11079)*s(11034) s(11081) =< s(11059) with precondition: [V2=2,V>=1,V12>=1,Out>=0,2*V12>=Out+1] #### Cost of chains of start(V,V2,V12): * Chain [93]: 5915*s(12412)+1887*s(12418)+10225*s(12423)+72*s(12430)+9*s(12431)+573*s(12434)+15956*s(12449)+360*s(12462)+9*s(12471)+700*s(12492)+630*s(12494)+280*s(12495)+350*s(12496)+70*s(12497)+630*s(12498)+70*s(12499)+70*s(12500)+770*s(12503)+70*s(12512)+70*s(12515)+70*s(12516)+70*s(12517)+70*s(12518)+70*s(12519)+1120*s(12534)+4200*s(12535)+490*s(12536)+3080*s(12537)+210*s(12538)+350*s(12539)+840*s(12540)+140*s(12541)+280*s(12542)+4200*s(12543)+3080*s(12544)+210*s(12545)+2240*s(12546)+4200*s(12547)+490*s(12548)+3220*s(12549)+280*s(12550)+490*s(12551)+140*s(12552)+840*s(12553)+140*s(12554)+420*s(12555)+215*s(12793)+440*s(12794)+396*s(12796)+176*s(12797)+220*s(12798)+44*s(12799)+396*s(12800)+44*s(12801)+44*s(12802)+484*s(12805)+44*s(12814)+44*s(12817)+44*s(12818)+44*s(12819)+44*s(12820)+44*s(12821)+704*s(12836)+2640*s(12837)+308*s(12838)+1936*s(12839)+132*s(12840)+220*s(12841)+528*s(12842)+88*s(12843)+176*s(12844)+2640*s(12845)+1936*s(12846)+132*s(12847)+1408*s(12848)+2640*s(12849)+308*s(12850)+2024*s(12851)+176*s(12852)+308*s(12853)+88*s(12854)+528*s(12855)+88*s(12856)+264*s(12857)+184*s(13376)+184*s(13442)+9*s(13466)+9*s(13597)+9*s(13598)+9*s(13600)+90*s(13783)+260*s(13785)+234*s(13787)+104*s(13788)+130*s(13789)+26*s(13790)+234*s(13791)+26*s(13792)+26*s(13793)+286*s(13796)+26*s(13805)+26*s(13808)+26*s(13809)+26*s(13810)+26*s(13811)+26*s(13812)+416*s(13827)+1560*s(13828)+182*s(13829)+1144*s(13830)+78*s(13831)+130*s(13832)+312*s(13833)+52*s(13834)+104*s(13835)+1560*s(13836)+1144*s(13837)+78*s(13838)+832*s(13839)+1560*s(13840)+182*s(13841)+1196*s(13842)+104*s(13843)+182*s(13844)+52*s(13845)+312*s(13846)+52*s(13847)+156*s(13848)+7*s(13914)+7*s(13915)+9*s(13980)+9*s(14353)+11 Such that:aux(465) =< 1 aux(466) =< 2 aux(467) =< 4 aux(468) =< V aux(469) =< 2*V aux(470) =< 2*V+1 aux(471) =< 4*V aux(472) =< V/2 aux(473) =< 2/3*V aux(474) =< 3/5*V aux(475) =< 4/5*V aux(476) =< 4/7*V aux(477) =< V2 aux(478) =< 2*V2 aux(479) =< 2*V2+1 aux(480) =< V2/2 aux(481) =< 2/3*V2 aux(482) =< 3/5*V2 aux(483) =< 4/5*V2 aux(484) =< 4/7*V2 aux(485) =< V12 aux(486) =< 2*V12 aux(487) =< 2*V12+1 aux(488) =< V12/2 aux(489) =< 2/3*V12 aux(490) =< 3/5*V12 aux(491) =< 4/5*V12 aux(492) =< 4/7*V12 s(12418) =< aux(465) s(12434) =< aux(466) s(12449) =< aux(468) s(12423) =< aux(477) s(12412) =< aux(485) s(12430) =< aux(480) s(12431) =< s(12430)*aux(485) s(12462) =< aux(469) s(12471) =< s(12449)*aux(477) s(12794) =< aux(477) s(12796) =< aux(477) s(12797) =< aux(477) s(12798) =< aux(477) s(12799) =< aux(477) s(12800) =< aux(477) s(12801) =< aux(477) s(12802) =< aux(480) s(12803) =< aux(481) s(12797) =< aux(481) s(12799) =< aux(481) s(12801) =< aux(481) s(12804) =< aux(482) s(12805) =< aux(482) s(12798) =< aux(483) s(12799) =< aux(483) s(12801) =< aux(483) s(12806) =< aux(484) s(12796) =< aux(484) s(12801) =< aux(484) s(12807) =< aux(478)+2 s(12808) =< aux(478)+4 s(12809) =< aux(478) s(12810) =< aux(478)+1 s(12811) =< aux(478)+3 s(12812) =< aux(478)*(1/2)+1 s(12813) =< aux(478)*(1/2) s(12798) =< aux(479)*(1/5)+aux(483) s(12799) =< aux(479)*(1/5)+aux(483) s(12800) =< aux(479)*(1/5)+aux(483) s(12801) =< aux(479)*(1/5)+aux(483) s(12796) =< aux(479)*(3/7)+aux(484) s(12797) =< aux(479)*(3/7)+aux(484) s(12798) =< aux(479)*(3/7)+aux(484) s(12799) =< aux(479)*(3/7)+aux(484) s(12800) =< aux(479)*(3/7)+aux(484) s(12801) =< aux(479)*(3/7)+aux(484) s(12797) =< aux(479)*(1/3)+aux(481) s(12798) =< aux(479)*(1/3)+aux(481) s(12799) =< aux(479)*(1/3)+aux(481) s(12800) =< aux(479)*(1/3)+aux(481) s(12801) =< aux(479)*(1/3)+aux(481) s(12803) =< aux(479)*(1/3)+aux(481) s(12806) =< aux(479)*(3/7)+aux(484) s(12804) =< aux(479)*(1/5)+aux(482) s(12794) =< aux(479)*(1/5)+aux(482) s(12805) =< aux(479)*(1/5)+aux(482) s(12802) =< aux(479)*(1/4)+aux(480) s(12805) =< aux(479)*(1/4)+aux(480) s(12794) =< aux(479)*(1/4)+aux(480) s(12814) =< s(12800)*s(12807) s(12815) =< s(12800)*s(12807) s(12816) =< s(12800)*s(12808) s(12817) =< s(12801)*s(12809) s(12818) =< s(12799)*s(12810) s(12819) =< s(12798)*s(12807) s(12820) =< s(12797)*s(12810) s(12821) =< s(12803) s(12822) =< s(12796)*s(12809) s(12823) =< s(12796)*s(12811) s(12824) =< s(12423)*s(12808) s(12825) =< s(12423)*s(12807) s(12826) =< s(12794)*s(12807) s(12827) =< s(12794)*s(12812) s(12828) =< s(12805)*s(12810) s(12829) =< s(12805)*s(12813) s(12830) =< s(12804)*2 s(12831) =< s(12815)*2 s(12832) =< s(12823)*2 s(12833) =< s(12824)*2 s(12834) =< s(12827)*2 s(12835) =< s(12829)*2 s(12836) =< s(12816) s(12837) =< s(12815) s(12838) =< s(12837)*s(12808) s(12839) =< s(12831) s(12840) =< s(12806) s(12841) =< s(12822) s(12842) =< s(12823) s(12843) =< s(12842)*aux(478) s(12844) =< s(12832) s(12845) =< s(12824) s(12846) =< s(12833) s(12847) =< s(12825) s(12848) =< s(12826) s(12849) =< s(12827) s(12850) =< s(12849)*s(12807) s(12851) =< s(12834) s(12852) =< s(12804) s(12853) =< s(12828) s(12854) =< s(12830) s(12855) =< s(12829) s(12856) =< s(12855)*s(12810) s(12857) =< s(12835) s(12492) =< aux(468) s(12494) =< aux(468) s(12495) =< aux(468) s(12496) =< aux(468) s(12497) =< aux(468) s(12498) =< aux(468) s(12499) =< aux(468) s(12500) =< aux(472) s(12501) =< aux(473) s(12495) =< aux(473) s(12497) =< aux(473) s(12499) =< aux(473) s(12502) =< aux(474) s(12503) =< aux(474) s(12496) =< aux(475) s(12497) =< aux(475) s(12499) =< aux(475) s(12504) =< aux(476) s(12494) =< aux(476) s(12499) =< aux(476) s(12505) =< aux(469)+2 s(12506) =< aux(469)+4 s(12507) =< aux(469) s(12508) =< aux(469)+1 s(12509) =< aux(469)+3 s(12510) =< aux(469)*(1/2)+1 s(12511) =< aux(469)*(1/2) s(12496) =< aux(470)*(1/5)+aux(475) s(12497) =< aux(470)*(1/5)+aux(475) s(12498) =< aux(470)*(1/5)+aux(475) s(12499) =< aux(470)*(1/5)+aux(475) s(12494) =< aux(470)*(3/7)+aux(476) s(12495) =< aux(470)*(3/7)+aux(476) s(12496) =< aux(470)*(3/7)+aux(476) s(12497) =< aux(470)*(3/7)+aux(476) s(12498) =< aux(470)*(3/7)+aux(476) s(12499) =< aux(470)*(3/7)+aux(476) s(12495) =< aux(470)*(1/3)+aux(473) s(12496) =< aux(470)*(1/3)+aux(473) s(12497) =< aux(470)*(1/3)+aux(473) s(12498) =< aux(470)*(1/3)+aux(473) s(12499) =< aux(470)*(1/3)+aux(473) s(12501) =< aux(470)*(1/3)+aux(473) s(12504) =< aux(470)*(3/7)+aux(476) s(12502) =< aux(470)*(1/5)+aux(474) s(12492) =< aux(470)*(1/5)+aux(474) s(12503) =< aux(470)*(1/5)+aux(474) s(12500) =< aux(470)*(1/4)+aux(472) s(12503) =< aux(470)*(1/4)+aux(472) s(12492) =< aux(470)*(1/4)+aux(472) s(12512) =< s(12498)*s(12505) s(12513) =< s(12498)*s(12505) s(12514) =< s(12498)*s(12506) s(12515) =< s(12499)*s(12507) s(12516) =< s(12497)*s(12508) s(12517) =< s(12496)*s(12505) s(12518) =< s(12495)*s(12508) s(12519) =< s(12501) s(12520) =< s(12494)*s(12507) s(12521) =< s(12494)*s(12509) s(12522) =< s(12449)*s(12506) s(12523) =< s(12449)*s(12505) s(12524) =< s(12492)*s(12505) s(12525) =< s(12492)*s(12510) s(12526) =< s(12503)*s(12508) s(12527) =< s(12503)*s(12511) s(12528) =< s(12502)*2 s(12529) =< s(12513)*2 s(12530) =< s(12521)*2 s(12531) =< s(12522)*2 s(12532) =< s(12525)*2 s(12533) =< s(12527)*2 s(12534) =< s(12514) s(12535) =< s(12513) s(12536) =< s(12535)*s(12506) s(12537) =< s(12529) s(12538) =< s(12504) s(12539) =< s(12520) s(12540) =< s(12521) s(12541) =< s(12540)*aux(469) s(12542) =< s(12530) s(12543) =< s(12522) s(12544) =< s(12531) s(12545) =< s(12523) s(12546) =< s(12524) s(12547) =< s(12525) s(12548) =< s(12547)*s(12505) s(12549) =< s(12532) s(12550) =< s(12502) s(12551) =< s(12526) s(12552) =< s(12528) s(12553) =< s(12527) s(12554) =< s(12553)*s(12508) s(12555) =< s(12533) s(13376) =< aux(471) s(13442) =< aux(467) s(13466) =< s(12462)*aux(466) s(12793) =< aux(478) s(13597) =< s(12462)*aux(478) s(13598) =< s(12434)*aux(478) s(13600) =< s(12434)*aux(466) s(13783) =< aux(486) s(13785) =< aux(485) s(13787) =< aux(485) s(13788) =< aux(485) s(13789) =< aux(485) s(13790) =< aux(485) s(13791) =< aux(485) s(13792) =< aux(485) s(13793) =< aux(488) s(13794) =< aux(489) s(13788) =< aux(489) s(13790) =< aux(489) s(13792) =< aux(489) s(13795) =< aux(490) s(13796) =< aux(490) s(13789) =< aux(491) s(13790) =< aux(491) s(13792) =< aux(491) s(13797) =< aux(492) s(13787) =< aux(492) s(13792) =< aux(492) s(13798) =< aux(486)+2 s(13799) =< aux(486)+4 s(13800) =< aux(486) s(13801) =< aux(486)+1 s(13802) =< aux(486)+3 s(13803) =< aux(486)*(1/2)+1 s(13804) =< aux(486)*(1/2) s(13789) =< aux(487)*(1/5)+aux(491) s(13790) =< aux(487)*(1/5)+aux(491) s(13791) =< aux(487)*(1/5)+aux(491) s(13792) =< aux(487)*(1/5)+aux(491) s(13787) =< aux(487)*(3/7)+aux(492) s(13788) =< aux(487)*(3/7)+aux(492) s(13789) =< aux(487)*(3/7)+aux(492) s(13790) =< aux(487)*(3/7)+aux(492) s(13791) =< aux(487)*(3/7)+aux(492) s(13792) =< aux(487)*(3/7)+aux(492) s(13788) =< aux(487)*(1/3)+aux(489) s(13789) =< aux(487)*(1/3)+aux(489) s(13790) =< aux(487)*(1/3)+aux(489) s(13791) =< aux(487)*(1/3)+aux(489) s(13792) =< aux(487)*(1/3)+aux(489) s(13794) =< aux(487)*(1/3)+aux(489) s(13797) =< aux(487)*(3/7)+aux(492) s(13795) =< aux(487)*(1/5)+aux(490) s(13785) =< aux(487)*(1/5)+aux(490) s(13796) =< aux(487)*(1/5)+aux(490) s(13793) =< aux(487)*(1/4)+aux(488) s(13796) =< aux(487)*(1/4)+aux(488) s(13785) =< aux(487)*(1/4)+aux(488) s(13805) =< s(13791)*s(13798) s(13806) =< s(13791)*s(13798) s(13807) =< s(13791)*s(13799) s(13808) =< s(13792)*s(13800) s(13809) =< s(13790)*s(13801) s(13810) =< s(13789)*s(13798) s(13811) =< s(13788)*s(13801) s(13812) =< s(13794) s(13813) =< s(13787)*s(13800) s(13814) =< s(13787)*s(13802) s(13815) =< s(12412)*s(13799) s(13816) =< s(12412)*s(13798) s(13817) =< s(13785)*s(13798) s(13818) =< s(13785)*s(13803) s(13819) =< s(13796)*s(13801) s(13820) =< s(13796)*s(13804) s(13821) =< s(13795)*2 s(13822) =< s(13806)*2 s(13823) =< s(13814)*2 s(13824) =< s(13815)*2 s(13825) =< s(13818)*2 s(13826) =< s(13820)*2 s(13827) =< s(13807) s(13828) =< s(13806) s(13829) =< s(13828)*s(13799) s(13830) =< s(13822) s(13831) =< s(13797) s(13832) =< s(13813) s(13833) =< s(13814) s(13834) =< s(13833)*aux(486) s(13835) =< s(13823) s(13836) =< s(13815) s(13837) =< s(13824) s(13838) =< s(13816) s(13839) =< s(13817) s(13840) =< s(13818) s(13841) =< s(13840)*s(13798) s(13842) =< s(13825) s(13843) =< s(13795) s(13844) =< s(13819) s(13845) =< s(13821) s(13846) =< s(13820) s(13847) =< s(13846)*s(13801) s(13848) =< s(13826) s(13914) =< s(12418)*aux(486) s(13915) =< s(12418)*aux(466) s(13980) =< s(12423)*aux(486) s(14353) =< s(12423)*aux(466) with precondition: [] Closed-form bounds of start(V,V2,V12): ------------------------------------- * Chain [93] with precondition: [] - Upper bound: nat(V)*110386+3830+nat(V)*9*nat(V2)+nat(V)*36050*nat(2*V)+nat(V)*875*nat(2*V)*nat(2*V)+nat(V2)*69599+nat(V2)*22660*nat(2*V2)+nat(V2)*550*nat(2*V2)*nat(2*V2)+nat(V2)*9*nat(2*V12)+nat(V12)*40989+nat(V12)*13390*nat(2*V12)+nat(V12)*325*nat(2*V12)*nat(2*V12)+nat(V12)*9*nat(V2/2)+nat(2*V)*378+nat(2*V)*70*nat(2*V)*nat(3/5*V)+nat(2*V)*9*nat(2*V2)+nat(2*V)*1400*nat(3/5*V)+nat(2*V2)*233+nat(2*V2)*44*nat(2*V2)*nat(3/5*V2)+nat(2*V2)*880*nat(3/5*V2)+nat(2*V12)*97+nat(2*V12)*26*nat(2*V12)*nat(3/5*V12)+nat(2*V12)*520*nat(3/5*V12)+nat(4*V)*184+nat(2/3*V)*70+nat(2/3*V2)*44+nat(2/3*V12)*26+nat(3/5*V)*1820+nat(3/5*V2)*1144+nat(3/5*V12)*676+nat(4/7*V)*210+nat(4/7*V2)*132+nat(4/7*V12)*78+nat(V/2)*70+nat(V2/2)*116+nat(V12/2)*26 - Complexity: n^3 ### Maximum cost of start(V,V2,V12): nat(V)*110386+3830+nat(V)*9*nat(V2)+nat(V)*36050*nat(2*V)+nat(V)*875*nat(2*V)*nat(2*V)+nat(V2)*69599+nat(V2)*22660*nat(2*V2)+nat(V2)*550*nat(2*V2)*nat(2*V2)+nat(V2)*9*nat(2*V12)+nat(V12)*40989+nat(V12)*13390*nat(2*V12)+nat(V12)*325*nat(2*V12)*nat(2*V12)+nat(V12)*9*nat(V2/2)+nat(2*V)*378+nat(2*V)*70*nat(2*V)*nat(3/5*V)+nat(2*V)*9*nat(2*V2)+nat(2*V)*1400*nat(3/5*V)+nat(2*V2)*233+nat(2*V2)*44*nat(2*V2)*nat(3/5*V2)+nat(2*V2)*880*nat(3/5*V2)+nat(2*V12)*97+nat(2*V12)*26*nat(2*V12)*nat(3/5*V12)+nat(2*V12)*520*nat(3/5*V12)+nat(4*V)*184+nat(2/3*V)*70+nat(2/3*V2)*44+nat(2/3*V12)*26+nat(3/5*V)*1820+nat(3/5*V2)*1144+nat(3/5*V12)*676+nat(4/7*V)*210+nat(4/7*V2)*132+nat(4/7*V12)*78+nat(V/2)*70+nat(V2/2)*116+nat(V12/2)*26 Asymptotic class: n^3 * Total analysis performed in 82428 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: half(0') -> 0' half(s(0')) -> 0' half(s(s(x))) -> s(half(x)) le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) inc(0') -> 0' inc(s(x)) -> s(inc(x)) log(x) -> log2(x, 0') log2(x, y) -> if(le(x, s(0')), x, inc(y)) if(true, x, s(y)) -> y if(false, x, y) -> log2(half(x), y) The (relative) TRS S consists of the following rules: encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_half(x_1)) -> half(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_inc(x_1)) -> inc(encArg(x_1)) encArg(cons_log(x_1)) -> log(encArg(x_1)) encArg(cons_log2(x_1, x_2)) -> log2(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_half(x_1) -> half(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_inc(x_1) -> inc(encArg(x_1)) encode_log(x_1) -> log(encArg(x_1)) encode_log2(x_1, x_2) -> log2(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: half(0') -> 0' half(s(0')) -> 0' half(s(s(x))) -> s(half(x)) le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) inc(0') -> 0' inc(s(x)) -> s(inc(x)) log(x) -> log2(x, 0') log2(x, y) -> if(le(x, s(0')), x, inc(y)) if(true, x, s(y)) -> y if(false, x, y) -> log2(half(x), y) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_half(x_1)) -> half(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_inc(x_1)) -> inc(encArg(x_1)) encArg(cons_log(x_1)) -> log(encArg(x_1)) encArg(cons_log2(x_1, x_2)) -> log2(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_half(x_1) -> half(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_inc(x_1) -> inc(encArg(x_1)) encode_log(x_1) -> log(encArg(x_1)) encode_log2(x_1, x_2) -> log2(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: half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if 0' :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if s :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if true :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if false :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encArg :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_0 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_s :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_true :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_false :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if hole_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if1_4 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4 :: Nat -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if ---------------------------------------- (19) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: half, le, inc, log2, if, encArg They will be analysed ascendingly in the following order: half < if half < encArg le < log2 le < encArg inc < log2 inc < encArg log2 = if log2 < encArg if < encArg ---------------------------------------- (20) Obligation: Innermost TRS: Rules: half(0') -> 0' half(s(0')) -> 0' half(s(s(x))) -> s(half(x)) le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) inc(0') -> 0' inc(s(x)) -> s(inc(x)) log(x) -> log2(x, 0') log2(x, y) -> if(le(x, s(0')), x, inc(y)) if(true, x, s(y)) -> y if(false, x, y) -> log2(half(x), y) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_half(x_1)) -> half(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_inc(x_1)) -> inc(encArg(x_1)) encArg(cons_log(x_1)) -> log(encArg(x_1)) encArg(cons_log2(x_1, x_2)) -> log2(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_half(x_1) -> half(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_inc(x_1) -> inc(encArg(x_1)) encode_log(x_1) -> log(encArg(x_1)) encode_log2(x_1, x_2) -> log2(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: half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if 0' :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if s :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if true :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if false :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encArg :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_0 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_s :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_true :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_false :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if hole_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if1_4 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4 :: Nat -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if Generator Equations: gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(0) <=> 0' gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(+(x, 1)) <=> s(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(x)) The following defined symbols remain to be analysed: half, le, inc, log2, if, encArg They will be analysed ascendingly in the following order: half < if half < encArg le < log2 le < encArg inc < log2 inc < encArg log2 = if log2 < encArg if < encArg ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: half(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(*(2, n4_4))) -> gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n4_4), rt in Omega(1 + n4_4) Induction Base: half(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(*(2, 0))) ->_R^Omega(1) 0' Induction Step: half(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(*(2, +(n4_4, 1)))) ->_R^Omega(1) s(half(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(*(2, n4_4)))) ->_IH s(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(c5_4)) 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: half(0') -> 0' half(s(0')) -> 0' half(s(s(x))) -> s(half(x)) le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) inc(0') -> 0' inc(s(x)) -> s(inc(x)) log(x) -> log2(x, 0') log2(x, y) -> if(le(x, s(0')), x, inc(y)) if(true, x, s(y)) -> y if(false, x, y) -> log2(half(x), y) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_half(x_1)) -> half(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_inc(x_1)) -> inc(encArg(x_1)) encArg(cons_log(x_1)) -> log(encArg(x_1)) encArg(cons_log2(x_1, x_2)) -> log2(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_half(x_1) -> half(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_inc(x_1) -> inc(encArg(x_1)) encode_log(x_1) -> log(encArg(x_1)) encode_log2(x_1, x_2) -> log2(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: half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if 0' :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if s :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if true :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if false :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encArg :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_0 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_s :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_true :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_false :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if hole_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if1_4 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4 :: Nat -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if Generator Equations: gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(0) <=> 0' gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(+(x, 1)) <=> s(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(x)) The following defined symbols remain to be analysed: half, le, inc, log2, if, encArg They will be analysed ascendingly in the following order: half < if half < encArg le < log2 le < encArg inc < log2 inc < encArg log2 = if log2 < encArg if < encArg ---------------------------------------- (24) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (25) BOUNDS(n^1, INF) ---------------------------------------- (26) Obligation: Innermost TRS: Rules: half(0') -> 0' half(s(0')) -> 0' half(s(s(x))) -> s(half(x)) le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) inc(0') -> 0' inc(s(x)) -> s(inc(x)) log(x) -> log2(x, 0') log2(x, y) -> if(le(x, s(0')), x, inc(y)) if(true, x, s(y)) -> y if(false, x, y) -> log2(half(x), y) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_half(x_1)) -> half(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_inc(x_1)) -> inc(encArg(x_1)) encArg(cons_log(x_1)) -> log(encArg(x_1)) encArg(cons_log2(x_1, x_2)) -> log2(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_half(x_1) -> half(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_inc(x_1) -> inc(encArg(x_1)) encode_log(x_1) -> log(encArg(x_1)) encode_log2(x_1, x_2) -> log2(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: half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if 0' :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if s :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if true :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if false :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encArg :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_0 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_s :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_true :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_false :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if hole_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if1_4 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4 :: Nat -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if Lemmas: half(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(*(2, n4_4))) -> gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n4_4), rt in Omega(1 + n4_4) Generator Equations: gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(0) <=> 0' gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(+(x, 1)) <=> s(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(x)) The following defined symbols remain to be analysed: le, inc, log2, if, encArg They will be analysed ascendingly in the following order: le < log2 le < encArg inc < log2 inc < encArg log2 = if log2 < encArg if < encArg ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: le(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n514_4), gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n514_4)) -> true, rt in Omega(1 + n514_4) Induction Base: le(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(0), gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(0)) ->_R^Omega(1) true Induction Step: le(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(+(n514_4, 1)), gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(+(n514_4, 1))) ->_R^Omega(1) le(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n514_4), gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n514_4)) ->_IH true We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (28) Obligation: Innermost TRS: Rules: half(0') -> 0' half(s(0')) -> 0' half(s(s(x))) -> s(half(x)) le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) inc(0') -> 0' inc(s(x)) -> s(inc(x)) log(x) -> log2(x, 0') log2(x, y) -> if(le(x, s(0')), x, inc(y)) if(true, x, s(y)) -> y if(false, x, y) -> log2(half(x), y) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_half(x_1)) -> half(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_inc(x_1)) -> inc(encArg(x_1)) encArg(cons_log(x_1)) -> log(encArg(x_1)) encArg(cons_log2(x_1, x_2)) -> log2(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_half(x_1) -> half(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_inc(x_1) -> inc(encArg(x_1)) encode_log(x_1) -> log(encArg(x_1)) encode_log2(x_1, x_2) -> log2(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: half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if 0' :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if s :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if true :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if false :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encArg :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_0 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_s :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_true :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_false :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if hole_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if1_4 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4 :: Nat -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if Lemmas: half(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(*(2, n4_4))) -> gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n4_4), rt in Omega(1 + n4_4) le(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n514_4), gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n514_4)) -> true, rt in Omega(1 + n514_4) Generator Equations: gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(0) <=> 0' gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(+(x, 1)) <=> s(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(x)) The following defined symbols remain to be analysed: inc, log2, if, encArg They will be analysed ascendingly in the following order: inc < log2 inc < encArg log2 = if log2 < encArg if < encArg ---------------------------------------- (29) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: inc(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n1091_4)) -> gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n1091_4), rt in Omega(1 + n1091_4) Induction Base: inc(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(0)) ->_R^Omega(1) 0' Induction Step: inc(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(+(n1091_4, 1))) ->_R^Omega(1) s(inc(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n1091_4))) ->_IH s(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(c1092_4)) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (30) Obligation: Innermost TRS: Rules: half(0') -> 0' half(s(0')) -> 0' half(s(s(x))) -> s(half(x)) le(0', y) -> true le(s(x), 0') -> false le(s(x), s(y)) -> le(x, y) inc(0') -> 0' inc(s(x)) -> s(inc(x)) log(x) -> log2(x, 0') log2(x, y) -> if(le(x, s(0')), x, inc(y)) if(true, x, s(y)) -> y if(false, x, y) -> log2(half(x), y) encArg(0') -> 0' encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_half(x_1)) -> half(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_inc(x_1)) -> inc(encArg(x_1)) encArg(cons_log(x_1)) -> log(encArg(x_1)) encArg(cons_log2(x_1, x_2)) -> log2(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_half(x_1) -> half(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_inc(x_1) -> inc(encArg(x_1)) encode_log(x_1) -> log(encArg(x_1)) encode_log2(x_1, x_2) -> log2(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: half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if 0' :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if s :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if true :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if false :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encArg :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if cons_if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_half :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_0 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_s :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_le :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_true :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_false :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_inc :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_log :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_log2 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if encode_if :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if hole_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if1_4 :: 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4 :: Nat -> 0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if Lemmas: half(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(*(2, n4_4))) -> gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n4_4), rt in Omega(1 + n4_4) le(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n514_4), gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n514_4)) -> true, rt in Omega(1 + n514_4) inc(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n1091_4)) -> gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n1091_4), rt in Omega(1 + n1091_4) Generator Equations: gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(0) <=> 0' gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(+(x, 1)) <=> s(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(x)) The following defined symbols remain to be analysed: if, log2, encArg They will be analysed ascendingly in the following order: log2 = if log2 < encArg if < encArg ---------------------------------------- (31) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n1587_4)) -> gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n1587_4), rt in Omega(0) Induction Base: encArg(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(0)) ->_R^Omega(0) 0' Induction Step: encArg(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(+(n1587_4, 1))) ->_R^Omega(0) s(encArg(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(n1587_4))) ->_IH s(gen_0':s:true:false:cons_half:cons_le:cons_inc:cons_log:cons_log2:cons_if2_4(c1588_4)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (32) BOUNDS(1, INF)