/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 248 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, 41.6 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), 478 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), 245 ms] (28) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(gr(x, 0), y, y) cond2(false, x, y) -> cond1(gr(x, 0), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) p(0) -> 0 p(s(x)) -> x S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(true) -> true encArg(0) -> 0 encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(gr(x, 0), y, y) cond2(false, x, y) -> cond1(gr(x, 0), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(0) -> 0 encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(gr(x, 0), y, y) cond2(false, x, y) -> cond1(gr(x, 0), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(0) -> 0 encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) [1] cond2(true, x, y) -> cond1(gr(x, 0), y, y) [1] cond2(false, x, y) -> cond1(gr(x, 0), p(x), y) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(true) -> true [0] encArg(0) -> 0 [0] encArg(false) -> false [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_true -> true [0] encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_false -> false [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) [1] cond2(true, x, y) -> cond1(gr(x, 0), y, y) [1] cond2(false, x, y) -> cond1(gr(x, 0), p(x), y) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(true) -> true [0] encArg(0) -> 0 [0] encArg(false) -> false [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_true -> true [0] encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_false -> false [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] The TRS has the following type information: cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p 0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p encArg :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p Rewrite Strategy: INNERMOST ---------------------------------------- (9) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: encArg(v0) -> null_encArg [0] encode_cond1(v0, v1, v2) -> null_encode_cond1 [0] encode_true -> null_encode_true [0] encode_cond2(v0, v1, v2) -> null_encode_cond2 [0] encode_gr(v0, v1) -> null_encode_gr [0] encode_0 -> null_encode_0 [0] encode_false -> null_encode_false [0] encode_p(v0) -> null_encode_p [0] encode_s(v0) -> null_encode_s [0] cond1(v0, v1, v2) -> null_cond1 [0] cond2(v0, v1, v2) -> null_cond2 [0] gr(v0, v1) -> null_gr [0] p(v0) -> null_p [0] And the following fresh constants: null_encArg, null_encode_cond1, null_encode_true, null_encode_cond2, null_encode_gr, null_encode_0, null_encode_false, null_encode_p, null_encode_s, null_cond1, null_cond2, null_gr, null_p ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) [1] cond2(true, x, y) -> cond1(gr(x, 0), y, y) [1] cond2(false, x, y) -> cond1(gr(x, 0), p(x), y) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(true) -> true [0] encArg(0) -> 0 [0] encArg(false) -> false [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) [0] encArg(cons_p(x_1)) -> p(encArg(x_1)) [0] encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_true -> true [0] encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_false -> false [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encArg(v0) -> null_encArg [0] encode_cond1(v0, v1, v2) -> null_encode_cond1 [0] encode_true -> null_encode_true [0] encode_cond2(v0, v1, v2) -> null_encode_cond2 [0] encode_gr(v0, v1) -> null_encode_gr [0] encode_0 -> null_encode_0 [0] encode_false -> null_encode_false [0] encode_p(v0) -> null_encode_p [0] encode_s(v0) -> null_encode_s [0] cond1(v0, v1, v2) -> null_cond1 [0] cond2(v0, v1, v2) -> null_cond2 [0] gr(v0, v1) -> null_gr [0] p(v0) -> null_p [0] The TRS has the following type information: cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p 0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p encArg :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p cons_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p cons_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p cons_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p cons_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p encode_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p encode_true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p encode_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p encode_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p encode_0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p encode_false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p encode_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p encode_s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p -> true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p null_encArg :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p null_encode_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p null_encode_true :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p null_encode_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p null_encode_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p null_encode_0 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p null_encode_false :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p null_encode_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p null_encode_s :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p null_cond1 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p null_cond2 :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p null_gr :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p null_p :: true:0:false:s:cons_cond1:cons_cond2:cons_gr:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_0:null_encode_false:null_encode_p:null_encode_s:null_cond1:null_cond2:null_gr:null_p Rewrite Strategy: INNERMOST ---------------------------------------- (11) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: true => 2 0 => 0 false => 1 null_encArg => 0 null_encode_cond1 => 0 null_encode_true => 0 null_encode_cond2 => 0 null_encode_gr => 0 null_encode_0 => 0 null_encode_false => 0 null_encode_p => 0 null_encode_s => 0 null_cond1 => 0 null_cond2 => 0 null_gr => 0 null_p => 0 ---------------------------------------- (12) Obligation: Complexity RNTS consisting of the following rules: cond1(z, z', z'') -{ 1 }-> cond2(gr(x, y), x, y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0 cond1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 cond2(z, z', z'') -{ 1 }-> cond1(gr(x, 0), y, y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0 cond2(z, z', z'') -{ 1 }-> cond1(gr(x, 0), p(x), y) :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0 cond2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encArg(z) -{ 0 }-> p(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encArg(z) -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encArg(z) -{ 0 }-> 2 :|: z = 2 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0 encode_0 -{ 0 }-> 0 :|: encode_cond1(z, z', z'') -{ 0 }-> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3 encode_cond1(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_cond2(z, z', z'') -{ 0 }-> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3 encode_cond2(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_false -{ 0 }-> 1 :|: encode_false -{ 0 }-> 0 :|: encode_gr(z, z') -{ 0 }-> gr(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_p(z) -{ 0 }-> p(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_s(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 encode_true -{ 0 }-> 2 :|: encode_true -{ 0 }-> 0 :|: gr(z, z') -{ 1 }-> gr(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x gr(z, z') -{ 1 }-> 2 :|: x >= 0, z = 1 + x, z' = 0 gr(z, z') -{ 1 }-> 1 :|: z' = x, x >= 0, z = 0 gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 p(z) -{ 1 }-> x :|: x >= 0, z = 1 + x p(z) -{ 1 }-> 0 :|: z = 0 p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (13) CompleteCoflocoProof (FINISHED) Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: eq(start(V1, V, V2),0,[cond1(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]). eq(start(V1, V, V2),0,[cond2(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]). eq(start(V1, V, V2),0,[gr(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V2),0,[p(V1, Out)],[V1 >= 0]). eq(start(V1, V, V2),0,[encArg(V1, Out)],[V1 >= 0]). eq(start(V1, V, V2),0,[fun(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]). eq(start(V1, V, V2),0,[fun1(Out)],[]). eq(start(V1, V, V2),0,[fun2(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]). eq(start(V1, V, V2),0,[fun3(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V2),0,[fun4(Out)],[]). eq(start(V1, V, V2),0,[fun5(Out)],[]). eq(start(V1, V, V2),0,[fun6(V1, Out)],[V1 >= 0]). eq(start(V1, V, V2),0,[fun7(V1, Out)],[V1 >= 0]). eq(cond1(V1, V, V2, Out),1,[gr(V4, V3, Ret0),cond2(Ret0, V4, V3, Ret)],[Out = Ret,V1 = 2,V = V4,V2 = V3,V4 >= 0,V3 >= 0]). eq(cond2(V1, V, V2, Out),1,[gr(V5, 0, Ret01),cond1(Ret01, V6, V6, Ret1)],[Out = Ret1,V1 = 2,V = V5,V2 = V6,V5 >= 0,V6 >= 0]). eq(cond2(V1, V, V2, Out),1,[gr(V8, 0, Ret02),p(V8, Ret11),cond1(Ret02, Ret11, V7, Ret2)],[Out = Ret2,V = V8,V2 = V7,V1 = 1,V8 >= 0,V7 >= 0]). eq(gr(V1, V, Out),1,[],[Out = 1,V = V9,V9 >= 0,V1 = 0]). eq(gr(V1, V, Out),1,[],[Out = 2,V10 >= 0,V1 = 1 + V10,V = 0]). eq(gr(V1, V, Out),1,[gr(V12, V11, Ret3)],[Out = Ret3,V = 1 + V11,V12 >= 0,V11 >= 0,V1 = 1 + V12]). eq(p(V1, Out),1,[],[Out = 0,V1 = 0]). eq(p(V1, Out),1,[],[Out = V13,V13 >= 0,V1 = 1 + V13]). eq(encArg(V1, Out),0,[],[Out = 2,V1 = 2]). eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]). eq(encArg(V1, Out),0,[],[Out = 1,V1 = 1]). eq(encArg(V1, Out),0,[encArg(V14, Ret12)],[Out = 1 + Ret12,V1 = 1 + V14,V14 >= 0]). eq(encArg(V1, Out),0,[encArg(V16, Ret03),encArg(V17, Ret13),encArg(V15, Ret21),cond1(Ret03, Ret13, Ret21, Ret4)],[Out = Ret4,V16 >= 0,V1 = 1 + V15 + V16 + V17,V15 >= 0,V17 >= 0]). eq(encArg(V1, Out),0,[encArg(V18, Ret04),encArg(V20, Ret14),encArg(V19, Ret22),cond2(Ret04, Ret14, Ret22, Ret5)],[Out = Ret5,V18 >= 0,V1 = 1 + V18 + V19 + V20,V19 >= 0,V20 >= 0]). eq(encArg(V1, Out),0,[encArg(V22, Ret05),encArg(V21, Ret15),gr(Ret05, Ret15, Ret6)],[Out = Ret6,V22 >= 0,V1 = 1 + V21 + V22,V21 >= 0]). eq(encArg(V1, Out),0,[encArg(V23, Ret06),p(Ret06, Ret7)],[Out = Ret7,V1 = 1 + V23,V23 >= 0]). eq(fun(V1, V, V2, Out),0,[encArg(V26, Ret07),encArg(V24, Ret16),encArg(V25, Ret23),cond1(Ret07, Ret16, Ret23, Ret8)],[Out = Ret8,V26 >= 0,V25 >= 0,V24 >= 0,V1 = V26,V = V24,V2 = V25]). eq(fun1(Out),0,[],[Out = 2]). eq(fun2(V1, V, V2, Out),0,[encArg(V28, Ret08),encArg(V29, Ret17),encArg(V27, Ret24),cond2(Ret08, Ret17, Ret24, Ret9)],[Out = Ret9,V28 >= 0,V27 >= 0,V29 >= 0,V1 = V28,V = V29,V2 = V27]). eq(fun3(V1, V, Out),0,[encArg(V31, Ret09),encArg(V30, Ret18),gr(Ret09, Ret18, Ret10)],[Out = Ret10,V31 >= 0,V30 >= 0,V1 = V31,V = V30]). eq(fun4(Out),0,[],[Out = 0]). eq(fun5(Out),0,[],[Out = 1]). eq(fun6(V1, Out),0,[encArg(V32, Ret010),p(Ret010, Ret19)],[Out = Ret19,V32 >= 0,V1 = V32]). eq(fun7(V1, Out),0,[encArg(V33, Ret110)],[Out = 1 + Ret110,V33 >= 0,V1 = V33]). eq(encArg(V1, Out),0,[],[Out = 0,V34 >= 0,V1 = V34]). eq(fun(V1, V, V2, Out),0,[],[Out = 0,V36 >= 0,V2 = V37,V35 >= 0,V1 = V36,V = V35,V37 >= 0]). eq(fun1(Out),0,[],[Out = 0]). eq(fun2(V1, V, V2, Out),0,[],[Out = 0,V40 >= 0,V2 = V38,V39 >= 0,V1 = V40,V = V39,V38 >= 0]). eq(fun3(V1, V, Out),0,[],[Out = 0,V41 >= 0,V42 >= 0,V1 = V41,V = V42]). eq(fun5(Out),0,[],[Out = 0]). eq(fun6(V1, Out),0,[],[Out = 0,V43 >= 0,V1 = V43]). eq(fun7(V1, Out),0,[],[Out = 0,V44 >= 0,V1 = V44]). eq(cond1(V1, V, V2, Out),0,[],[Out = 0,V45 >= 0,V2 = V46,V47 >= 0,V1 = V45,V = V47,V46 >= 0]). eq(cond2(V1, V, V2, Out),0,[],[Out = 0,V48 >= 0,V2 = V50,V49 >= 0,V1 = V48,V = V49,V50 >= 0]). eq(gr(V1, V, Out),0,[],[Out = 0,V51 >= 0,V52 >= 0,V1 = V51,V = V52]). eq(p(V1, Out),0,[],[Out = 0,V53 >= 0,V1 = V53]). input_output_vars(cond1(V1,V,V2,Out),[V1,V,V2],[Out]). input_output_vars(cond2(V1,V,V2,Out),[V1,V,V2],[Out]). input_output_vars(gr(V1,V,Out),[V1,V],[Out]). input_output_vars(p(V1,Out),[V1],[Out]). input_output_vars(encArg(V1,Out),[V1],[Out]). input_output_vars(fun(V1,V,V2,Out),[V1,V,V2],[Out]). input_output_vars(fun1(Out),[],[Out]). input_output_vars(fun2(V1,V,V2,Out),[V1,V,V2],[Out]). input_output_vars(fun3(V1,V,Out),[V1,V],[Out]). input_output_vars(fun4(Out),[],[Out]). input_output_vars(fun5(Out),[],[Out]). input_output_vars(fun6(V1,Out),[V1],[Out]). input_output_vars(fun7(V1,Out),[V1],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [gr/3] 1. non_recursive : [p/2] 2. recursive : [cond1/4,cond2/4] 3. recursive [non_tail,multiple] : [encArg/2] 4. non_recursive : [fun/4] 5. non_recursive : [fun1/1] 6. non_recursive : [fun2/4] 7. non_recursive : [fun3/3] 8. non_recursive : [fun4/1] 9. non_recursive : [fun5/1] 10. non_recursive : [fun6/2] 11. non_recursive : [fun7/2] 12. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into gr/3 1. SCC is partially evaluated into p/2 2. SCC is partially evaluated into cond2/4 3. SCC is partially evaluated into encArg/2 4. SCC is partially evaluated into fun/4 5. SCC is partially evaluated into fun1/1 6. SCC is partially evaluated into fun2/4 7. SCC is partially evaluated into fun3/3 8. SCC is completely evaluated into other SCCs 9. SCC is partially evaluated into fun5/1 10. SCC is partially evaluated into fun6/2 11. SCC is partially evaluated into fun7/2 12. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations gr/3 * CE 17 is refined into CE [50] * CE 15 is refined into CE [51] * CE 14 is refined into CE [52] * CE 16 is refined into CE [53] ### Cost equations --> "Loop" of gr/3 * CEs [53] --> Loop 28 * CEs [50] --> Loop 29 * CEs [51] --> Loop 30 * CEs [52] --> Loop 31 ### Ranking functions of CR gr(V1,V,Out) * RF of phase [28]: [V,V1] #### Partial ranking functions of CR gr(V1,V,Out) * Partial RF of phase [28]: - RF of loop [28:1]: V V1 ### Specialization of cost equations p/2 * CE 24 is refined into CE [54] * CE 23 is refined into CE [55] * CE 25 is refined into CE [56] ### Cost equations --> "Loop" of p/2 * CEs [54] --> Loop 32 * CEs [55,56] --> Loop 33 ### Ranking functions of CR p(V1,Out) #### Partial ranking functions of CR p(V1,Out) ### Specialization of cost equations cond2/4 * CE 19 is refined into CE [57,58,59] * CE 18 is refined into CE [60,61,62,63,64] * CE 22 is refined into CE [65] * CE 21 is refined into CE [66,67,68] * CE 20 is refined into CE [69,70,71,72,73,74,75] ### Cost equations --> "Loop" of cond2/4 * CEs [68] --> Loop 34 * CEs [67] --> Loop 35 * CEs [66] --> Loop 36 * CEs [75] --> Loop 37 * CEs [74] --> Loop 38 * CEs [73] --> Loop 39 * CEs [70] --> Loop 40 * CEs [72] --> Loop 41 * CEs [69,71] --> Loop 42 * CEs [57,58,59] --> Loop 43 * CEs [60,61,62,63,64,65] --> Loop 44 ### Ranking functions of CR cond2(V1,V,V2,Out) * RF of phase [38]: [V-1] #### Partial ranking functions of CR cond2(V1,V,V2,Out) * Partial RF of phase [38]: - RF of loop [38:1]: V-1 ### Specialization of cost equations encArg/2 * CE 29 is refined into CE [76] * CE 28 is refined into CE [77] * CE 30 is refined into CE [78] * CE 31 is refined into CE [79] * CE 34 is refined into CE [80,81] * CE 33 is refined into CE [82,83,84,85,86] * CE 27 is refined into CE [87,88,89,90,91,92,93] * CE 26 is refined into CE [94] * CE 32 is refined into CE [95,96] ### Cost equations --> "Loop" of encArg/2 * CEs [88,89] --> Loop 45 * CEs [87,90,91,92,93,94,95,96] --> Loop 46 * CEs [86] --> Loop 47 * CEs [83] --> Loop 48 * CEs [85] --> Loop 49 * CEs [82] --> Loop 50 * CEs [84] --> Loop 51 * CEs [79] --> Loop 52 * CEs [81] --> Loop 53 * CEs [80] --> Loop 54 * CEs [76] --> Loop 55 * CEs [77] --> Loop 56 * CEs [78] --> Loop 57 ### Ranking functions of CR encArg(V1,Out) * RF of phase [45,46,47,48,49,50,51,52,53,54]: [V1] #### Partial ranking functions of CR encArg(V1,Out) * Partial RF of phase [45,46,47,48,49,50,51,52,53,54]: - RF of loop [45:1,45:2,45:3,46:1,46:2,46:3,47:1,47:2,48:1,48:2,49:1,49:2,50:1,50:2,51:1,51:2,52:1,53:1,54:1]: V1 ### Specialization of cost equations fun/4 * CE 35 is refined into CE [97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123] * CE 36 is refined into CE [124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189] * CE 37 is refined into CE [190] ### Cost equations --> "Loop" of fun/4 * CEs [100,101,102,118,119,120,140,141,142,143,144,145,146,147,148,149,150] --> Loop 58 * CEs [98,104,107,113,116,122,131,132,133,134,135,153,154,164,165,166,167,168,186,187] --> Loop 59 * CEs [97,99,103,105,106,108,109,110,111,112,114,115,117,121,123,124,125,126,127,128,129,130,136,137,138,139,151,152,155,156,157,158,159,160,161,162,163,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,188,189,190] --> Loop 60 ### Ranking functions of CR fun(V1,V,V2,Out) #### Partial ranking functions of CR fun(V1,V,V2,Out) ### Specialization of cost equations fun1/1 * CE 38 is refined into CE [191] * CE 39 is refined into CE [192] ### Cost equations --> "Loop" of fun1/1 * CEs [191] --> Loop 61 * CEs [192] --> Loop 62 ### Ranking functions of CR fun1(Out) #### Partial ranking functions of CR fun1(Out) ### Specialization of cost equations fun2/4 * CE 40 is refined into CE [193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237] * CE 41 is refined into CE [238] ### Cost equations --> "Loop" of fun2/4 * CEs [199,200,201,202,203,204,232,233,234] --> Loop 63 * CEs [195,196,207,208,213,214,225,226,230,236] --> Loop 64 * CEs [193,194,197,198,205,206,209,210,211,212,215,216,217,218,219,220,221,222,223,224,227,228,229,231,235,237,238] --> Loop 65 ### Ranking functions of CR fun2(V1,V,V2,Out) #### Partial ranking functions of CR fun2(V1,V,V2,Out) ### Specialization of cost equations fun3/3 * CE 42 is refined into CE [239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264] * CE 43 is refined into CE [265] ### Cost equations --> "Loop" of fun3/3 * CEs [247] --> Loop 66 * CEs [244,246,261] --> Loop 67 * CEs [245,262] --> Loop 68 * CEs [240,243,249,251,254,257] --> Loop 69 * CEs [239,242,248,253,256,259,263] --> Loop 70 * CEs [241,250,252,255,258,260,264,265] --> Loop 71 ### Ranking functions of CR fun3(V1,V,Out) #### Partial ranking functions of CR fun3(V1,V,Out) ### Specialization of cost equations fun5/1 * CE 44 is refined into CE [266] * CE 45 is refined into CE [267] ### Cost equations --> "Loop" of fun5/1 * CEs [266] --> Loop 72 * CEs [267] --> Loop 73 ### Ranking functions of CR fun5(Out) #### Partial ranking functions of CR fun5(Out) ### Specialization of cost equations fun6/2 * CE 46 is refined into CE [268,269,270,271,272] * CE 47 is refined into CE [273] ### Cost equations --> "Loop" of fun6/2 * CEs [269,271] --> Loop 74 * CEs [268,270,272,273] --> Loop 75 ### Ranking functions of CR fun6(V1,Out) #### Partial ranking functions of CR fun6(V1,Out) ### Specialization of cost equations fun7/2 * CE 48 is refined into CE [274,275,276] * CE 49 is refined into CE [277] ### Cost equations --> "Loop" of fun7/2 * CEs [276] --> Loop 76 * CEs [277] --> Loop 77 * CEs [274,275] --> Loop 78 ### Ranking functions of CR fun7(V1,Out) #### Partial ranking functions of CR fun7(V1,Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [278] * CE 2 is refined into CE [279,280,281,282,283,284,285] * CE 3 is refined into CE [286,287] * CE 4 is refined into CE [288,289,290,291,292] * CE 5 is refined into CE [293,294] * CE 6 is refined into CE [295,296,297] * CE 7 is refined into CE [298,299] * CE 8 is refined into CE [300,301] * CE 9 is refined into CE [302,303] * CE 10 is refined into CE [304,305,306] * CE 11 is refined into CE [307,308] * CE 12 is refined into CE [309,310] * CE 13 is refined into CE [311,312,313] ### Cost equations --> "Loop" of start/3 * CEs [278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313] --> Loop 79 ### Ranking functions of CR start(V1,V,V2) #### Partial ranking functions of CR start(V1,V,V2) Computing Bounds ===================================== #### Cost of chains of gr(V1,V,Out): * Chain [[28],31]: 1*it(28)+1 Such that:it(28) =< V1 with precondition: [Out=1,V1>=1,V>=V1] * Chain [[28],30]: 1*it(28)+1 Such that:it(28) =< V with precondition: [Out=2,V>=1,V1>=V+1] * Chain [[28],29]: 1*it(28)+0 Such that:it(28) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [31]: 1 with precondition: [V1=0,Out=1,V>=0] * Chain [30]: 1 with precondition: [V=0,Out=2,V1>=1] * Chain [29]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of p(V1,Out): * Chain [33]: 1 with precondition: [Out=0,V1>=0] * Chain [32]: 1 with precondition: [V1=Out+1,V1>=1] #### Cost of chains of cond2(V1,V,V2,Out): * Chain [[38],44]: 5*it(38)+1*s(6)+3 Such that:aux(3) =< V it(38) =< aux(3) s(6) =< it(38)*aux(3) with precondition: [V1=1,Out=0,V>=2,V2+1>=V] * Chain [[38],42,44]: 5*it(38)+1*s(6)+8 Such that:aux(4) =< V it(38) =< aux(4) s(6) =< it(38)*aux(4) with precondition: [V1=1,Out=0,V>=2,V2+1>=V] * Chain [[38],40,44]: 5*it(38)+1*s(6)+1*s(7)+7 Such that:s(7) =< V2 aux(5) =< V it(38) =< aux(5) s(6) =< it(38)*aux(5) with precondition: [V1=1,Out=0,V>=2,V2+1>=V] * Chain [[38],39,44]: 5*it(38)+1*s(6)+1*s(8)+7 Such that:s(8) =< V2 aux(6) =< V it(38) =< aux(6) s(6) =< it(38)*aux(6) with precondition: [V1=1,Out=0,V>=2,V2+1>=V] * Chain [44]: 3 with precondition: [Out=0,V1>=0,V>=0,V2>=0] * Chain [43]: 2 with precondition: [V1=2,Out=0,V>=0,V2>=0] * Chain [42,44]: 8 with precondition: [V1=1,Out=0,V>=1,V2>=0] * Chain [41,44]: 8 with precondition: [V1=1,V2=0,Out=0,V>=2] * Chain [41,43]: 7 with precondition: [V1=1,V2=0,Out=0,V>=2] * Chain [41,36,44]: 12 with precondition: [V1=1,V2=0,Out=0,V>=2] * Chain [41,35,44]: 11 with precondition: [V1=1,V2=0,Out=0,V>=2] * Chain [40,44]: 1*s(7)+7 Such that:s(7) =< V2 with precondition: [V1=1,Out=0,V>=1,V2>=0] * Chain [39,44]: 1*s(8)+7 Such that:s(8) =< V2 with precondition: [V1=1,Out=0,V>=1,V2>=0] * Chain [37,44]: 1*s(11)+8 Such that:s(11) =< V2 with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [37,43]: 1*s(11)+7 Such that:s(11) =< V2 with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [37,35,44]: 2*s(10)+11 Such that:aux(7) =< V2 s(10) =< aux(7) with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [37,34,[38],44]: 7*it(38)+1*s(6)+12 Such that:aux(9) =< V2 it(38) =< aux(9) s(6) =< it(38)*aux(9) with precondition: [V1=1,Out=0,V2>=2,V>=V2+2] * Chain [37,34,[38],42,44]: 7*it(38)+1*s(6)+17 Such that:aux(11) =< V2 it(38) =< aux(11) s(6) =< it(38)*aux(11) with precondition: [V1=1,Out=0,V2>=2,V>=V2+2] * Chain [37,34,[38],40,44]: 8*it(38)+1*s(6)+16 Such that:aux(13) =< V2 it(38) =< aux(13) s(6) =< it(38)*aux(13) with precondition: [V1=1,Out=0,V2>=2,V>=V2+2] * Chain [37,34,[38],39,44]: 8*it(38)+1*s(6)+16 Such that:aux(15) =< V2 it(38) =< aux(15) s(6) =< it(38)*aux(15) with precondition: [V1=1,Out=0,V2>=2,V>=V2+2] * Chain [37,34,44]: 2*s(11)+12 Such that:aux(16) =< V2 s(11) =< aux(16) with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [37,34,42,44]: 2*s(11)+17 Such that:aux(17) =< V2 s(11) =< aux(17) with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [37,34,40,44]: 3*s(7)+16 Such that:aux(19) =< V2 s(7) =< aux(19) with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [37,34,39,44]: 3*s(8)+16 Such that:aux(21) =< V2 s(8) =< aux(21) with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [36,44]: 7 with precondition: [V1=2,V2=0,Out=0,V>=1] * Chain [35,44]: 1*s(10)+6 Such that:s(10) =< V2 with precondition: [V1=2,Out=0,V>=1,V2>=0] * Chain [34,[38],44]: 6*it(38)+1*s(6)+7 Such that:aux(8) =< V2 it(38) =< aux(8) s(6) =< it(38)*aux(8) with precondition: [V1=2,Out=0,V>=1,V2>=2] * Chain [34,[38],42,44]: 6*it(38)+1*s(6)+12 Such that:aux(10) =< V2 it(38) =< aux(10) s(6) =< it(38)*aux(10) with precondition: [V1=2,Out=0,V>=1,V2>=2] * Chain [34,[38],40,44]: 7*it(38)+1*s(6)+11 Such that:aux(12) =< V2 it(38) =< aux(12) s(6) =< it(38)*aux(12) with precondition: [V1=2,Out=0,V>=1,V2>=2] * Chain [34,[38],39,44]: 7*it(38)+1*s(6)+11 Such that:aux(14) =< V2 it(38) =< aux(14) s(6) =< it(38)*aux(14) with precondition: [V1=2,Out=0,V>=1,V2>=2] * Chain [34,44]: 1*s(12)+7 Such that:s(12) =< V2 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [34,42,44]: 1*s(12)+12 Such that:s(12) =< V2 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [34,40,44]: 2*s(7)+11 Such that:aux(18) =< V2 s(7) =< aux(18) with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [34,39,44]: 2*s(8)+11 Such that:aux(20) =< V2 s(8) =< aux(20) with precondition: [V1=2,Out=0,V>=1,V2>=1] #### Cost of chains of encArg(V1,Out): * Chain [57]: 0 with precondition: [V1=1,Out=1] * Chain [56]: 0 with precondition: [V1=2,Out=2] * Chain [55]: 0 with precondition: [Out=0,V1>=0] * Chain [multiple([45,46,47,48,49,50,51,52,53,54],[[57],[56],[55]])]: 19*it(45)+19*it(46)+1*it(47)+1*it(48)+1*it(49)+1*it(50)+2*it(53)+20*s(136)+4*s(137)+260*s(139)+24*s(140)+130*s(141)+20*s(142)+1*s(145)+1*s(146)+1*s(147)+0 Such that:it([57]) =< 2/3*V1+1/3 aux(41) =< V1 aux(42) =< 2*V1+1 aux(43) =< V1/2 aux(44) =< V1/3 aux(45) =< 2/3*V1 aux(46) =< 2/5*V1 it(46) =< aux(41) it(47) =< aux(41) it(48) =< aux(41) it(49) =< aux(41) it(50) =< aux(41) it(51) =< aux(41) it(53) =< aux(41) it([57]) =< aux(41) it([55]) =< aux(42) it([57]) =< aux(42) it(49) =< aux(43) it(45) =< aux(44) it(48) =< aux(45) it(49) =< aux(45) it(47) =< aux(46) aux(34) =< aux(41)+2 aux(39) =< aux(41)+1 aux(32) =< aux(41) aux(33) =< aux(41)+3 it(49) =< it([55])*(1/2)+aux(43) it(50) =< it([55])*(1/2)+aux(43) it(51) =< it([55])*(1/2)+aux(43) it(48) =< it([55])*(1/3)+aux(45) it(49) =< it([55])*(1/3)+aux(45) it(50) =< it([55])*(1/3)+aux(45) it(51) =< it([55])*(1/3)+aux(45) it(47) =< it([55])*(3/5)+it([57])*(1/5)+aux(46) it(48) =< it([55])*(3/5)+it([57])*(1/5)+aux(46) it(49) =< it([55])*(3/5)+it([57])*(1/5)+aux(46) it(50) =< it([55])*(3/5)+it([57])*(1/5)+aux(46) it(51) =< it([55])*(3/5)+it([57])*(1/5)+aux(46) it(45) =< it([55])*(1/3)+aux(44) it(46) =< it([55])*(1/3)+aux(44) s(147) =< it(51)*aux(34) s(146) =< it(49)*aux(39) s(145) =< it(47)*aux(32) s(143) =< it(46)*aux(34) s(144) =< it(46)*aux(33) s(138) =< it(45)*aux(32) s(141) =< s(144) s(142) =< s(141)*aux(33) s(139) =< s(143) s(140) =< s(139)*aux(34) s(136) =< s(138) s(137) =< s(136)*aux(41) with precondition: [V1>=1,Out>=0,V1>=Out] #### Cost of chains of fun(V1,V,V2,Out): * Chain [60]: 361*s(187)+19*s(188)+19*s(189)+19*s(190)+19*s(191)+38*s(193)+361*s(194)+19*s(199)+19*s(200)+19*s(201)+2470*s(205)+380*s(206)+4940*s(207)+456*s(208)+380*s(209)+76*s(210)+532*s(218)+28*s(219)+28*s(220)+28*s(221)+28*s(222)+360*s(224)+532*s(225)+28*s(230)+28*s(231)+28*s(232)+3640*s(236)+560*s(237)+7280*s(238)+672*s(239)+560*s(240)+112*s(241)+589*s(249)+31*s(250)+31*s(251)+31*s(252)+31*s(253)+747*s(255)+589*s(256)+31*s(261)+31*s(262)+31*s(263)+4030*s(267)+620*s(268)+8060*s(269)+744*s(270)+620*s(271)+124*s(272)+60*s(805)+52*s(903)+259*s(2534)+40*s(2535)+83*s(2678)+8*s(2684)+19 Such that:aux(87) =< 1 aux(88) =< 2 aux(89) =< V1 aux(90) =< 2*V1+1 aux(91) =< V1/2 aux(92) =< V1/3 aux(93) =< 2/3*V1 aux(94) =< 2/3*V1+1/3 aux(95) =< 2/5*V1 aux(96) =< V aux(97) =< 2*V+1 aux(98) =< V/2 aux(99) =< V/3 aux(100) =< 2/3*V aux(101) =< 2/3*V+1/3 aux(102) =< 2/5*V aux(103) =< V2 aux(104) =< 2*V2+1 aux(105) =< V2/2 aux(106) =< V2/3 aux(107) =< 2/3*V2 aux(108) =< 2/3*V2+1/3 aux(109) =< 2/5*V2 s(185) =< aux(94) s(216) =< aux(101) s(247) =< aux(108) s(2534) =< aux(88) s(2535) =< s(2534)*aux(88) s(249) =< aux(103) s(250) =< aux(103) s(251) =< aux(103) s(252) =< aux(103) s(253) =< aux(103) s(254) =< aux(103) s(255) =< aux(103) s(247) =< aux(103) s(247) =< aux(104) s(252) =< aux(105) s(256) =< aux(106) s(251) =< aux(107) s(252) =< aux(107) s(250) =< aux(109) s(257) =< aux(103)+2 s(258) =< aux(103)+1 s(259) =< aux(103) s(260) =< aux(103)+3 s(252) =< aux(104)*(1/2)+aux(105) s(253) =< aux(104)*(1/2)+aux(105) s(254) =< aux(104)*(1/2)+aux(105) s(251) =< aux(104)*(1/3)+aux(107) s(252) =< aux(104)*(1/3)+aux(107) s(253) =< aux(104)*(1/3)+aux(107) s(254) =< aux(104)*(1/3)+aux(107) s(250) =< aux(104)*(3/5)+s(247)*(1/5)+aux(109) s(251) =< aux(104)*(3/5)+s(247)*(1/5)+aux(109) s(252) =< aux(104)*(3/5)+s(247)*(1/5)+aux(109) s(253) =< aux(104)*(3/5)+s(247)*(1/5)+aux(109) s(254) =< aux(104)*(3/5)+s(247)*(1/5)+aux(109) s(256) =< aux(104)*(1/3)+aux(106) s(249) =< aux(104)*(1/3)+aux(106) s(261) =< s(254)*s(257) s(262) =< s(252)*s(258) s(263) =< s(250)*s(259) s(264) =< s(249)*s(257) s(265) =< s(249)*s(260) s(266) =< s(256)*s(259) s(267) =< s(265) s(268) =< s(267)*s(260) s(269) =< s(264) s(270) =< s(269)*s(257) s(271) =< s(266) s(272) =< s(271)*aux(103) s(805) =< s(255)*aux(103) s(2678) =< aux(87) s(2684) =< s(2678)*aux(87) s(218) =< aux(96) s(219) =< aux(96) s(220) =< aux(96) s(221) =< aux(96) s(222) =< aux(96) s(223) =< aux(96) s(224) =< aux(96) s(216) =< aux(96) s(216) =< aux(97) s(221) =< aux(98) s(225) =< aux(99) s(220) =< aux(100) s(221) =< aux(100) s(219) =< aux(102) s(226) =< aux(96)+2 s(227) =< aux(96)+1 s(228) =< aux(96) s(229) =< aux(96)+3 s(221) =< aux(97)*(1/2)+aux(98) s(222) =< aux(97)*(1/2)+aux(98) s(223) =< aux(97)*(1/2)+aux(98) s(220) =< aux(97)*(1/3)+aux(100) s(221) =< aux(97)*(1/3)+aux(100) s(222) =< aux(97)*(1/3)+aux(100) s(223) =< aux(97)*(1/3)+aux(100) s(219) =< aux(97)*(3/5)+s(216)*(1/5)+aux(102) s(220) =< aux(97)*(3/5)+s(216)*(1/5)+aux(102) s(221) =< aux(97)*(3/5)+s(216)*(1/5)+aux(102) s(222) =< aux(97)*(3/5)+s(216)*(1/5)+aux(102) s(223) =< aux(97)*(3/5)+s(216)*(1/5)+aux(102) s(225) =< aux(97)*(1/3)+aux(99) s(218) =< aux(97)*(1/3)+aux(99) s(230) =< s(223)*s(226) s(231) =< s(221)*s(227) s(232) =< s(219)*s(228) s(233) =< s(218)*s(226) s(234) =< s(218)*s(229) s(235) =< s(225)*s(228) s(236) =< s(234) s(237) =< s(236)*s(229) s(238) =< s(233) s(239) =< s(238)*s(226) s(240) =< s(235) s(241) =< s(240)*aux(96) s(187) =< aux(89) s(188) =< aux(89) s(189) =< aux(89) s(190) =< aux(89) s(191) =< aux(89) s(192) =< aux(89) s(193) =< aux(89) s(185) =< aux(89) s(185) =< aux(90) s(190) =< aux(91) s(194) =< aux(92) s(189) =< aux(93) s(190) =< aux(93) s(188) =< aux(95) s(195) =< aux(89)+2 s(196) =< aux(89)+1 s(197) =< aux(89) s(198) =< aux(89)+3 s(190) =< aux(90)*(1/2)+aux(91) s(191) =< aux(90)*(1/2)+aux(91) s(192) =< aux(90)*(1/2)+aux(91) s(189) =< aux(90)*(1/3)+aux(93) s(190) =< aux(90)*(1/3)+aux(93) s(191) =< aux(90)*(1/3)+aux(93) s(192) =< aux(90)*(1/3)+aux(93) s(188) =< aux(90)*(3/5)+s(185)*(1/5)+aux(95) s(189) =< aux(90)*(3/5)+s(185)*(1/5)+aux(95) s(190) =< aux(90)*(3/5)+s(185)*(1/5)+aux(95) s(191) =< aux(90)*(3/5)+s(185)*(1/5)+aux(95) s(192) =< aux(90)*(3/5)+s(185)*(1/5)+aux(95) s(194) =< aux(90)*(1/3)+aux(92) s(187) =< aux(90)*(1/3)+aux(92) s(199) =< s(192)*s(195) s(200) =< s(190)*s(196) s(201) =< s(188)*s(197) s(202) =< s(187)*s(195) s(203) =< s(187)*s(198) s(204) =< s(194)*s(197) s(205) =< s(203) s(206) =< s(205)*s(198) s(207) =< s(202) s(208) =< s(207)*s(195) s(209) =< s(204) s(210) =< s(209)*aux(89) s(903) =< s(224)*aux(96) with precondition: [Out=0,V1>=0,V>=0,V2>=0] * Chain [59]: 171*s(2845)+9*s(2846)+9*s(2847)+9*s(2848)+9*s(2849)+18*s(2851)+171*s(2852)+9*s(2857)+9*s(2858)+9*s(2859)+1170*s(2863)+180*s(2864)+2340*s(2865)+216*s(2866)+180*s(2867)+36*s(2868)+247*s(2876)+13*s(2877)+13*s(2878)+13*s(2879)+13*s(2880)+148*s(2882)+247*s(2883)+13*s(2888)+13*s(2889)+13*s(2890)+1690*s(2894)+260*s(2895)+3380*s(2896)+312*s(2897)+260*s(2898)+52*s(2899)+650*s(3057)+56*s(3060)+24*s(3128)+19 Such that:aux(124) =< 2 aux(125) =< V1 aux(126) =< 2*V1+1 aux(127) =< V1/2 aux(128) =< V1/3 aux(129) =< 2/3*V1 aux(130) =< 2/3*V1+1/3 aux(131) =< 2/5*V1 aux(132) =< V aux(133) =< 2*V+1 aux(134) =< V/2 aux(135) =< V/3 aux(136) =< 2/3*V aux(137) =< 2/3*V+1/3 aux(138) =< 2/5*V s(2843) =< aux(130) s(2874) =< aux(137) s(3057) =< aux(124) s(3060) =< s(3057)*aux(124) s(2876) =< aux(132) s(2877) =< aux(132) s(2878) =< aux(132) s(2879) =< aux(132) s(2880) =< aux(132) s(2881) =< aux(132) s(2882) =< aux(132) s(2874) =< aux(132) s(2874) =< aux(133) s(2879) =< aux(134) s(2883) =< aux(135) s(2878) =< aux(136) s(2879) =< aux(136) s(2877) =< aux(138) s(2884) =< aux(132)+2 s(2885) =< aux(132)+1 s(2886) =< aux(132) s(2887) =< aux(132)+3 s(2879) =< aux(133)*(1/2)+aux(134) s(2880) =< aux(133)*(1/2)+aux(134) s(2881) =< aux(133)*(1/2)+aux(134) s(2878) =< aux(133)*(1/3)+aux(136) s(2879) =< aux(133)*(1/3)+aux(136) s(2880) =< aux(133)*(1/3)+aux(136) s(2881) =< aux(133)*(1/3)+aux(136) s(2877) =< aux(133)*(3/5)+s(2874)*(1/5)+aux(138) s(2878) =< aux(133)*(3/5)+s(2874)*(1/5)+aux(138) s(2879) =< aux(133)*(3/5)+s(2874)*(1/5)+aux(138) s(2880) =< aux(133)*(3/5)+s(2874)*(1/5)+aux(138) s(2881) =< aux(133)*(3/5)+s(2874)*(1/5)+aux(138) s(2883) =< aux(133)*(1/3)+aux(135) s(2876) =< aux(133)*(1/3)+aux(135) s(2888) =< s(2881)*s(2884) s(2889) =< s(2879)*s(2885) s(2890) =< s(2877)*s(2886) s(2891) =< s(2876)*s(2884) s(2892) =< s(2876)*s(2887) s(2893) =< s(2883)*s(2886) s(2894) =< s(2892) s(2895) =< s(2894)*s(2887) s(2896) =< s(2891) s(2897) =< s(2896)*s(2884) s(2898) =< s(2893) s(2899) =< s(2898)*aux(132) s(2845) =< aux(125) s(2846) =< aux(125) s(2847) =< aux(125) s(2848) =< aux(125) s(2849) =< aux(125) s(2850) =< aux(125) s(2851) =< aux(125) s(2843) =< aux(125) s(2843) =< aux(126) s(2848) =< aux(127) s(2852) =< aux(128) s(2847) =< aux(129) s(2848) =< aux(129) s(2846) =< aux(131) s(2853) =< aux(125)+2 s(2854) =< aux(125)+1 s(2855) =< aux(125) s(2856) =< aux(125)+3 s(2848) =< aux(126)*(1/2)+aux(127) s(2849) =< aux(126)*(1/2)+aux(127) s(2850) =< aux(126)*(1/2)+aux(127) s(2847) =< aux(126)*(1/3)+aux(129) s(2848) =< aux(126)*(1/3)+aux(129) s(2849) =< aux(126)*(1/3)+aux(129) s(2850) =< aux(126)*(1/3)+aux(129) s(2846) =< aux(126)*(3/5)+s(2843)*(1/5)+aux(131) s(2847) =< aux(126)*(3/5)+s(2843)*(1/5)+aux(131) s(2848) =< aux(126)*(3/5)+s(2843)*(1/5)+aux(131) s(2849) =< aux(126)*(3/5)+s(2843)*(1/5)+aux(131) s(2850) =< aux(126)*(3/5)+s(2843)*(1/5)+aux(131) s(2852) =< aux(126)*(1/3)+aux(128) s(2845) =< aux(126)*(1/3)+aux(128) s(2857) =< s(2850)*s(2853) s(2858) =< s(2848)*s(2854) s(2859) =< s(2846)*s(2855) s(2860) =< s(2845)*s(2853) s(2861) =< s(2845)*s(2856) s(2862) =< s(2852)*s(2855) s(2863) =< s(2861) s(2864) =< s(2863)*s(2856) s(2865) =< s(2860) s(2866) =< s(2865)*s(2853) s(2867) =< s(2862) s(2868) =< s(2867)*aux(125) s(3128) =< s(2882)*aux(132) with precondition: [V2=2,Out=0,V1>=0,V>=0] * Chain [58]: 266*s(3615)+14*s(3616)+14*s(3617)+14*s(3618)+14*s(3619)+28*s(3621)+266*s(3622)+14*s(3627)+14*s(3628)+14*s(3629)+1820*s(3633)+280*s(3634)+3640*s(3635)+336*s(3636)+280*s(3637)+56*s(3638)+152*s(3646)+8*s(3647)+8*s(3648)+8*s(3649)+8*s(3650)+113*s(3652)+152*s(3653)+8*s(3658)+8*s(3659)+8*s(3660)+1040*s(3664)+160*s(3665)+2080*s(3666)+192*s(3667)+160*s(3668)+32*s(3669)+259*s(3828)+40*s(3829)+8*s(3964)+83*s(4096)+8*s(4102)+19 Such that:aux(147) =< 1 aux(148) =< 2 aux(149) =< V1 aux(150) =< 2*V1+1 aux(151) =< V1/2 aux(152) =< V1/3 aux(153) =< 2/3*V1 aux(154) =< 2/3*V1+1/3 aux(155) =< 2/5*V1 aux(156) =< V2 aux(157) =< 2*V2+1 aux(158) =< V2/2 aux(159) =< V2/3 aux(160) =< 2/3*V2 aux(161) =< 2/3*V2+1/3 aux(162) =< 2/5*V2 s(3613) =< aux(154) s(3644) =< aux(161) s(3828) =< aux(148) s(3829) =< s(3828)*aux(148) s(3646) =< aux(156) s(3647) =< aux(156) s(3648) =< aux(156) s(3649) =< aux(156) s(3650) =< aux(156) s(3651) =< aux(156) s(3652) =< aux(156) s(3644) =< aux(156) s(3644) =< aux(157) s(3649) =< aux(158) s(3653) =< aux(159) s(3648) =< aux(160) s(3649) =< aux(160) s(3647) =< aux(162) s(3654) =< aux(156)+2 s(3655) =< aux(156)+1 s(3656) =< aux(156) s(3657) =< aux(156)+3 s(3649) =< aux(157)*(1/2)+aux(158) s(3650) =< aux(157)*(1/2)+aux(158) s(3651) =< aux(157)*(1/2)+aux(158) s(3648) =< aux(157)*(1/3)+aux(160) s(3649) =< aux(157)*(1/3)+aux(160) s(3650) =< aux(157)*(1/3)+aux(160) s(3651) =< aux(157)*(1/3)+aux(160) s(3647) =< aux(157)*(3/5)+s(3644)*(1/5)+aux(162) s(3648) =< aux(157)*(3/5)+s(3644)*(1/5)+aux(162) s(3649) =< aux(157)*(3/5)+s(3644)*(1/5)+aux(162) s(3650) =< aux(157)*(3/5)+s(3644)*(1/5)+aux(162) s(3651) =< aux(157)*(3/5)+s(3644)*(1/5)+aux(162) s(3653) =< aux(157)*(1/3)+aux(159) s(3646) =< aux(157)*(1/3)+aux(159) s(3658) =< s(3651)*s(3654) s(3659) =< s(3649)*s(3655) s(3660) =< s(3647)*s(3656) s(3661) =< s(3646)*s(3654) s(3662) =< s(3646)*s(3657) s(3663) =< s(3653)*s(3656) s(3664) =< s(3662) s(3665) =< s(3664)*s(3657) s(3666) =< s(3661) s(3667) =< s(3666)*s(3654) s(3668) =< s(3663) s(3669) =< s(3668)*aux(156) s(3615) =< aux(149) s(3616) =< aux(149) s(3617) =< aux(149) s(3618) =< aux(149) s(3619) =< aux(149) s(3620) =< aux(149) s(3621) =< aux(149) s(3613) =< aux(149) s(3613) =< aux(150) s(3618) =< aux(151) s(3622) =< aux(152) s(3617) =< aux(153) s(3618) =< aux(153) s(3616) =< aux(155) s(3623) =< aux(149)+2 s(3624) =< aux(149)+1 s(3625) =< aux(149) s(3626) =< aux(149)+3 s(3618) =< aux(150)*(1/2)+aux(151) s(3619) =< aux(150)*(1/2)+aux(151) s(3620) =< aux(150)*(1/2)+aux(151) s(3617) =< aux(150)*(1/3)+aux(153) s(3618) =< aux(150)*(1/3)+aux(153) s(3619) =< aux(150)*(1/3)+aux(153) s(3620) =< aux(150)*(1/3)+aux(153) s(3616) =< aux(150)*(3/5)+s(3613)*(1/5)+aux(155) s(3617) =< aux(150)*(3/5)+s(3613)*(1/5)+aux(155) s(3618) =< aux(150)*(3/5)+s(3613)*(1/5)+aux(155) s(3619) =< aux(150)*(3/5)+s(3613)*(1/5)+aux(155) s(3620) =< aux(150)*(3/5)+s(3613)*(1/5)+aux(155) s(3622) =< aux(150)*(1/3)+aux(152) s(3615) =< aux(150)*(1/3)+aux(152) s(3627) =< s(3620)*s(3623) s(3628) =< s(3618)*s(3624) s(3629) =< s(3616)*s(3625) s(3630) =< s(3615)*s(3623) s(3631) =< s(3615)*s(3626) s(3632) =< s(3622)*s(3625) s(3633) =< s(3631) s(3634) =< s(3633)*s(3626) s(3635) =< s(3630) s(3636) =< s(3635)*s(3623) s(3637) =< s(3632) s(3638) =< s(3637)*aux(149) s(3964) =< s(3652)*aux(156) s(4096) =< aux(147) s(4102) =< s(4096)*aux(147) with precondition: [V=2,Out=0,V1>=0,V2>=0] #### Cost of chains of fun1(Out): * Chain [62]: 0 with precondition: [Out=0] * Chain [61]: 0 with precondition: [Out=2] #### Cost of chains of fun2(V1,V,V2,Out): * Chain [65]: 152*s(4536)+8*s(4537)+8*s(4538)+8*s(4539)+8*s(4540)+16*s(4542)+152*s(4543)+8*s(4548)+8*s(4549)+8*s(4550)+1040*s(4554)+160*s(4555)+2080*s(4556)+192*s(4557)+160*s(4558)+32*s(4559)+190*s(4567)+10*s(4568)+10*s(4569)+10*s(4570)+10*s(4571)+140*s(4573)+190*s(4574)+10*s(4579)+10*s(4580)+10*s(4581)+1300*s(4585)+200*s(4586)+2600*s(4587)+240*s(4588)+200*s(4589)+40*s(4590)+228*s(4598)+12*s(4599)+12*s(4600)+12*s(4601)+12*s(4602)+525*s(4604)+228*s(4605)+12*s(4610)+12*s(4611)+12*s(4612)+1560*s(4616)+240*s(4617)+3120*s(4618)+288*s(4619)+240*s(4620)+48*s(4621)+24*s(4626)+48*s(4627)+141*s(5299)+20*s(5300)+17 Such that:aux(201) =< 2 aux(202) =< V1 aux(203) =< 2*V1+1 aux(204) =< V1/2 aux(205) =< V1/3 aux(206) =< 2/3*V1 aux(207) =< 2/3*V1+1/3 aux(208) =< 2/5*V1 aux(209) =< V aux(210) =< 2*V+1 aux(211) =< V/2 aux(212) =< V/3 aux(213) =< 2/3*V aux(214) =< 2/3*V+1/3 aux(215) =< 2/5*V aux(216) =< V2 aux(217) =< 2*V2+1 aux(218) =< V2/2 aux(219) =< V2/3 aux(220) =< 2/3*V2 aux(221) =< 2/3*V2+1/3 aux(222) =< 2/5*V2 s(4534) =< aux(207) s(4565) =< aux(214) s(4596) =< aux(221) s(5299) =< aux(201) s(5300) =< s(5299)*aux(201) s(4604) =< aux(216) s(4627) =< s(4604)*aux(216) s(4598) =< aux(216) s(4599) =< aux(216) s(4600) =< aux(216) s(4601) =< aux(216) s(4602) =< aux(216) s(4603) =< aux(216) s(4596) =< aux(216) s(4596) =< aux(217) s(4601) =< aux(218) s(4605) =< aux(219) s(4600) =< aux(220) s(4601) =< aux(220) s(4599) =< aux(222) s(4606) =< aux(216)+2 s(4607) =< aux(216)+1 s(4608) =< aux(216) s(4609) =< aux(216)+3 s(4601) =< aux(217)*(1/2)+aux(218) s(4602) =< aux(217)*(1/2)+aux(218) s(4603) =< aux(217)*(1/2)+aux(218) s(4600) =< aux(217)*(1/3)+aux(220) s(4601) =< aux(217)*(1/3)+aux(220) s(4602) =< aux(217)*(1/3)+aux(220) s(4603) =< aux(217)*(1/3)+aux(220) s(4599) =< aux(217)*(3/5)+s(4596)*(1/5)+aux(222) s(4600) =< aux(217)*(3/5)+s(4596)*(1/5)+aux(222) s(4601) =< aux(217)*(3/5)+s(4596)*(1/5)+aux(222) s(4602) =< aux(217)*(3/5)+s(4596)*(1/5)+aux(222) s(4603) =< aux(217)*(3/5)+s(4596)*(1/5)+aux(222) s(4605) =< aux(217)*(1/3)+aux(219) s(4598) =< aux(217)*(1/3)+aux(219) s(4610) =< s(4603)*s(4606) s(4611) =< s(4601)*s(4607) s(4612) =< s(4599)*s(4608) s(4613) =< s(4598)*s(4606) s(4614) =< s(4598)*s(4609) s(4615) =< s(4605)*s(4608) s(4616) =< s(4614) s(4617) =< s(4616)*s(4609) s(4618) =< s(4613) s(4619) =< s(4618)*s(4606) s(4620) =< s(4615) s(4621) =< s(4620)*aux(216) s(4573) =< aux(209) s(4626) =< s(4573)*aux(209) s(4567) =< aux(209) s(4568) =< aux(209) s(4569) =< aux(209) s(4570) =< aux(209) s(4571) =< aux(209) s(4572) =< aux(209) s(4565) =< aux(209) s(4565) =< aux(210) s(4570) =< aux(211) s(4574) =< aux(212) s(4569) =< aux(213) s(4570) =< aux(213) s(4568) =< aux(215) s(4575) =< aux(209)+2 s(4576) =< aux(209)+1 s(4577) =< aux(209) s(4578) =< aux(209)+3 s(4570) =< aux(210)*(1/2)+aux(211) s(4571) =< aux(210)*(1/2)+aux(211) s(4572) =< aux(210)*(1/2)+aux(211) s(4569) =< aux(210)*(1/3)+aux(213) s(4570) =< aux(210)*(1/3)+aux(213) s(4571) =< aux(210)*(1/3)+aux(213) s(4572) =< aux(210)*(1/3)+aux(213) s(4568) =< aux(210)*(3/5)+s(4565)*(1/5)+aux(215) s(4569) =< aux(210)*(3/5)+s(4565)*(1/5)+aux(215) s(4570) =< aux(210)*(3/5)+s(4565)*(1/5)+aux(215) s(4571) =< aux(210)*(3/5)+s(4565)*(1/5)+aux(215) s(4572) =< aux(210)*(3/5)+s(4565)*(1/5)+aux(215) s(4574) =< aux(210)*(1/3)+aux(212) s(4567) =< aux(210)*(1/3)+aux(212) s(4579) =< s(4572)*s(4575) s(4580) =< s(4570)*s(4576) s(4581) =< s(4568)*s(4577) s(4582) =< s(4567)*s(4575) s(4583) =< s(4567)*s(4578) s(4584) =< s(4574)*s(4577) s(4585) =< s(4583) s(4586) =< s(4585)*s(4578) s(4587) =< s(4582) s(4588) =< s(4587)*s(4575) s(4589) =< s(4584) s(4590) =< s(4589)*aux(209) s(4536) =< aux(202) s(4537) =< aux(202) s(4538) =< aux(202) s(4539) =< aux(202) s(4540) =< aux(202) s(4541) =< aux(202) s(4542) =< aux(202) s(4534) =< aux(202) s(4534) =< aux(203) s(4539) =< aux(204) s(4543) =< aux(205) s(4538) =< aux(206) s(4539) =< aux(206) s(4537) =< aux(208) s(4544) =< aux(202)+2 s(4545) =< aux(202)+1 s(4546) =< aux(202) s(4547) =< aux(202)+3 s(4539) =< aux(203)*(1/2)+aux(204) s(4540) =< aux(203)*(1/2)+aux(204) s(4541) =< aux(203)*(1/2)+aux(204) s(4538) =< aux(203)*(1/3)+aux(206) s(4539) =< aux(203)*(1/3)+aux(206) s(4540) =< aux(203)*(1/3)+aux(206) s(4541) =< aux(203)*(1/3)+aux(206) s(4537) =< aux(203)*(3/5)+s(4534)*(1/5)+aux(208) s(4538) =< aux(203)*(3/5)+s(4534)*(1/5)+aux(208) s(4539) =< aux(203)*(3/5)+s(4534)*(1/5)+aux(208) s(4540) =< aux(203)*(3/5)+s(4534)*(1/5)+aux(208) s(4541) =< aux(203)*(3/5)+s(4534)*(1/5)+aux(208) s(4543) =< aux(203)*(1/3)+aux(205) s(4536) =< aux(203)*(1/3)+aux(205) s(4548) =< s(4541)*s(4544) s(4549) =< s(4539)*s(4545) s(4550) =< s(4537)*s(4546) s(4551) =< s(4536)*s(4544) s(4552) =< s(4536)*s(4547) s(4553) =< s(4543)*s(4546) s(4554) =< s(4552) s(4555) =< s(4554)*s(4547) s(4556) =< s(4551) s(4557) =< s(4556)*s(4544) s(4558) =< s(4553) s(4559) =< s(4558)*aux(202) with precondition: [Out=0,V1>=0,V>=0,V2>=0] * Chain [64]: 76*s(5589)+4*s(5590)+4*s(5591)+4*s(5592)+4*s(5593)+8*s(5595)+76*s(5596)+4*s(5601)+4*s(5602)+4*s(5603)+520*s(5607)+80*s(5608)+1040*s(5609)+96*s(5610)+80*s(5611)+16*s(5612)+95*s(5620)+5*s(5621)+5*s(5622)+5*s(5623)+5*s(5624)+70*s(5626)+95*s(5627)+5*s(5632)+5*s(5633)+5*s(5634)+650*s(5638)+100*s(5639)+1300*s(5640)+120*s(5641)+100*s(5642)+20*s(5643)+420*s(5646)+12*s(5648)+40*s(5649)+17 Such that:aux(226) =< 2 aux(227) =< V1 aux(228) =< 2*V1+1 aux(229) =< V1/2 aux(230) =< V1/3 aux(231) =< 2/3*V1 aux(232) =< 2/3*V1+1/3 aux(233) =< 2/5*V1 aux(234) =< V aux(235) =< 2*V+1 aux(236) =< V/2 aux(237) =< V/3 aux(238) =< 2/3*V aux(239) =< 2/3*V+1/3 aux(240) =< 2/5*V s(5587) =< aux(232) s(5618) =< aux(239) s(5646) =< aux(226) s(5626) =< aux(234) s(5648) =< s(5626)*aux(234) s(5649) =< s(5646)*aux(226) s(5620) =< aux(234) s(5621) =< aux(234) s(5622) =< aux(234) s(5623) =< aux(234) s(5624) =< aux(234) s(5625) =< aux(234) s(5618) =< aux(234) s(5618) =< aux(235) s(5623) =< aux(236) s(5627) =< aux(237) s(5622) =< aux(238) s(5623) =< aux(238) s(5621) =< aux(240) s(5628) =< aux(234)+2 s(5629) =< aux(234)+1 s(5630) =< aux(234) s(5631) =< aux(234)+3 s(5623) =< aux(235)*(1/2)+aux(236) s(5624) =< aux(235)*(1/2)+aux(236) s(5625) =< aux(235)*(1/2)+aux(236) s(5622) =< aux(235)*(1/3)+aux(238) s(5623) =< aux(235)*(1/3)+aux(238) s(5624) =< aux(235)*(1/3)+aux(238) s(5625) =< aux(235)*(1/3)+aux(238) s(5621) =< aux(235)*(3/5)+s(5618)*(1/5)+aux(240) s(5622) =< aux(235)*(3/5)+s(5618)*(1/5)+aux(240) s(5623) =< aux(235)*(3/5)+s(5618)*(1/5)+aux(240) s(5624) =< aux(235)*(3/5)+s(5618)*(1/5)+aux(240) s(5625) =< aux(235)*(3/5)+s(5618)*(1/5)+aux(240) s(5627) =< aux(235)*(1/3)+aux(237) s(5620) =< aux(235)*(1/3)+aux(237) s(5632) =< s(5625)*s(5628) s(5633) =< s(5623)*s(5629) s(5634) =< s(5621)*s(5630) s(5635) =< s(5620)*s(5628) s(5636) =< s(5620)*s(5631) s(5637) =< s(5627)*s(5630) s(5638) =< s(5636) s(5639) =< s(5638)*s(5631) s(5640) =< s(5635) s(5641) =< s(5640)*s(5628) s(5642) =< s(5637) s(5643) =< s(5642)*aux(234) s(5589) =< aux(227) s(5590) =< aux(227) s(5591) =< aux(227) s(5592) =< aux(227) s(5593) =< aux(227) s(5594) =< aux(227) s(5595) =< aux(227) s(5587) =< aux(227) s(5587) =< aux(228) s(5592) =< aux(229) s(5596) =< aux(230) s(5591) =< aux(231) s(5592) =< aux(231) s(5590) =< aux(233) s(5597) =< aux(227)+2 s(5598) =< aux(227)+1 s(5599) =< aux(227) s(5600) =< aux(227)+3 s(5592) =< aux(228)*(1/2)+aux(229) s(5593) =< aux(228)*(1/2)+aux(229) s(5594) =< aux(228)*(1/2)+aux(229) s(5591) =< aux(228)*(1/3)+aux(231) s(5592) =< aux(228)*(1/3)+aux(231) s(5593) =< aux(228)*(1/3)+aux(231) s(5594) =< aux(228)*(1/3)+aux(231) s(5590) =< aux(228)*(3/5)+s(5587)*(1/5)+aux(233) s(5591) =< aux(228)*(3/5)+s(5587)*(1/5)+aux(233) s(5592) =< aux(228)*(3/5)+s(5587)*(1/5)+aux(233) s(5593) =< aux(228)*(3/5)+s(5587)*(1/5)+aux(233) s(5594) =< aux(228)*(3/5)+s(5587)*(1/5)+aux(233) s(5596) =< aux(228)*(1/3)+aux(230) s(5589) =< aux(228)*(1/3)+aux(230) s(5601) =< s(5594)*s(5597) s(5602) =< s(5592)*s(5598) s(5603) =< s(5590)*s(5599) s(5604) =< s(5589)*s(5597) s(5605) =< s(5589)*s(5600) s(5606) =< s(5596)*s(5599) s(5607) =< s(5605) s(5608) =< s(5607)*s(5600) s(5609) =< s(5604) s(5610) =< s(5609)*s(5597) s(5611) =< s(5606) s(5612) =< s(5611)*aux(227) with precondition: [V2=2,Out=0,V1>=0,V>=0] * Chain [63]: 114*s(5916)+6*s(5917)+6*s(5918)+6*s(5919)+6*s(5920)+12*s(5922)+114*s(5923)+6*s(5928)+6*s(5929)+6*s(5930)+780*s(5934)+120*s(5935)+1560*s(5936)+144*s(5937)+120*s(5938)+24*s(5939)+57*s(5947)+3*s(5948)+3*s(5949)+3*s(5950)+3*s(5951)+135*s(5953)+57*s(5954)+3*s(5959)+3*s(5960)+3*s(5961)+390*s(5965)+60*s(5966)+780*s(5967)+72*s(5968)+60*s(5969)+12*s(5970)+249*s(5974)+36*s(5975)+12*s(5976)+17 Such that:aux(246) =< 2 aux(247) =< V1 aux(248) =< 2*V1+1 aux(249) =< V1/2 aux(250) =< V1/3 aux(251) =< 2/3*V1 aux(252) =< 2/3*V1+1/3 aux(253) =< 2/5*V1 aux(254) =< V2 aux(255) =< 2*V2+1 aux(256) =< V2/2 aux(257) =< V2/3 aux(258) =< 2/3*V2 aux(259) =< 2/3*V2+1/3 aux(260) =< 2/5*V2 s(5914) =< aux(252) s(5945) =< aux(259) s(5974) =< aux(246) s(5975) =< s(5974)*aux(246) s(5953) =< aux(254) s(5976) =< s(5953)*aux(254) s(5947) =< aux(254) s(5948) =< aux(254) s(5949) =< aux(254) s(5950) =< aux(254) s(5951) =< aux(254) s(5952) =< aux(254) s(5945) =< aux(254) s(5945) =< aux(255) s(5950) =< aux(256) s(5954) =< aux(257) s(5949) =< aux(258) s(5950) =< aux(258) s(5948) =< aux(260) s(5955) =< aux(254)+2 s(5956) =< aux(254)+1 s(5957) =< aux(254) s(5958) =< aux(254)+3 s(5950) =< aux(255)*(1/2)+aux(256) s(5951) =< aux(255)*(1/2)+aux(256) s(5952) =< aux(255)*(1/2)+aux(256) s(5949) =< aux(255)*(1/3)+aux(258) s(5950) =< aux(255)*(1/3)+aux(258) s(5951) =< aux(255)*(1/3)+aux(258) s(5952) =< aux(255)*(1/3)+aux(258) s(5948) =< aux(255)*(3/5)+s(5945)*(1/5)+aux(260) s(5949) =< aux(255)*(3/5)+s(5945)*(1/5)+aux(260) s(5950) =< aux(255)*(3/5)+s(5945)*(1/5)+aux(260) s(5951) =< aux(255)*(3/5)+s(5945)*(1/5)+aux(260) s(5952) =< aux(255)*(3/5)+s(5945)*(1/5)+aux(260) s(5954) =< aux(255)*(1/3)+aux(257) s(5947) =< aux(255)*(1/3)+aux(257) s(5959) =< s(5952)*s(5955) s(5960) =< s(5950)*s(5956) s(5961) =< s(5948)*s(5957) s(5962) =< s(5947)*s(5955) s(5963) =< s(5947)*s(5958) s(5964) =< s(5954)*s(5957) s(5965) =< s(5963) s(5966) =< s(5965)*s(5958) s(5967) =< s(5962) s(5968) =< s(5967)*s(5955) s(5969) =< s(5964) s(5970) =< s(5969)*aux(254) s(5916) =< aux(247) s(5917) =< aux(247) s(5918) =< aux(247) s(5919) =< aux(247) s(5920) =< aux(247) s(5921) =< aux(247) s(5922) =< aux(247) s(5914) =< aux(247) s(5914) =< aux(248) s(5919) =< aux(249) s(5923) =< aux(250) s(5918) =< aux(251) s(5919) =< aux(251) s(5917) =< aux(253) s(5924) =< aux(247)+2 s(5925) =< aux(247)+1 s(5926) =< aux(247) s(5927) =< aux(247)+3 s(5919) =< aux(248)*(1/2)+aux(249) s(5920) =< aux(248)*(1/2)+aux(249) s(5921) =< aux(248)*(1/2)+aux(249) s(5918) =< aux(248)*(1/3)+aux(251) s(5919) =< aux(248)*(1/3)+aux(251) s(5920) =< aux(248)*(1/3)+aux(251) s(5921) =< aux(248)*(1/3)+aux(251) s(5917) =< aux(248)*(3/5)+s(5914)*(1/5)+aux(253) s(5918) =< aux(248)*(3/5)+s(5914)*(1/5)+aux(253) s(5919) =< aux(248)*(3/5)+s(5914)*(1/5)+aux(253) s(5920) =< aux(248)*(3/5)+s(5914)*(1/5)+aux(253) s(5921) =< aux(248)*(3/5)+s(5914)*(1/5)+aux(253) s(5923) =< aux(248)*(1/3)+aux(250) s(5916) =< aux(248)*(1/3)+aux(250) s(5928) =< s(5921)*s(5924) s(5929) =< s(5919)*s(5925) s(5930) =< s(5917)*s(5926) s(5931) =< s(5916)*s(5924) s(5932) =< s(5916)*s(5927) s(5933) =< s(5923)*s(5926) s(5934) =< s(5932) s(5935) =< s(5934)*s(5927) s(5936) =< s(5931) s(5937) =< s(5936)*s(5924) s(5938) =< s(5933) s(5939) =< s(5938)*aux(247) with precondition: [V=2,Out=0,V1>=0,V2>=0] #### Cost of chains of fun3(V1,V,Out): * Chain [71]: 38*s(6409)+2*s(6410)+2*s(6411)+2*s(6412)+2*s(6413)+4*s(6415)+38*s(6416)+2*s(6421)+2*s(6422)+2*s(6423)+260*s(6427)+40*s(6428)+520*s(6429)+48*s(6430)+40*s(6431)+8*s(6432)+57*s(6440)+3*s(6441)+3*s(6442)+3*s(6443)+3*s(6444)+9*s(6446)+57*s(6447)+3*s(6452)+3*s(6453)+3*s(6454)+390*s(6458)+60*s(6459)+780*s(6460)+72*s(6461)+60*s(6462)+12*s(6463)+1*s(6529)+0 Such that:s(6529) =< 2 aux(279) =< V1 aux(280) =< 2*V1+1 aux(281) =< V1/2 aux(282) =< V1/3 aux(283) =< 2/3*V1 aux(284) =< 2/3*V1+1/3 aux(285) =< 2/5*V1 aux(286) =< V aux(287) =< 2*V+1 aux(288) =< V/2 aux(289) =< V/3 aux(290) =< 2/3*V aux(291) =< 2/3*V+1/3 aux(292) =< 2/5*V s(6407) =< aux(284) s(6438) =< aux(291) s(6446) =< aux(286) s(6440) =< aux(286) s(6441) =< aux(286) s(6442) =< aux(286) s(6443) =< aux(286) s(6444) =< aux(286) s(6445) =< aux(286) s(6438) =< aux(286) s(6438) =< aux(287) s(6443) =< aux(288) s(6447) =< aux(289) s(6442) =< aux(290) s(6443) =< aux(290) s(6441) =< aux(292) s(6448) =< aux(286)+2 s(6449) =< aux(286)+1 s(6450) =< aux(286) s(6451) =< aux(286)+3 s(6443) =< aux(287)*(1/2)+aux(288) s(6444) =< aux(287)*(1/2)+aux(288) s(6445) =< aux(287)*(1/2)+aux(288) s(6442) =< aux(287)*(1/3)+aux(290) s(6443) =< aux(287)*(1/3)+aux(290) s(6444) =< aux(287)*(1/3)+aux(290) s(6445) =< aux(287)*(1/3)+aux(290) s(6441) =< aux(287)*(3/5)+s(6438)*(1/5)+aux(292) s(6442) =< aux(287)*(3/5)+s(6438)*(1/5)+aux(292) s(6443) =< aux(287)*(3/5)+s(6438)*(1/5)+aux(292) s(6444) =< aux(287)*(3/5)+s(6438)*(1/5)+aux(292) s(6445) =< aux(287)*(3/5)+s(6438)*(1/5)+aux(292) s(6447) =< aux(287)*(1/3)+aux(289) s(6440) =< aux(287)*(1/3)+aux(289) s(6452) =< s(6445)*s(6448) s(6453) =< s(6443)*s(6449) s(6454) =< s(6441)*s(6450) s(6455) =< s(6440)*s(6448) s(6456) =< s(6440)*s(6451) s(6457) =< s(6447)*s(6450) s(6458) =< s(6456) s(6459) =< s(6458)*s(6451) s(6460) =< s(6455) s(6461) =< s(6460)*s(6448) s(6462) =< s(6457) s(6463) =< s(6462)*aux(286) s(6409) =< aux(279) s(6410) =< aux(279) s(6411) =< aux(279) s(6412) =< aux(279) s(6413) =< aux(279) s(6414) =< aux(279) s(6415) =< aux(279) s(6407) =< aux(279) s(6407) =< aux(280) s(6412) =< aux(281) s(6416) =< aux(282) s(6411) =< aux(283) s(6412) =< aux(283) s(6410) =< aux(285) s(6417) =< aux(279)+2 s(6418) =< aux(279)+1 s(6419) =< aux(279) s(6420) =< aux(279)+3 s(6412) =< aux(280)*(1/2)+aux(281) s(6413) =< aux(280)*(1/2)+aux(281) s(6414) =< aux(280)*(1/2)+aux(281) s(6411) =< aux(280)*(1/3)+aux(283) s(6412) =< aux(280)*(1/3)+aux(283) s(6413) =< aux(280)*(1/3)+aux(283) s(6414) =< aux(280)*(1/3)+aux(283) s(6410) =< aux(280)*(3/5)+s(6407)*(1/5)+aux(285) s(6411) =< aux(280)*(3/5)+s(6407)*(1/5)+aux(285) s(6412) =< aux(280)*(3/5)+s(6407)*(1/5)+aux(285) s(6413) =< aux(280)*(3/5)+s(6407)*(1/5)+aux(285) s(6414) =< aux(280)*(3/5)+s(6407)*(1/5)+aux(285) s(6416) =< aux(280)*(1/3)+aux(282) s(6409) =< aux(280)*(1/3)+aux(282) s(6421) =< s(6414)*s(6417) s(6422) =< s(6412)*s(6418) s(6423) =< s(6410)*s(6419) s(6424) =< s(6409)*s(6417) s(6425) =< s(6409)*s(6420) s(6426) =< s(6416)*s(6419) s(6427) =< s(6425) s(6428) =< s(6427)*s(6420) s(6429) =< s(6424) s(6430) =< s(6429)*s(6417) s(6431) =< s(6426) s(6432) =< s(6431)*aux(279) with precondition: [Out=0,V1>=0,V>=0] * Chain [70]: 57*s(6571)+3*s(6572)+3*s(6573)+3*s(6574)+3*s(6575)+6*s(6577)+57*s(6578)+3*s(6583)+3*s(6584)+3*s(6585)+390*s(6589)+60*s(6590)+780*s(6591)+72*s(6592)+60*s(6593)+12*s(6594)+76*s(6602)+4*s(6603)+4*s(6604)+4*s(6605)+4*s(6606)+9*s(6608)+76*s(6609)+4*s(6614)+4*s(6615)+4*s(6616)+520*s(6620)+80*s(6621)+1040*s(6622)+96*s(6623)+80*s(6624)+16*s(6625)+2*s(6751)+1 Such that:aux(294) =< 2 aux(295) =< V1 aux(296) =< 2*V1+1 aux(297) =< V1/2 aux(298) =< V1/3 aux(299) =< 2/3*V1 aux(300) =< 2/3*V1+1/3 aux(301) =< 2/5*V1 aux(302) =< V aux(303) =< 2*V+1 aux(304) =< V/2 aux(305) =< V/3 aux(306) =< 2/3*V aux(307) =< 2/3*V+1/3 aux(308) =< 2/5*V s(6751) =< aux(294) s(6569) =< aux(300) s(6600) =< aux(307) s(6602) =< aux(302) s(6603) =< aux(302) s(6604) =< aux(302) s(6605) =< aux(302) s(6606) =< aux(302) s(6607) =< aux(302) s(6608) =< aux(302) s(6600) =< aux(302) s(6600) =< aux(303) s(6605) =< aux(304) s(6609) =< aux(305) s(6604) =< aux(306) s(6605) =< aux(306) s(6603) =< aux(308) s(6610) =< aux(302)+2 s(6611) =< aux(302)+1 s(6612) =< aux(302) s(6613) =< aux(302)+3 s(6605) =< aux(303)*(1/2)+aux(304) s(6606) =< aux(303)*(1/2)+aux(304) s(6607) =< aux(303)*(1/2)+aux(304) s(6604) =< aux(303)*(1/3)+aux(306) s(6605) =< aux(303)*(1/3)+aux(306) s(6606) =< aux(303)*(1/3)+aux(306) s(6607) =< aux(303)*(1/3)+aux(306) s(6603) =< aux(303)*(3/5)+s(6600)*(1/5)+aux(308) s(6604) =< aux(303)*(3/5)+s(6600)*(1/5)+aux(308) s(6605) =< aux(303)*(3/5)+s(6600)*(1/5)+aux(308) s(6606) =< aux(303)*(3/5)+s(6600)*(1/5)+aux(308) s(6607) =< aux(303)*(3/5)+s(6600)*(1/5)+aux(308) s(6609) =< aux(303)*(1/3)+aux(305) s(6602) =< aux(303)*(1/3)+aux(305) s(6614) =< s(6607)*s(6610) s(6615) =< s(6605)*s(6611) s(6616) =< s(6603)*s(6612) s(6617) =< s(6602)*s(6610) s(6618) =< s(6602)*s(6613) s(6619) =< s(6609)*s(6612) s(6620) =< s(6618) s(6621) =< s(6620)*s(6613) s(6622) =< s(6617) s(6623) =< s(6622)*s(6610) s(6624) =< s(6619) s(6625) =< s(6624)*aux(302) s(6571) =< aux(295) s(6572) =< aux(295) s(6573) =< aux(295) s(6574) =< aux(295) s(6575) =< aux(295) s(6576) =< aux(295) s(6577) =< aux(295) s(6569) =< aux(295) s(6569) =< aux(296) s(6574) =< aux(297) s(6578) =< aux(298) s(6573) =< aux(299) s(6574) =< aux(299) s(6572) =< aux(301) s(6579) =< aux(295)+2 s(6580) =< aux(295)+1 s(6581) =< aux(295) s(6582) =< aux(295)+3 s(6574) =< aux(296)*(1/2)+aux(297) s(6575) =< aux(296)*(1/2)+aux(297) s(6576) =< aux(296)*(1/2)+aux(297) s(6573) =< aux(296)*(1/3)+aux(299) s(6574) =< aux(296)*(1/3)+aux(299) s(6575) =< aux(296)*(1/3)+aux(299) s(6576) =< aux(296)*(1/3)+aux(299) s(6572) =< aux(296)*(3/5)+s(6569)*(1/5)+aux(301) s(6573) =< aux(296)*(3/5)+s(6569)*(1/5)+aux(301) s(6574) =< aux(296)*(3/5)+s(6569)*(1/5)+aux(301) s(6575) =< aux(296)*(3/5)+s(6569)*(1/5)+aux(301) s(6576) =< aux(296)*(3/5)+s(6569)*(1/5)+aux(301) s(6578) =< aux(296)*(1/3)+aux(298) s(6571) =< aux(296)*(1/3)+aux(298) s(6583) =< s(6576)*s(6579) s(6584) =< s(6574)*s(6580) s(6585) =< s(6572)*s(6581) s(6586) =< s(6571)*s(6579) s(6587) =< s(6571)*s(6582) s(6588) =< s(6578)*s(6581) s(6589) =< s(6587) s(6590) =< s(6589)*s(6582) s(6591) =< s(6586) s(6592) =< s(6591)*s(6579) s(6593) =< s(6588) s(6594) =< s(6593)*aux(295) with precondition: [Out=1,V1>=0,V>=0] * Chain [69]: 57*s(6791)+3*s(6792)+3*s(6793)+3*s(6794)+3*s(6795)+6*s(6797)+57*s(6798)+3*s(6803)+3*s(6804)+3*s(6805)+390*s(6809)+60*s(6810)+780*s(6811)+72*s(6812)+60*s(6813)+12*s(6814)+76*s(6822)+4*s(6823)+4*s(6824)+4*s(6825)+4*s(6826)+9*s(6828)+76*s(6829)+4*s(6834)+4*s(6835)+4*s(6836)+520*s(6840)+80*s(6841)+1040*s(6842)+96*s(6843)+80*s(6844)+16*s(6845)+1*s(7002)+1 Such that:s(7002) =< 1 aux(310) =< V1 aux(311) =< 2*V1+1 aux(312) =< V1/2 aux(313) =< V1/3 aux(314) =< 2/3*V1 aux(315) =< 2/3*V1+1/3 aux(316) =< 2/5*V1 aux(317) =< V aux(318) =< 2*V+1 aux(319) =< V/2 aux(320) =< V/3 aux(321) =< 2/3*V aux(322) =< 2/3*V+1/3 aux(323) =< 2/5*V s(6789) =< aux(315) s(6820) =< aux(322) s(6822) =< aux(317) s(6823) =< aux(317) s(6824) =< aux(317) s(6825) =< aux(317) s(6826) =< aux(317) s(6827) =< aux(317) s(6828) =< aux(317) s(6820) =< aux(317) s(6820) =< aux(318) s(6825) =< aux(319) s(6829) =< aux(320) s(6824) =< aux(321) s(6825) =< aux(321) s(6823) =< aux(323) s(6830) =< aux(317)+2 s(6831) =< aux(317)+1 s(6832) =< aux(317) s(6833) =< aux(317)+3 s(6825) =< aux(318)*(1/2)+aux(319) s(6826) =< aux(318)*(1/2)+aux(319) s(6827) =< aux(318)*(1/2)+aux(319) s(6824) =< aux(318)*(1/3)+aux(321) s(6825) =< aux(318)*(1/3)+aux(321) s(6826) =< aux(318)*(1/3)+aux(321) s(6827) =< aux(318)*(1/3)+aux(321) s(6823) =< aux(318)*(3/5)+s(6820)*(1/5)+aux(323) s(6824) =< aux(318)*(3/5)+s(6820)*(1/5)+aux(323) s(6825) =< aux(318)*(3/5)+s(6820)*(1/5)+aux(323) s(6826) =< aux(318)*(3/5)+s(6820)*(1/5)+aux(323) s(6827) =< aux(318)*(3/5)+s(6820)*(1/5)+aux(323) s(6829) =< aux(318)*(1/3)+aux(320) s(6822) =< aux(318)*(1/3)+aux(320) s(6834) =< s(6827)*s(6830) s(6835) =< s(6825)*s(6831) s(6836) =< s(6823)*s(6832) s(6837) =< s(6822)*s(6830) s(6838) =< s(6822)*s(6833) s(6839) =< s(6829)*s(6832) s(6840) =< s(6838) s(6841) =< s(6840)*s(6833) s(6842) =< s(6837) s(6843) =< s(6842)*s(6830) s(6844) =< s(6839) s(6845) =< s(6844)*aux(317) s(6791) =< aux(310) s(6792) =< aux(310) s(6793) =< aux(310) s(6794) =< aux(310) s(6795) =< aux(310) s(6796) =< aux(310) s(6797) =< aux(310) s(6789) =< aux(310) s(6789) =< aux(311) s(6794) =< aux(312) s(6798) =< aux(313) s(6793) =< aux(314) s(6794) =< aux(314) s(6792) =< aux(316) s(6799) =< aux(310)+2 s(6800) =< aux(310)+1 s(6801) =< aux(310) s(6802) =< aux(310)+3 s(6794) =< aux(311)*(1/2)+aux(312) s(6795) =< aux(311)*(1/2)+aux(312) s(6796) =< aux(311)*(1/2)+aux(312) s(6793) =< aux(311)*(1/3)+aux(314) s(6794) =< aux(311)*(1/3)+aux(314) s(6795) =< aux(311)*(1/3)+aux(314) s(6796) =< aux(311)*(1/3)+aux(314) s(6792) =< aux(311)*(3/5)+s(6789)*(1/5)+aux(316) s(6793) =< aux(311)*(3/5)+s(6789)*(1/5)+aux(316) s(6794) =< aux(311)*(3/5)+s(6789)*(1/5)+aux(316) s(6795) =< aux(311)*(3/5)+s(6789)*(1/5)+aux(316) s(6796) =< aux(311)*(3/5)+s(6789)*(1/5)+aux(316) s(6798) =< aux(311)*(1/3)+aux(313) s(6791) =< aux(311)*(1/3)+aux(313) s(6803) =< s(6796)*s(6799) s(6804) =< s(6794)*s(6800) s(6805) =< s(6792)*s(6801) s(6806) =< s(6791)*s(6799) s(6807) =< s(6791)*s(6802) s(6808) =< s(6798)*s(6801) s(6809) =< s(6807) s(6810) =< s(6809)*s(6802) s(6811) =< s(6806) s(6812) =< s(6811)*s(6799) s(6813) =< s(6808) s(6814) =< s(6813)*aux(310) with precondition: [Out=2,V1>=1,V>=0] * Chain [68]: 19*s(7010)+1*s(7011)+1*s(7012)+1*s(7013)+1*s(7014)+2*s(7016)+19*s(7017)+1*s(7022)+1*s(7023)+1*s(7024)+130*s(7028)+20*s(7029)+260*s(7030)+24*s(7031)+20*s(7032)+4*s(7033)+2*s(7034)+0 Such that:s(7003) =< V1 s(7004) =< 2*V1+1 s(7005) =< V1/2 s(7006) =< V1/3 s(7007) =< 2/3*V1 s(7008) =< 2/3*V1+1/3 s(7009) =< 2/5*V1 aux(324) =< 2 s(7034) =< aux(324) s(7010) =< s(7003) s(7011) =< s(7003) s(7012) =< s(7003) s(7013) =< s(7003) s(7014) =< s(7003) s(7015) =< s(7003) s(7016) =< s(7003) s(7008) =< s(7003) s(7008) =< s(7004) s(7013) =< s(7005) s(7017) =< s(7006) s(7012) =< s(7007) s(7013) =< s(7007) s(7011) =< s(7009) s(7018) =< s(7003)+2 s(7019) =< s(7003)+1 s(7020) =< s(7003) s(7021) =< s(7003)+3 s(7013) =< s(7004)*(1/2)+s(7005) s(7014) =< s(7004)*(1/2)+s(7005) s(7015) =< s(7004)*(1/2)+s(7005) s(7012) =< s(7004)*(1/3)+s(7007) s(7013) =< s(7004)*(1/3)+s(7007) s(7014) =< s(7004)*(1/3)+s(7007) s(7015) =< s(7004)*(1/3)+s(7007) s(7011) =< s(7004)*(3/5)+s(7008)*(1/5)+s(7009) s(7012) =< s(7004)*(3/5)+s(7008)*(1/5)+s(7009) s(7013) =< s(7004)*(3/5)+s(7008)*(1/5)+s(7009) s(7014) =< s(7004)*(3/5)+s(7008)*(1/5)+s(7009) s(7015) =< s(7004)*(3/5)+s(7008)*(1/5)+s(7009) s(7017) =< s(7004)*(1/3)+s(7006) s(7010) =< s(7004)*(1/3)+s(7006) s(7022) =< s(7015)*s(7018) s(7023) =< s(7013)*s(7019) s(7024) =< s(7011)*s(7020) s(7025) =< s(7010)*s(7018) s(7026) =< s(7010)*s(7021) s(7027) =< s(7017)*s(7020) s(7028) =< s(7026) s(7029) =< s(7028)*s(7021) s(7030) =< s(7025) s(7031) =< s(7030)*s(7018) s(7032) =< s(7027) s(7033) =< s(7032)*s(7003) with precondition: [V=2,Out=0,V1>=0] * Chain [67]: 38*s(7043)+2*s(7044)+2*s(7045)+2*s(7046)+2*s(7047)+5*s(7049)+38*s(7050)+2*s(7055)+2*s(7056)+2*s(7057)+260*s(7061)+40*s(7062)+520*s(7063)+48*s(7064)+40*s(7065)+8*s(7066)+1 Such that:aux(326) =< V1 aux(327) =< 2*V1+1 aux(328) =< V1/2 aux(329) =< V1/3 aux(330) =< 2/3*V1 aux(331) =< 2/3*V1+1/3 aux(332) =< 2/5*V1 s(7041) =< aux(331) s(7043) =< aux(326) s(7044) =< aux(326) s(7045) =< aux(326) s(7046) =< aux(326) s(7047) =< aux(326) s(7048) =< aux(326) s(7049) =< aux(326) s(7041) =< aux(326) s(7041) =< aux(327) s(7046) =< aux(328) s(7050) =< aux(329) s(7045) =< aux(330) s(7046) =< aux(330) s(7044) =< aux(332) s(7051) =< aux(326)+2 s(7052) =< aux(326)+1 s(7053) =< aux(326) s(7054) =< aux(326)+3 s(7046) =< aux(327)*(1/2)+aux(328) s(7047) =< aux(327)*(1/2)+aux(328) s(7048) =< aux(327)*(1/2)+aux(328) s(7045) =< aux(327)*(1/3)+aux(330) s(7046) =< aux(327)*(1/3)+aux(330) s(7047) =< aux(327)*(1/3)+aux(330) s(7048) =< aux(327)*(1/3)+aux(330) s(7044) =< aux(327)*(3/5)+s(7041)*(1/5)+aux(332) s(7045) =< aux(327)*(3/5)+s(7041)*(1/5)+aux(332) s(7046) =< aux(327)*(3/5)+s(7041)*(1/5)+aux(332) s(7047) =< aux(327)*(3/5)+s(7041)*(1/5)+aux(332) s(7048) =< aux(327)*(3/5)+s(7041)*(1/5)+aux(332) s(7050) =< aux(327)*(1/3)+aux(329) s(7043) =< aux(327)*(1/3)+aux(329) s(7055) =< s(7048)*s(7051) s(7056) =< s(7046)*s(7052) s(7057) =< s(7044)*s(7053) s(7058) =< s(7043)*s(7051) s(7059) =< s(7043)*s(7054) s(7060) =< s(7050)*s(7053) s(7061) =< s(7059) s(7062) =< s(7061)*s(7054) s(7063) =< s(7058) s(7064) =< s(7063)*s(7051) s(7065) =< s(7060) s(7066) =< s(7065)*aux(326) with precondition: [V=2,Out=1,V1>=0] * Chain [66]: 19*s(7106)+1*s(7107)+1*s(7108)+1*s(7109)+1*s(7110)+2*s(7112)+19*s(7113)+1*s(7118)+1*s(7119)+1*s(7120)+130*s(7124)+20*s(7125)+260*s(7126)+24*s(7127)+20*s(7128)+4*s(7129)+1*s(7130)+1 Such that:s(7130) =< 2 s(7099) =< V1 s(7100) =< 2*V1+1 s(7101) =< V1/2 s(7102) =< V1/3 s(7103) =< 2/3*V1 s(7104) =< 2/3*V1+1/3 s(7105) =< 2/5*V1 s(7106) =< s(7099) s(7107) =< s(7099) s(7108) =< s(7099) s(7109) =< s(7099) s(7110) =< s(7099) s(7111) =< s(7099) s(7112) =< s(7099) s(7104) =< s(7099) s(7104) =< s(7100) s(7109) =< s(7101) s(7113) =< s(7102) s(7108) =< s(7103) s(7109) =< s(7103) s(7107) =< s(7105) s(7114) =< s(7099)+2 s(7115) =< s(7099)+1 s(7116) =< s(7099) s(7117) =< s(7099)+3 s(7109) =< s(7100)*(1/2)+s(7101) s(7110) =< s(7100)*(1/2)+s(7101) s(7111) =< s(7100)*(1/2)+s(7101) s(7108) =< s(7100)*(1/3)+s(7103) s(7109) =< s(7100)*(1/3)+s(7103) s(7110) =< s(7100)*(1/3)+s(7103) s(7111) =< s(7100)*(1/3)+s(7103) s(7107) =< s(7100)*(3/5)+s(7104)*(1/5)+s(7105) s(7108) =< s(7100)*(3/5)+s(7104)*(1/5)+s(7105) s(7109) =< s(7100)*(3/5)+s(7104)*(1/5)+s(7105) s(7110) =< s(7100)*(3/5)+s(7104)*(1/5)+s(7105) s(7111) =< s(7100)*(3/5)+s(7104)*(1/5)+s(7105) s(7113) =< s(7100)*(1/3)+s(7102) s(7106) =< s(7100)*(1/3)+s(7102) s(7118) =< s(7111)*s(7114) s(7119) =< s(7109)*s(7115) s(7120) =< s(7107)*s(7116) s(7121) =< s(7106)*s(7114) s(7122) =< s(7106)*s(7117) s(7123) =< s(7113)*s(7116) s(7124) =< s(7122) s(7125) =< s(7124)*s(7117) s(7126) =< s(7121) s(7127) =< s(7126)*s(7114) s(7128) =< s(7123) s(7129) =< s(7128)*s(7099) with precondition: [V=2,Out=2,V1>=3] #### Cost of chains of fun5(Out): * Chain [73]: 0 with precondition: [Out=0] * Chain [72]: 0 with precondition: [Out=1] #### Cost of chains of fun6(V1,Out): * Chain [75]: 19*s(7431)+1*s(7432)+1*s(7433)+1*s(7434)+1*s(7435)+2*s(7437)+19*s(7438)+1*s(7443)+1*s(7444)+1*s(7445)+130*s(7449)+20*s(7450)+260*s(7451)+24*s(7452)+20*s(7453)+4*s(7454)+1 Such that:s(7424) =< V1 s(7425) =< 2*V1+1 s(7426) =< V1/2 s(7427) =< V1/3 s(7428) =< 2/3*V1 s(7429) =< 2/3*V1+1/3 s(7430) =< 2/5*V1 s(7431) =< s(7424) s(7432) =< s(7424) s(7433) =< s(7424) s(7434) =< s(7424) s(7435) =< s(7424) s(7436) =< s(7424) s(7437) =< s(7424) s(7429) =< s(7424) s(7429) =< s(7425) s(7434) =< s(7426) s(7438) =< s(7427) s(7433) =< s(7428) s(7434) =< s(7428) s(7432) =< s(7430) s(7439) =< s(7424)+2 s(7440) =< s(7424)+1 s(7441) =< s(7424) s(7442) =< s(7424)+3 s(7434) =< s(7425)*(1/2)+s(7426) s(7435) =< s(7425)*(1/2)+s(7426) s(7436) =< s(7425)*(1/2)+s(7426) s(7433) =< s(7425)*(1/3)+s(7428) s(7434) =< s(7425)*(1/3)+s(7428) s(7435) =< s(7425)*(1/3)+s(7428) s(7436) =< s(7425)*(1/3)+s(7428) s(7432) =< s(7425)*(3/5)+s(7429)*(1/5)+s(7430) s(7433) =< s(7425)*(3/5)+s(7429)*(1/5)+s(7430) s(7434) =< s(7425)*(3/5)+s(7429)*(1/5)+s(7430) s(7435) =< s(7425)*(3/5)+s(7429)*(1/5)+s(7430) s(7436) =< s(7425)*(3/5)+s(7429)*(1/5)+s(7430) s(7438) =< s(7425)*(1/3)+s(7427) s(7431) =< s(7425)*(1/3)+s(7427) s(7443) =< s(7436)*s(7439) s(7444) =< s(7434)*s(7440) s(7445) =< s(7432)*s(7441) s(7446) =< s(7431)*s(7439) s(7447) =< s(7431)*s(7442) s(7448) =< s(7438)*s(7441) s(7449) =< s(7447) s(7450) =< s(7449)*s(7442) s(7451) =< s(7446) s(7452) =< s(7451)*s(7439) s(7453) =< s(7448) s(7454) =< s(7453)*s(7424) with precondition: [Out=0,V1>=0] * Chain [74]: 19*s(7462)+1*s(7463)+1*s(7464)+1*s(7465)+1*s(7466)+2*s(7468)+19*s(7469)+1*s(7474)+1*s(7475)+1*s(7476)+130*s(7480)+20*s(7481)+260*s(7482)+24*s(7483)+20*s(7484)+4*s(7485)+1 Such that:s(7455) =< V1 s(7456) =< 2*V1+1 s(7457) =< V1/2 s(7458) =< V1/3 s(7459) =< 2/3*V1 s(7460) =< 2/3*V1+1/3 s(7461) =< 2/5*V1 s(7462) =< s(7455) s(7463) =< s(7455) s(7464) =< s(7455) s(7465) =< s(7455) s(7466) =< s(7455) s(7467) =< s(7455) s(7468) =< s(7455) s(7460) =< s(7455) s(7460) =< s(7456) s(7465) =< s(7457) s(7469) =< s(7458) s(7464) =< s(7459) s(7465) =< s(7459) s(7463) =< s(7461) s(7470) =< s(7455)+2 s(7471) =< s(7455)+1 s(7472) =< s(7455) s(7473) =< s(7455)+3 s(7465) =< s(7456)*(1/2)+s(7457) s(7466) =< s(7456)*(1/2)+s(7457) s(7467) =< s(7456)*(1/2)+s(7457) s(7464) =< s(7456)*(1/3)+s(7459) s(7465) =< s(7456)*(1/3)+s(7459) s(7466) =< s(7456)*(1/3)+s(7459) s(7467) =< s(7456)*(1/3)+s(7459) s(7463) =< s(7456)*(3/5)+s(7460)*(1/5)+s(7461) s(7464) =< s(7456)*(3/5)+s(7460)*(1/5)+s(7461) s(7465) =< s(7456)*(3/5)+s(7460)*(1/5)+s(7461) s(7466) =< s(7456)*(3/5)+s(7460)*(1/5)+s(7461) s(7467) =< s(7456)*(3/5)+s(7460)*(1/5)+s(7461) s(7469) =< s(7456)*(1/3)+s(7458) s(7462) =< s(7456)*(1/3)+s(7458) s(7474) =< s(7467)*s(7470) s(7475) =< s(7465)*s(7471) s(7476) =< s(7463)*s(7472) s(7477) =< s(7462)*s(7470) s(7478) =< s(7462)*s(7473) s(7479) =< s(7469)*s(7472) s(7480) =< s(7478) s(7481) =< s(7480)*s(7473) s(7482) =< s(7477) s(7483) =< s(7482)*s(7470) s(7484) =< s(7479) s(7485) =< s(7484)*s(7455) with precondition: [Out>=0,V1>=Out+1] #### Cost of chains of fun7(V1,Out): * Chain [78]: 19*s(7493)+1*s(7494)+1*s(7495)+1*s(7496)+1*s(7497)+2*s(7499)+19*s(7500)+1*s(7505)+1*s(7506)+1*s(7507)+130*s(7511)+20*s(7512)+260*s(7513)+24*s(7514)+20*s(7515)+4*s(7516)+0 Such that:s(7486) =< V1 s(7487) =< 2*V1+1 s(7488) =< V1/2 s(7489) =< V1/3 s(7490) =< 2/3*V1 s(7491) =< 2/3*V1+1/3 s(7492) =< 2/5*V1 s(7493) =< s(7486) s(7494) =< s(7486) s(7495) =< s(7486) s(7496) =< s(7486) s(7497) =< s(7486) s(7498) =< s(7486) s(7499) =< s(7486) s(7491) =< s(7486) s(7491) =< s(7487) s(7496) =< s(7488) s(7500) =< s(7489) s(7495) =< s(7490) s(7496) =< s(7490) s(7494) =< s(7492) s(7501) =< s(7486)+2 s(7502) =< s(7486)+1 s(7503) =< s(7486) s(7504) =< s(7486)+3 s(7496) =< s(7487)*(1/2)+s(7488) s(7497) =< s(7487)*(1/2)+s(7488) s(7498) =< s(7487)*(1/2)+s(7488) s(7495) =< s(7487)*(1/3)+s(7490) s(7496) =< s(7487)*(1/3)+s(7490) s(7497) =< s(7487)*(1/3)+s(7490) s(7498) =< s(7487)*(1/3)+s(7490) s(7494) =< s(7487)*(3/5)+s(7491)*(1/5)+s(7492) s(7495) =< s(7487)*(3/5)+s(7491)*(1/5)+s(7492) s(7496) =< s(7487)*(3/5)+s(7491)*(1/5)+s(7492) s(7497) =< s(7487)*(3/5)+s(7491)*(1/5)+s(7492) s(7498) =< s(7487)*(3/5)+s(7491)*(1/5)+s(7492) s(7500) =< s(7487)*(1/3)+s(7489) s(7493) =< s(7487)*(1/3)+s(7489) s(7505) =< s(7498)*s(7501) s(7506) =< s(7496)*s(7502) s(7507) =< s(7494)*s(7503) s(7508) =< s(7493)*s(7501) s(7509) =< s(7493)*s(7504) s(7510) =< s(7500)*s(7503) s(7511) =< s(7509) s(7512) =< s(7511)*s(7504) s(7513) =< s(7508) s(7514) =< s(7513)*s(7501) s(7515) =< s(7510) s(7516) =< s(7515)*s(7486) with precondition: [V1>=1,Out>=1,V1+1>=Out] * Chain [77]: 0 with precondition: [Out=0,V1>=0] * Chain [76]: 0 with precondition: [Out=1,V1>=0] #### Cost of chains of start(V1,V,V2): * Chain [79]: 1829*s(7519)+156*s(7522)+848*s(7526)+132*s(7527)+154*s(7567)+1444*s(7576)+76*s(7577)+76*s(7578)+76*s(7579)+76*s(7580)+1444*s(7583)+76*s(7588)+76*s(7589)+76*s(7590)+9880*s(7594)+1520*s(7595)+19760*s(7596)+1824*s(7597)+1520*s(7598)+304*s(7599)+1984*s(7625)+232*s(7626)+1026*s(7627)+54*s(7628)+54*s(7629)+54*s(7630)+54*s(7631)+1026*s(7634)+54*s(7639)+54*s(7640)+54*s(7641)+7020*s(7645)+1080*s(7646)+14040*s(7647)+1296*s(7648)+1080*s(7649)+216*s(7650)+167*s(7676)+16*s(7677)+1273*s(7679)+67*s(7680)+67*s(7681)+67*s(7682)+67*s(7683)+1273*s(7686)+67*s(7691)+67*s(7692)+67*s(7693)+8710*s(7697)+1340*s(7698)+17420*s(7699)+1608*s(7700)+1340*s(7701)+268*s(7702)+19 Such that:aux(359) =< 1 aux(360) =< 2 aux(361) =< V1 aux(362) =< 2*V1+1 aux(363) =< V1/2 aux(364) =< V1/3 aux(365) =< 2/3*V1 aux(366) =< 2/3*V1+1/3 aux(367) =< 2/5*V1 aux(368) =< V aux(369) =< 2*V+1 aux(370) =< V/2 aux(371) =< V/3 aux(372) =< 2/3*V aux(373) =< 2/3*V+1/3 aux(374) =< 2/5*V aux(375) =< V2 aux(376) =< 2*V2+1 aux(377) =< V2/2 aux(378) =< V2/3 aux(379) =< 2/3*V2 aux(380) =< 2/3*V2+1/3 aux(381) =< 2/5*V2 s(7676) =< aux(359) s(7625) =< aux(360) s(7567) =< aux(361) s(7574) =< aux(366) s(7526) =< aux(368) s(7624) =< aux(380) s(7626) =< s(7625)*aux(360) s(7627) =< aux(375) s(7628) =< aux(375) s(7629) =< aux(375) s(7630) =< aux(375) s(7631) =< aux(375) s(7632) =< aux(375) s(7519) =< aux(375) s(7624) =< aux(375) s(7624) =< aux(376) s(7630) =< aux(377) s(7634) =< aux(378) s(7629) =< aux(379) s(7630) =< aux(379) s(7628) =< aux(381) s(7635) =< aux(375)+2 s(7636) =< aux(375)+1 s(7637) =< aux(375) s(7638) =< aux(375)+3 s(7630) =< aux(376)*(1/2)+aux(377) s(7631) =< aux(376)*(1/2)+aux(377) s(7632) =< aux(376)*(1/2)+aux(377) s(7629) =< aux(376)*(1/3)+aux(379) s(7630) =< aux(376)*(1/3)+aux(379) s(7631) =< aux(376)*(1/3)+aux(379) s(7632) =< aux(376)*(1/3)+aux(379) s(7628) =< aux(376)*(3/5)+s(7624)*(1/5)+aux(381) s(7629) =< aux(376)*(3/5)+s(7624)*(1/5)+aux(381) s(7630) =< aux(376)*(3/5)+s(7624)*(1/5)+aux(381) s(7631) =< aux(376)*(3/5)+s(7624)*(1/5)+aux(381) s(7632) =< aux(376)*(3/5)+s(7624)*(1/5)+aux(381) s(7634) =< aux(376)*(1/3)+aux(378) s(7627) =< aux(376)*(1/3)+aux(378) s(7639) =< s(7632)*s(7635) s(7640) =< s(7630)*s(7636) s(7641) =< s(7628)*s(7637) s(7642) =< s(7627)*s(7635) s(7643) =< s(7627)*s(7638) s(7644) =< s(7634)*s(7637) s(7645) =< s(7643) s(7646) =< s(7645)*s(7638) s(7647) =< s(7642) s(7648) =< s(7647)*s(7635) s(7649) =< s(7644) s(7650) =< s(7649)*aux(375) s(7576) =< aux(361) s(7577) =< aux(361) s(7578) =< aux(361) s(7579) =< aux(361) s(7580) =< aux(361) s(7581) =< aux(361) s(7574) =< aux(361) s(7574) =< aux(362) s(7579) =< aux(363) s(7583) =< aux(364) s(7578) =< aux(365) s(7579) =< aux(365) s(7577) =< aux(367) s(7584) =< aux(361)+2 s(7585) =< aux(361)+1 s(7586) =< aux(361) s(7587) =< aux(361)+3 s(7579) =< aux(362)*(1/2)+aux(363) s(7580) =< aux(362)*(1/2)+aux(363) s(7581) =< aux(362)*(1/2)+aux(363) s(7578) =< aux(362)*(1/3)+aux(365) s(7579) =< aux(362)*(1/3)+aux(365) s(7580) =< aux(362)*(1/3)+aux(365) s(7581) =< aux(362)*(1/3)+aux(365) s(7577) =< aux(362)*(3/5)+s(7574)*(1/5)+aux(367) s(7578) =< aux(362)*(3/5)+s(7574)*(1/5)+aux(367) s(7579) =< aux(362)*(3/5)+s(7574)*(1/5)+aux(367) s(7580) =< aux(362)*(3/5)+s(7574)*(1/5)+aux(367) s(7581) =< aux(362)*(3/5)+s(7574)*(1/5)+aux(367) s(7583) =< aux(362)*(1/3)+aux(364) s(7576) =< aux(362)*(1/3)+aux(364) s(7588) =< s(7581)*s(7584) s(7589) =< s(7579)*s(7585) s(7590) =< s(7577)*s(7586) s(7591) =< s(7576)*s(7584) s(7592) =< s(7576)*s(7587) s(7593) =< s(7583)*s(7586) s(7594) =< s(7592) s(7595) =< s(7594)*s(7587) s(7596) =< s(7591) s(7597) =< s(7596)*s(7584) s(7598) =< s(7593) s(7599) =< s(7598)*aux(361) s(7522) =< s(7519)*aux(375) s(7677) =< s(7676)*aux(359) s(7678) =< aux(373) s(7679) =< aux(368) s(7680) =< aux(368) s(7681) =< aux(368) s(7682) =< aux(368) s(7683) =< aux(368) s(7684) =< aux(368) s(7678) =< aux(368) s(7678) =< aux(369) s(7682) =< aux(370) s(7686) =< aux(371) s(7681) =< aux(372) s(7682) =< aux(372) s(7680) =< aux(374) s(7687) =< aux(368)+2 s(7688) =< aux(368)+1 s(7689) =< aux(368) s(7690) =< aux(368)+3 s(7682) =< aux(369)*(1/2)+aux(370) s(7683) =< aux(369)*(1/2)+aux(370) s(7684) =< aux(369)*(1/2)+aux(370) s(7681) =< aux(369)*(1/3)+aux(372) s(7682) =< aux(369)*(1/3)+aux(372) s(7683) =< aux(369)*(1/3)+aux(372) s(7684) =< aux(369)*(1/3)+aux(372) s(7680) =< aux(369)*(3/5)+s(7678)*(1/5)+aux(374) s(7681) =< aux(369)*(3/5)+s(7678)*(1/5)+aux(374) s(7682) =< aux(369)*(3/5)+s(7678)*(1/5)+aux(374) s(7683) =< aux(369)*(3/5)+s(7678)*(1/5)+aux(374) s(7684) =< aux(369)*(3/5)+s(7678)*(1/5)+aux(374) s(7686) =< aux(369)*(1/3)+aux(371) s(7679) =< aux(369)*(1/3)+aux(371) s(7691) =< s(7684)*s(7687) s(7692) =< s(7682)*s(7688) s(7693) =< s(7680)*s(7689) s(7694) =< s(7679)*s(7687) s(7695) =< s(7679)*s(7690) s(7696) =< s(7686)*s(7689) s(7697) =< s(7695) s(7698) =< s(7697)*s(7690) s(7699) =< s(7694) s(7700) =< s(7699)*s(7687) s(7701) =< s(7696) s(7702) =< s(7701)*aux(368) s(7527) =< s(7526)*aux(368) with precondition: [] Closed-form bounds of start(V1,V,V2): ------------------------------------- * Chain [79] with precondition: [] - Upper bound: nat(V1)*92266+5098+nat(V1)*46284*nat(V1)+nat(V1)*3344*nat(V1)*nat(V1)+nat(V1)*304*nat(V1)*nat(V1/3)+nat(V1)*1520*nat(V1/3)+nat(V)*82052+nat(V)*40935*nat(V)+nat(V)*2948*nat(V)*nat(V)+nat(V)*268*nat(V)*nat(V/3)+nat(V)*1340*nat(V/3)+nat(V2)*67277+nat(V2)*33042*nat(V2)+nat(V2)*2376*nat(V2)*nat(V2)+nat(V2)*216*nat(V2)*nat(V2/3)+nat(V2)*1080*nat(V2/3)+nat(V1/3)*1444+nat(V/3)*1273+nat(V2/3)*1026 - Complexity: n^3 ### Maximum cost of start(V1,V,V2): nat(V1)*92266+5098+nat(V1)*46284*nat(V1)+nat(V1)*3344*nat(V1)*nat(V1)+nat(V1)*304*nat(V1)*nat(V1/3)+nat(V1)*1520*nat(V1/3)+nat(V)*82052+nat(V)*40935*nat(V)+nat(V)*2948*nat(V)*nat(V)+nat(V)*268*nat(V)*nat(V/3)+nat(V)*1340*nat(V/3)+nat(V2)*67277+nat(V2)*33042*nat(V2)+nat(V2)*2376*nat(V2)*nat(V2)+nat(V2)*216*nat(V2)*nat(V2/3)+nat(V2)*1080*nat(V2/3)+nat(V1/3)*1444+nat(V/3)*1273+nat(V2/3)*1026 Asymptotic class: n^3 * Total analysis performed in 36406 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: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(gr(x, 0'), y, y) cond2(false, x, y) -> cond1(gr(x, 0'), p(x), y) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(0') -> 0' encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (17) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (18) Obligation: Innermost TRS: Rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(gr(x, 0'), y, y) cond2(false, x, y) -> cond1(gr(x, 0'), p(x), y) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x encArg(true) -> true encArg(0') -> 0' encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) Types: cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p 0' :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encArg :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_0 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p hole_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p ---------------------------------------- (19) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: cond1, cond2, gr, encArg They will be analysed ascendingly in the following order: cond1 = cond2 gr < cond1 cond1 < encArg gr < cond2 cond2 < encArg gr < encArg ---------------------------------------- (20) Obligation: Innermost TRS: Rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(gr(x, 0'), y, y) cond2(false, x, y) -> cond1(gr(x, 0'), p(x), y) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x encArg(true) -> true encArg(0') -> 0' encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) Types: cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p 0' :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encArg :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_0 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p hole_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p Generator Equations: gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(0) <=> true gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(x)) The following defined symbols remain to be analysed: gr, cond1, cond2, encArg They will be analysed ascendingly in the following order: cond1 = cond2 gr < cond1 cond1 < encArg gr < cond2 cond2 < encArg gr < encArg ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) Induction Base: gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, 0)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, 0))) Induction Step: gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, +(n4_4, 1))), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, +(n4_4, 1)))) ->_R^Omega(1) gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, n4_4))) ->_IH *3_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: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(gr(x, 0'), y, y) cond2(false, x, y) -> cond1(gr(x, 0'), p(x), y) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x encArg(true) -> true encArg(0') -> 0' encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) Types: cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p 0' :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encArg :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_0 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p hole_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p Generator Equations: gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(0) <=> true gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(x)) The following defined symbols remain to be analysed: gr, cond1, cond2, encArg They will be analysed ascendingly in the following order: cond1 = cond2 gr < cond1 cond1 < encArg gr < cond2 cond2 < encArg gr < encArg ---------------------------------------- (24) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (25) BOUNDS(n^1, INF) ---------------------------------------- (26) Obligation: Innermost TRS: Rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(gr(x, 0'), y, y) cond2(false, x, y) -> cond1(gr(x, 0'), p(x), y) gr(0', x) -> false gr(s(x), 0') -> true gr(s(x), s(y)) -> gr(x, y) p(0') -> 0' p(s(x)) -> x encArg(true) -> true encArg(0') -> 0' encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) Types: cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p 0' :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encArg :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p cons_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_cond1 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_true :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_cond2 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_gr :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_0 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_false :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_p :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p encode_s :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p hole_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p1_4 :: true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4 :: Nat -> true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p Lemmas: gr(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, n4_4)), gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(1, n4_4))) -> *3_4, rt in Omega(n4_4) Generator Equations: gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(0) <=> true gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(x, 1)) <=> s(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(x)) The following defined symbols remain to be analysed: cond2, cond1, encArg They will be analysed ascendingly in the following order: cond1 = cond2 cond1 < encArg cond2 < encArg ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(n3394_4)) -> gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(n3394_4), rt in Omega(0) Induction Base: encArg(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(0)) ->_R^Omega(0) true Induction Step: encArg(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(+(n3394_4, 1))) ->_R^Omega(0) s(encArg(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(n3394_4))) ->_IH s(gen_true:0':false:s:cons_cond1:cons_cond2:cons_gr:cons_p2_4(c3395_4)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (28) BOUNDS(1, INF)