/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 338 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, 43.0 s] (14) BOUNDS(1, n^3) (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (16) TRS for Loop Detection (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) TRS for Loop Detection ---------------------------------------- (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(gr0(x), y, y) cond2(false, x, y) -> cond1(gr0(x), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) gr0(0) -> false gr0(s(x)) -> true 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(false) -> false encArg(0) -> 0 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_gr0(x_1)) -> gr0(encArg(x_1)) 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_gr0(x_1) -> gr0(encArg(x_1)) encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0 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(gr0(x), y, y) cond2(false, x, y) -> cond1(gr0(x), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) gr0(0) -> false gr0(s(x)) -> true p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(false) -> false encArg(0) -> 0 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_gr0(x_1)) -> gr0(encArg(x_1)) 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_gr0(x_1) -> gr0(encArg(x_1)) encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0 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(gr0(x), y, y) cond2(false, x, y) -> cond1(gr0(x), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) gr0(0) -> false gr0(s(x)) -> true p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(false) -> false encArg(0) -> 0 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_gr0(x_1)) -> gr0(encArg(x_1)) 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_gr0(x_1) -> gr0(encArg(x_1)) encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0 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(gr0(x), y, y) [1] cond2(false, x, y) -> cond1(gr0(x), p(x), y) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] gr0(0) -> false [1] gr0(s(x)) -> true [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(true) -> true [0] encArg(false) -> false [0] encArg(0) -> 0 [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_gr0(x_1)) -> gr0(encArg(x_1)) [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_gr0(x_1) -> gr0(encArg(x_1)) [0] encode_false -> false [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_0 -> 0 [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(gr0(x), y, y) [1] cond2(false, x, y) -> cond1(gr0(x), p(x), y) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] gr0(0) -> false [1] gr0(s(x)) -> true [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(true) -> true [0] encArg(false) -> false [0] encArg(0) -> 0 [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_gr0(x_1)) -> gr0(encArg(x_1)) [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_gr0(x_1) -> gr0(encArg(x_1)) [0] encode_false -> false [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] The TRS has the following type information: cond1 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p true :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p cond2 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p gr :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p gr0 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p false :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p p :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p 0 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p s :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p encArg :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p cons_cond1 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p cons_cond2 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p cons_gr :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p cons_gr0 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p cons_p :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p encode_cond1 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p encode_true :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p encode_cond2 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p encode_gr :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p encode_gr0 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p encode_false :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p encode_p :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p encode_0 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p encode_s :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0: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_gr0(v0) -> null_encode_gr0 [0] encode_false -> null_encode_false [0] encode_p(v0) -> null_encode_p [0] encode_0 -> null_encode_0 [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] gr0(v0) -> null_gr0 [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_gr0, null_encode_false, null_encode_p, null_encode_0, null_encode_s, null_cond1, null_cond2, null_gr, null_gr0, 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(gr0(x), y, y) [1] cond2(false, x, y) -> cond1(gr0(x), p(x), y) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] gr0(0) -> false [1] gr0(s(x)) -> true [1] p(0) -> 0 [1] p(s(x)) -> x [1] encArg(true) -> true [0] encArg(false) -> false [0] encArg(0) -> 0 [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_gr0(x_1)) -> gr0(encArg(x_1)) [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_gr0(x_1) -> gr0(encArg(x_1)) [0] encode_false -> false [0] encode_p(x_1) -> p(encArg(x_1)) [0] encode_0 -> 0 [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_gr0(v0) -> null_encode_gr0 [0] encode_false -> null_encode_false [0] encode_p(v0) -> null_encode_p [0] encode_0 -> null_encode_0 [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] gr0(v0) -> null_gr0 [0] p(v0) -> null_p [0] The TRS has the following type information: cond1 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p true :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p cond2 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p gr :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p gr0 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p false :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p p :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p 0 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p s :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p encArg :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p cons_cond1 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p cons_cond2 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p cons_gr :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p cons_gr0 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p cons_p :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p encode_cond1 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p encode_true :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p encode_cond2 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p encode_gr :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p encode_gr0 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p encode_false :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p encode_p :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p encode_0 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p encode_s :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p -> true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p null_encArg :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p null_encode_cond1 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p null_encode_true :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p null_encode_cond2 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p null_encode_gr :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p null_encode_gr0 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p null_encode_false :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p null_encode_p :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p null_encode_0 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p null_encode_s :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p null_cond1 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p null_cond2 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p null_gr :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p null_gr0 :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0:null_p null_p :: true:false:0:s:cons_cond1:cons_cond2:cons_gr:cons_gr0:cons_p:null_encArg:null_encode_cond1:null_encode_true:null_encode_cond2:null_encode_gr:null_encode_gr0:null_encode_false:null_encode_p:null_encode_0:null_encode_s:null_cond1:null_cond2:null_gr:null_gr0: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 false => 1 0 => 0 null_encArg => 0 null_encode_cond1 => 0 null_encode_true => 0 null_encode_cond2 => 0 null_encode_gr => 0 null_encode_gr0 => 0 null_encode_false => 0 null_encode_p => 0 null_encode_0 => 0 null_encode_s => 0 null_cond1 => 0 null_cond2 => 0 null_gr => 0 null_gr0 => 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(gr0(x), y, y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0 cond2(z, z', z'') -{ 1 }-> cond1(gr0(x), 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 }-> gr0(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_gr0(z) -{ 0 }-> gr0(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_gr0(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 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 gr0(z) -{ 1 }-> 2 :|: x >= 0, z = 1 + x gr0(z) -{ 1 }-> 1 :|: z = 0 gr0(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 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,[gr0(V1, Out)],[V1 >= 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(V1, Out)],[V1 >= 0]). 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(Out)],[]). eq(start(V1, V, V2),0,[fun8(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,[gr0(V5, 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,[gr0(V8, 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(gr0(V1, Out),1,[],[Out = 1,V1 = 0]). eq(gr0(V1, Out),1,[],[Out = 2,V13 >= 0,V1 = 1 + V13]). eq(p(V1, Out),1,[],[Out = 0,V1 = 0]). eq(p(V1, Out),1,[],[Out = V14,V14 >= 0,V1 = 1 + V14]). eq(encArg(V1, Out),0,[],[Out = 2,V1 = 2]). eq(encArg(V1, Out),0,[],[Out = 1,V1 = 1]). eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]). eq(encArg(V1, Out),0,[encArg(V15, Ret12)],[Out = 1 + Ret12,V1 = 1 + V15,V15 >= 0]). eq(encArg(V1, Out),0,[encArg(V17, Ret03),encArg(V18, Ret13),encArg(V16, Ret21),cond1(Ret03, Ret13, Ret21, Ret4)],[Out = Ret4,V17 >= 0,V1 = 1 + V16 + V17 + V18,V16 >= 0,V18 >= 0]). eq(encArg(V1, Out),0,[encArg(V19, Ret04),encArg(V21, Ret14),encArg(V20, Ret22),cond2(Ret04, Ret14, Ret22, Ret5)],[Out = Ret5,V19 >= 0,V1 = 1 + V19 + V20 + V21,V20 >= 0,V21 >= 0]). eq(encArg(V1, Out),0,[encArg(V23, Ret05),encArg(V22, Ret15),gr(Ret05, Ret15, Ret6)],[Out = Ret6,V23 >= 0,V1 = 1 + V22 + V23,V22 >= 0]). eq(encArg(V1, Out),0,[encArg(V24, Ret06),gr0(Ret06, Ret7)],[Out = Ret7,V1 = 1 + V24,V24 >= 0]). eq(encArg(V1, Out),0,[encArg(V25, Ret07),p(Ret07, Ret8)],[Out = Ret8,V1 = 1 + V25,V25 >= 0]). eq(fun(V1, V, V2, Out),0,[encArg(V28, Ret08),encArg(V26, Ret16),encArg(V27, Ret23),cond1(Ret08, Ret16, Ret23, Ret9)],[Out = Ret9,V28 >= 0,V27 >= 0,V26 >= 0,V1 = V28,V = V26,V2 = V27]). eq(fun1(Out),0,[],[Out = 2]). eq(fun2(V1, V, V2, Out),0,[encArg(V31, Ret09),encArg(V30, Ret17),encArg(V29, Ret24),cond2(Ret09, Ret17, Ret24, Ret10)],[Out = Ret10,V31 >= 0,V29 >= 0,V30 >= 0,V1 = V31,V = V30,V2 = V29]). eq(fun3(V1, V, Out),0,[encArg(V33, Ret010),encArg(V32, Ret18),gr(Ret010, Ret18, Ret19)],[Out = Ret19,V33 >= 0,V32 >= 0,V1 = V33,V = V32]). eq(fun4(V1, Out),0,[encArg(V34, Ret011),gr0(Ret011, Ret20)],[Out = Ret20,V34 >= 0,V1 = V34]). eq(fun5(Out),0,[],[Out = 1]). eq(fun6(V1, Out),0,[encArg(V35, Ret012),p(Ret012, Ret25)],[Out = Ret25,V35 >= 0,V1 = V35]). eq(fun7(Out),0,[],[Out = 0]). eq(fun8(V1, Out),0,[encArg(V36, Ret110)],[Out = 1 + Ret110,V36 >= 0,V1 = V36]). eq(encArg(V1, Out),0,[],[Out = 0,V37 >= 0,V1 = V37]). eq(fun(V1, V, V2, Out),0,[],[Out = 0,V39 >= 0,V2 = V40,V38 >= 0,V1 = V39,V = V38,V40 >= 0]). eq(fun1(Out),0,[],[Out = 0]). eq(fun2(V1, V, V2, Out),0,[],[Out = 0,V43 >= 0,V2 = V41,V42 >= 0,V1 = V43,V = V42,V41 >= 0]). eq(fun3(V1, V, Out),0,[],[Out = 0,V44 >= 0,V45 >= 0,V1 = V44,V = V45]). eq(fun4(V1, Out),0,[],[Out = 0,V46 >= 0,V1 = V46]). eq(fun5(Out),0,[],[Out = 0]). eq(fun6(V1, Out),0,[],[Out = 0,V47 >= 0,V1 = V47]). eq(fun8(V1, Out),0,[],[Out = 0,V48 >= 0,V1 = V48]). eq(cond1(V1, V, V2, Out),0,[],[Out = 0,V49 >= 0,V2 = V50,V51 >= 0,V1 = V49,V = V51,V50 >= 0]). eq(cond2(V1, V, V2, Out),0,[],[Out = 0,V52 >= 0,V2 = V54,V53 >= 0,V1 = V52,V = V53,V54 >= 0]). eq(gr(V1, V, Out),0,[],[Out = 0,V56 >= 0,V55 >= 0,V1 = V56,V = V55]). eq(gr0(V1, Out),0,[],[Out = 0,V57 >= 0,V1 = V57]). eq(p(V1, Out),0,[],[Out = 0,V58 >= 0,V1 = V58]). 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(gr0(V1,Out),[V1],[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(V1,Out),[V1],[Out]). input_output_vars(fun5(Out),[],[Out]). input_output_vars(fun6(V1,Out),[V1],[Out]). input_output_vars(fun7(Out),[],[Out]). input_output_vars(fun8(V1,Out),[V1],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. non_recursive : [gr0/2] 1. non_recursive : [p/2] 2. recursive : [gr/3] 3. recursive : [cond1/4,cond2/4] 4. recursive [non_tail,multiple] : [encArg/2] 5. non_recursive : [fun/4] 6. non_recursive : [fun1/1] 7. non_recursive : [fun2/4] 8. non_recursive : [fun3/3] 9. non_recursive : [fun4/2] 10. non_recursive : [fun5/1] 11. non_recursive : [fun6/2] 12. non_recursive : [fun7/1] 13. non_recursive : [fun8/2] 14. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into gr0/2 1. SCC is partially evaluated into p/2 2. SCC is partially evaluated into gr/3 3. SCC is partially evaluated into cond2/4 4. SCC is partially evaluated into encArg/2 5. SCC is partially evaluated into fun/4 6. SCC is partially evaluated into fun1/1 7. SCC is partially evaluated into fun2/4 8. SCC is partially evaluated into fun3/3 9. SCC is partially evaluated into fun4/2 10. SCC is partially evaluated into fun5/1 11. SCC is partially evaluated into fun6/2 12. SCC is completely evaluated into other SCCs 13. SCC is partially evaluated into fun8/2 14. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations gr0/2 * CE 26 is refined into CE [58] * CE 27 is refined into CE [59] * CE 25 is refined into CE [60] ### Cost equations --> "Loop" of gr0/2 * CEs [58] --> Loop 32 * CEs [59] --> Loop 33 * CEs [60] --> Loop 34 ### Ranking functions of CR gr0(V1,Out) #### Partial ranking functions of CR gr0(V1,Out) ### Specialization of cost equations p/2 * CE 29 is refined into CE [61] * CE 28 is refined into CE [62] * CE 30 is refined into CE [63] ### Cost equations --> "Loop" of p/2 * CEs [61] --> Loop 35 * CEs [62,63] --> Loop 36 ### Ranking functions of CR p(V1,Out) #### Partial ranking functions of CR p(V1,Out) ### Specialization of cost equations gr/3 * CE 19 is refined into CE [64] * CE 17 is refined into CE [65] * CE 16 is refined into CE [66] * CE 18 is refined into CE [67] ### Cost equations --> "Loop" of gr/3 * CEs [67] --> Loop 37 * CEs [64] --> Loop 38 * CEs [65] --> Loop 39 * CEs [66] --> Loop 40 ### Ranking functions of CR gr(V1,V,Out) * RF of phase [37]: [V,V1] #### Partial ranking functions of CR gr(V1,V,Out) * Partial RF of phase [37]: - RF of loop [37:1]: V V1 ### Specialization of cost equations cond2/4 * CE 21 is refined into CE [68,69,70] * CE 20 is refined into CE [71,72,73,74,75] * CE 24 is refined into CE [76] * CE 23 is refined into CE [77,78,79] * CE 22 is refined into CE [80,81,82,83,84,85,86] ### Cost equations --> "Loop" of cond2/4 * CEs [79] --> Loop 41 * CEs [78] --> Loop 42 * CEs [77] --> Loop 43 * CEs [86] --> Loop 44 * CEs [85] --> Loop 45 * CEs [84] --> Loop 46 * CEs [81] --> Loop 47 * CEs [83] --> Loop 48 * CEs [80,82] --> Loop 49 * CEs [68,69,70] --> Loop 50 * CEs [71,72,73,74,75,76] --> Loop 51 ### Ranking functions of CR cond2(V1,V,V2,Out) * RF of phase [45]: [V-1] #### Partial ranking functions of CR cond2(V1,V,V2,Out) * Partial RF of phase [45]: - RF of loop [45:1]: V-1 ### Specialization of cost equations encArg/2 * CE 35 is refined into CE [87] * CE 33 is refined into CE [88] * CE 34 is refined into CE [89] * CE 36 is refined into CE [90] * CE 39 is refined into CE [91,92,93] * CE 40 is refined into CE [94,95] * CE 38 is refined into CE [96,97,98,99,100] * CE 32 is refined into CE [101,102,103,104,105,106,107] * CE 31 is refined into CE [108] * CE 37 is refined into CE [109,110] ### Cost equations --> "Loop" of encArg/2 * CEs [102,103] --> Loop 52 * CEs [101,104,105,106,107,108,109,110] --> Loop 53 * CEs [100] --> Loop 54 * CEs [97] --> Loop 55 * CEs [99] --> Loop 56 * CEs [96] --> Loop 57 * CEs [98] --> Loop 58 * CEs [95] --> Loop 59 * CEs [93] --> Loop 60 * CEs [90,91] --> Loop 61 * CEs [92,94] --> Loop 62 * CEs [87] --> Loop 63 * CEs [88] --> Loop 64 * CEs [89] --> Loop 65 ### Ranking functions of CR encArg(V1,Out) * RF of phase [52,53,54,55,56,57,58,59,60,61,62]: [V1] #### Partial ranking functions of CR encArg(V1,Out) * Partial RF of phase [52,53,54,55,56,57,58,59,60,61,62]: - RF of loop [52:1,52:2,52:3,53:1,53:2,53:3,54:1,54:2,55:1,55:2,56:1,56:2,57:1,57:2,58:1,58:2,59:1,60:1,61:1,62:1]: V1 ### Specialization of cost equations fun/4 * CE 41 is refined into CE [111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137] * CE 42 is refined into CE [138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203] * CE 43 is refined into CE [204] ### Cost equations --> "Loop" of fun/4 * CEs [114,115,116,132,133,134,154,155,156,157,158,159,160,161,162,163,164] --> Loop 66 * CEs [112,118,121,127,130,136,145,146,147,148,149,167,168,178,179,180,181,182,200,201] --> Loop 67 * CEs [111,113,117,119,120,122,123,124,125,126,128,129,131,135,137,138,139,140,141,142,143,144,150,151,152,153,165,166,169,170,171,172,173,174,175,176,177,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,202,203,204] --> Loop 68 ### 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 44 is refined into CE [205] * CE 45 is refined into CE [206] ### Cost equations --> "Loop" of fun1/1 * CEs [205] --> Loop 69 * CEs [206] --> Loop 70 ### Ranking functions of CR fun1(Out) #### Partial ranking functions of CR fun1(Out) ### Specialization of cost equations fun2/4 * CE 46 is refined into CE [207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251] * CE 47 is refined into CE [252] ### Cost equations --> "Loop" of fun2/4 * CEs [213,214,215,216,217,218,246,247,248] --> Loop 71 * CEs [209,210,221,222,227,228,239,240,244,250] --> Loop 72 * CEs [207,208,211,212,219,220,223,224,225,226,229,230,231,232,233,234,235,236,237,238,241,242,243,245,249,251,252] --> Loop 73 ### 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 48 is refined into CE [253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278] * CE 49 is refined into CE [279] ### Cost equations --> "Loop" of fun3/3 * CEs [261] --> Loop 74 * CEs [258,260,275] --> Loop 75 * CEs [259,276] --> Loop 76 * CEs [254,257,263,265,268,271] --> Loop 77 * CEs [253,256,262,267,270,273,277] --> Loop 78 * CEs [255,264,266,269,272,274,278,279] --> Loop 79 ### Ranking functions of CR fun3(V1,V,Out) #### Partial ranking functions of CR fun3(V1,V,Out) ### Specialization of cost equations fun4/2 * CE 50 is refined into CE [280,281,282,283,284,285,286] * CE 51 is refined into CE [287] ### Cost equations --> "Loop" of fun4/2 * CEs [280,285] --> Loop 80 * CEs [282,284] --> Loop 81 * CEs [281,283,286,287] --> Loop 82 ### Ranking functions of CR fun4(V1,Out) #### Partial ranking functions of CR fun4(V1,Out) ### Specialization of cost equations fun5/1 * CE 52 is refined into CE [288] * CE 53 is refined into CE [289] ### Cost equations --> "Loop" of fun5/1 * CEs [288] --> Loop 83 * CEs [289] --> Loop 84 ### Ranking functions of CR fun5(Out) #### Partial ranking functions of CR fun5(Out) ### Specialization of cost equations fun6/2 * CE 54 is refined into CE [290,291,292,293,294] * CE 55 is refined into CE [295] ### Cost equations --> "Loop" of fun6/2 * CEs [291,293] --> Loop 85 * CEs [290,292,294,295] --> Loop 86 ### Ranking functions of CR fun6(V1,Out) #### Partial ranking functions of CR fun6(V1,Out) ### Specialization of cost equations fun8/2 * CE 56 is refined into CE [296,297,298] * CE 57 is refined into CE [299] ### Cost equations --> "Loop" of fun8/2 * CEs [298] --> Loop 87 * CEs [299] --> Loop 88 * CEs [296,297] --> Loop 89 ### Ranking functions of CR fun8(V1,Out) #### Partial ranking functions of CR fun8(V1,Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [300] * CE 2 is refined into CE [301,302,303,304,305,306,307] * CE 3 is refined into CE [308,309] * CE 4 is refined into CE [310,311,312,313,314] * CE 5 is refined into CE [315,316,317] * CE 6 is refined into CE [318,319] * CE 7 is refined into CE [320,321,322] * CE 8 is refined into CE [323,324] * CE 9 is refined into CE [325,326] * CE 10 is refined into CE [327,328] * CE 11 is refined into CE [329,330,331] * CE 12 is refined into CE [332,333,334] * CE 13 is refined into CE [335,336] * CE 14 is refined into CE [337,338] * CE 15 is refined into CE [339,340,341] ### Cost equations --> "Loop" of start/3 * CEs [300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341] --> Loop 90 ### Ranking functions of CR start(V1,V,V2) #### Partial ranking functions of CR start(V1,V,V2) Computing Bounds ===================================== #### Cost of chains of gr0(V1,Out): * Chain [34]: 1 with precondition: [V1=0,Out=1] * Chain [33]: 0 with precondition: [Out=0,V1>=0] * Chain [32]: 1 with precondition: [Out=2,V1>=1] #### Cost of chains of p(V1,Out): * Chain [36]: 1 with precondition: [Out=0,V1>=0] * Chain [35]: 1 with precondition: [V1=Out+1,V1>=1] #### Cost of chains of gr(V1,V,Out): * Chain [[37],40]: 1*it(37)+1 Such that:it(37) =< V1 with precondition: [Out=1,V1>=1,V>=V1] * Chain [[37],39]: 1*it(37)+1 Such that:it(37) =< V with precondition: [Out=2,V>=1,V1>=V+1] * Chain [[37],38]: 1*it(37)+0 Such that:it(37) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [40]: 1 with precondition: [V1=0,Out=1,V>=0] * Chain [39]: 1 with precondition: [V=0,Out=2,V1>=1] * Chain [38]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of cond2(V1,V,V2,Out): * Chain [[45],51]: 5*it(45)+1*s(4)+3 Such that:aux(3) =< V it(45) =< aux(3) s(4) =< it(45)*aux(3) with precondition: [V1=1,Out=0,V>=2,V2+1>=V] * Chain [[45],49,51]: 5*it(45)+1*s(4)+8 Such that:aux(4) =< V it(45) =< aux(4) s(4) =< it(45)*aux(4) with precondition: [V1=1,Out=0,V>=2,V2+1>=V] * Chain [[45],47,51]: 5*it(45)+1*s(4)+1*s(5)+7 Such that:s(5) =< V2 aux(5) =< V it(45) =< aux(5) s(4) =< it(45)*aux(5) with precondition: [V1=1,Out=0,V>=2,V2+1>=V] * Chain [[45],46,51]: 5*it(45)+1*s(4)+1*s(6)+7 Such that:s(6) =< V2 aux(6) =< V it(45) =< aux(6) s(4) =< it(45)*aux(6) with precondition: [V1=1,Out=0,V>=2,V2+1>=V] * Chain [51]: 3 with precondition: [Out=0,V1>=0,V>=0,V2>=0] * Chain [50]: 2 with precondition: [V1=2,Out=0,V>=0,V2>=0] * Chain [49,51]: 8 with precondition: [V1=1,Out=0,V>=1,V2>=0] * Chain [48,51]: 8 with precondition: [V1=1,V2=0,Out=0,V>=2] * Chain [48,50]: 7 with precondition: [V1=1,V2=0,Out=0,V>=2] * Chain [48,43,51]: 12 with precondition: [V1=1,V2=0,Out=0,V>=2] * Chain [48,42,51]: 11 with precondition: [V1=1,V2=0,Out=0,V>=2] * Chain [47,51]: 1*s(5)+7 Such that:s(5) =< V2 with precondition: [V1=1,Out=0,V>=1,V2>=0] * Chain [46,51]: 1*s(6)+7 Such that:s(6) =< V2 with precondition: [V1=1,Out=0,V>=1,V2>=0] * Chain [44,51]: 1*s(8)+8 Such that:s(8) =< V2 with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [44,50]: 1*s(8)+7 Such that:s(8) =< V2 with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [44,42,51]: 2*s(7)+11 Such that:aux(7) =< V2 s(7) =< aux(7) with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [44,41,[45],51]: 7*it(45)+1*s(4)+12 Such that:aux(9) =< V2 it(45) =< aux(9) s(4) =< it(45)*aux(9) with precondition: [V1=1,Out=0,V2>=2,V>=V2+2] * Chain [44,41,[45],49,51]: 7*it(45)+1*s(4)+17 Such that:aux(11) =< V2 it(45) =< aux(11) s(4) =< it(45)*aux(11) with precondition: [V1=1,Out=0,V2>=2,V>=V2+2] * Chain [44,41,[45],47,51]: 8*it(45)+1*s(4)+16 Such that:aux(13) =< V2 it(45) =< aux(13) s(4) =< it(45)*aux(13) with precondition: [V1=1,Out=0,V2>=2,V>=V2+2] * Chain [44,41,[45],46,51]: 8*it(45)+1*s(4)+16 Such that:aux(15) =< V2 it(45) =< aux(15) s(4) =< it(45)*aux(15) with precondition: [V1=1,Out=0,V2>=2,V>=V2+2] * Chain [44,41,51]: 2*s(8)+12 Such that:aux(16) =< V2 s(8) =< aux(16) with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [44,41,49,51]: 2*s(8)+17 Such that:aux(17) =< V2 s(8) =< aux(17) with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [44,41,47,51]: 3*s(5)+16 Such that:aux(19) =< V2 s(5) =< aux(19) with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [44,41,46,51]: 3*s(6)+16 Such that:aux(21) =< V2 s(6) =< aux(21) with precondition: [V1=1,Out=0,V2>=1,V>=V2+2] * Chain [43,51]: 7 with precondition: [V1=2,V2=0,Out=0,V>=1] * Chain [42,51]: 1*s(7)+6 Such that:s(7) =< V2 with precondition: [V1=2,Out=0,V>=1,V2>=0] * Chain [41,[45],51]: 6*it(45)+1*s(4)+7 Such that:aux(8) =< V2 it(45) =< aux(8) s(4) =< it(45)*aux(8) with precondition: [V1=2,Out=0,V>=1,V2>=2] * Chain [41,[45],49,51]: 6*it(45)+1*s(4)+12 Such that:aux(10) =< V2 it(45) =< aux(10) s(4) =< it(45)*aux(10) with precondition: [V1=2,Out=0,V>=1,V2>=2] * Chain [41,[45],47,51]: 7*it(45)+1*s(4)+11 Such that:aux(12) =< V2 it(45) =< aux(12) s(4) =< it(45)*aux(12) with precondition: [V1=2,Out=0,V>=1,V2>=2] * Chain [41,[45],46,51]: 7*it(45)+1*s(4)+11 Such that:aux(14) =< V2 it(45) =< aux(14) s(4) =< it(45)*aux(14) with precondition: [V1=2,Out=0,V>=1,V2>=2] * Chain [41,51]: 1*s(9)+7 Such that:s(9) =< V2 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [41,49,51]: 1*s(9)+12 Such that:s(9) =< V2 with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [41,47,51]: 2*s(5)+11 Such that:aux(18) =< V2 s(5) =< aux(18) with precondition: [V1=2,Out=0,V>=1,V2>=1] * Chain [41,46,51]: 2*s(6)+11 Such that:aux(20) =< V2 s(6) =< aux(20) with precondition: [V1=2,Out=0,V>=1,V2>=1] #### Cost of chains of encArg(V1,Out): * Chain [65]: 0 with precondition: [V1=1,Out=1] * Chain [64]: 0 with precondition: [V1=2,Out=2] * Chain [63]: 0 with precondition: [Out=0,V1>=0] * Chain [multiple([52,53,54,55,56,57,58,59,60,61,62],[[65],[64],[63]])]: 19*it(52)+19*it(53)+1*it(54)+1*it(55)+1*it(56)+1*it(57)+4*it(59)+20*s(133)+4*s(134)+260*s(136)+24*s(137)+130*s(138)+20*s(139)+1*s(142)+1*s(143)+1*s(144)+0 Such that:it([65]) =< 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(53) =< aux(41) it(54) =< aux(41) it(55) =< aux(41) it(56) =< aux(41) it(57) =< aux(41) it(58) =< aux(41) it(59) =< aux(41) it([65]) =< aux(41) it([63]) =< aux(42) it([65]) =< aux(42) it(56) =< aux(43) it(52) =< aux(44) it(55) =< aux(45) it(56) =< aux(45) it(54) =< aux(46) aux(34) =< aux(41)+2 aux(39) =< aux(41)+1 aux(32) =< aux(41) aux(33) =< aux(41)+3 it(56) =< it([63])*(1/2)+aux(43) it(57) =< it([63])*(1/2)+aux(43) it(58) =< it([63])*(1/2)+aux(43) it(55) =< it([63])*(1/3)+aux(45) it(56) =< it([63])*(1/3)+aux(45) it(57) =< it([63])*(1/3)+aux(45) it(58) =< it([63])*(1/3)+aux(45) it(54) =< it([63])*(3/5)+it([65])*(1/5)+aux(46) it(55) =< it([63])*(3/5)+it([65])*(1/5)+aux(46) it(56) =< it([63])*(3/5)+it([65])*(1/5)+aux(46) it(57) =< it([63])*(3/5)+it([65])*(1/5)+aux(46) it(58) =< it([63])*(3/5)+it([65])*(1/5)+aux(46) it(52) =< it([63])*(1/3)+aux(44) it(53) =< it([63])*(1/3)+aux(44) s(144) =< it(58)*aux(34) s(143) =< it(56)*aux(39) s(142) =< it(54)*aux(32) s(140) =< it(53)*aux(34) s(141) =< it(53)*aux(33) s(135) =< it(52)*aux(32) s(138) =< s(141) s(139) =< s(138)*aux(33) s(136) =< s(140) s(137) =< s(136)*aux(34) s(133) =< s(135) s(134) =< s(133)*aux(41) with precondition: [V1>=1,Out>=0,V1>=Out] #### Cost of chains of fun(V1,V,V2,Out): * Chain [68]: 361*s(184)+19*s(185)+19*s(186)+19*s(187)+19*s(188)+76*s(190)+361*s(191)+19*s(196)+19*s(197)+19*s(198)+2470*s(202)+380*s(203)+4940*s(204)+456*s(205)+380*s(206)+76*s(207)+532*s(215)+28*s(216)+28*s(217)+28*s(218)+28*s(219)+416*s(221)+532*s(222)+28*s(227)+28*s(228)+28*s(229)+3640*s(233)+560*s(234)+7280*s(235)+672*s(236)+560*s(237)+112*s(238)+589*s(246)+31*s(247)+31*s(248)+31*s(249)+31*s(250)+809*s(252)+589*s(253)+31*s(258)+31*s(259)+31*s(260)+4030*s(264)+620*s(265)+8060*s(266)+744*s(267)+620*s(268)+124*s(269)+60*s(802)+52*s(900)+259*s(2531)+40*s(2532)+83*s(2675)+8*s(2681)+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(182) =< aux(94) s(213) =< aux(101) s(244) =< aux(108) s(2531) =< aux(88) s(2532) =< s(2531)*aux(88) s(246) =< aux(103) s(247) =< aux(103) s(248) =< aux(103) s(249) =< aux(103) s(250) =< aux(103) s(251) =< aux(103) s(252) =< aux(103) s(244) =< aux(103) s(244) =< aux(104) s(249) =< aux(105) s(253) =< aux(106) s(248) =< aux(107) s(249) =< aux(107) s(247) =< aux(109) s(254) =< aux(103)+2 s(255) =< aux(103)+1 s(256) =< aux(103) s(257) =< aux(103)+3 s(249) =< aux(104)*(1/2)+aux(105) s(250) =< aux(104)*(1/2)+aux(105) s(251) =< aux(104)*(1/2)+aux(105) s(248) =< aux(104)*(1/3)+aux(107) s(249) =< aux(104)*(1/3)+aux(107) s(250) =< aux(104)*(1/3)+aux(107) s(251) =< aux(104)*(1/3)+aux(107) s(247) =< aux(104)*(3/5)+s(244)*(1/5)+aux(109) s(248) =< aux(104)*(3/5)+s(244)*(1/5)+aux(109) s(249) =< aux(104)*(3/5)+s(244)*(1/5)+aux(109) s(250) =< aux(104)*(3/5)+s(244)*(1/5)+aux(109) s(251) =< aux(104)*(3/5)+s(244)*(1/5)+aux(109) s(253) =< aux(104)*(1/3)+aux(106) s(246) =< aux(104)*(1/3)+aux(106) s(258) =< s(251)*s(254) s(259) =< s(249)*s(255) s(260) =< s(247)*s(256) s(261) =< s(246)*s(254) s(262) =< s(246)*s(257) s(263) =< s(253)*s(256) s(264) =< s(262) s(265) =< s(264)*s(257) s(266) =< s(261) s(267) =< s(266)*s(254) s(268) =< s(263) s(269) =< s(268)*aux(103) s(802) =< s(252)*aux(103) s(2675) =< aux(87) s(2681) =< s(2675)*aux(87) s(215) =< aux(96) s(216) =< aux(96) s(217) =< aux(96) s(218) =< aux(96) s(219) =< aux(96) s(220) =< aux(96) s(221) =< aux(96) s(213) =< aux(96) s(213) =< aux(97) s(218) =< aux(98) s(222) =< aux(99) s(217) =< aux(100) s(218) =< aux(100) s(216) =< aux(102) s(223) =< aux(96)+2 s(224) =< aux(96)+1 s(225) =< aux(96) s(226) =< aux(96)+3 s(218) =< aux(97)*(1/2)+aux(98) s(219) =< aux(97)*(1/2)+aux(98) s(220) =< aux(97)*(1/2)+aux(98) s(217) =< aux(97)*(1/3)+aux(100) s(218) =< aux(97)*(1/3)+aux(100) s(219) =< aux(97)*(1/3)+aux(100) s(220) =< aux(97)*(1/3)+aux(100) s(216) =< aux(97)*(3/5)+s(213)*(1/5)+aux(102) s(217) =< aux(97)*(3/5)+s(213)*(1/5)+aux(102) s(218) =< aux(97)*(3/5)+s(213)*(1/5)+aux(102) s(219) =< aux(97)*(3/5)+s(213)*(1/5)+aux(102) s(220) =< aux(97)*(3/5)+s(213)*(1/5)+aux(102) s(222) =< aux(97)*(1/3)+aux(99) s(215) =< aux(97)*(1/3)+aux(99) s(227) =< s(220)*s(223) s(228) =< s(218)*s(224) s(229) =< s(216)*s(225) s(230) =< s(215)*s(223) s(231) =< s(215)*s(226) s(232) =< s(222)*s(225) s(233) =< s(231) s(234) =< s(233)*s(226) s(235) =< s(230) s(236) =< s(235)*s(223) s(237) =< s(232) s(238) =< s(237)*aux(96) s(184) =< aux(89) s(185) =< aux(89) s(186) =< aux(89) s(187) =< aux(89) s(188) =< aux(89) s(189) =< aux(89) s(190) =< aux(89) s(182) =< aux(89) s(182) =< aux(90) s(187) =< aux(91) s(191) =< aux(92) s(186) =< aux(93) s(187) =< aux(93) s(185) =< aux(95) s(192) =< aux(89)+2 s(193) =< aux(89)+1 s(194) =< aux(89) s(195) =< aux(89)+3 s(187) =< aux(90)*(1/2)+aux(91) s(188) =< aux(90)*(1/2)+aux(91) s(189) =< aux(90)*(1/2)+aux(91) s(186) =< aux(90)*(1/3)+aux(93) s(187) =< aux(90)*(1/3)+aux(93) s(188) =< aux(90)*(1/3)+aux(93) s(189) =< aux(90)*(1/3)+aux(93) s(185) =< aux(90)*(3/5)+s(182)*(1/5)+aux(95) s(186) =< aux(90)*(3/5)+s(182)*(1/5)+aux(95) s(187) =< aux(90)*(3/5)+s(182)*(1/5)+aux(95) s(188) =< aux(90)*(3/5)+s(182)*(1/5)+aux(95) s(189) =< aux(90)*(3/5)+s(182)*(1/5)+aux(95) s(191) =< aux(90)*(1/3)+aux(92) s(184) =< aux(90)*(1/3)+aux(92) s(196) =< s(189)*s(192) s(197) =< s(187)*s(193) s(198) =< s(185)*s(194) s(199) =< s(184)*s(192) s(200) =< s(184)*s(195) s(201) =< s(191)*s(194) s(202) =< s(200) s(203) =< s(202)*s(195) s(204) =< s(199) s(205) =< s(204)*s(192) s(206) =< s(201) s(207) =< s(206)*aux(89) s(900) =< s(221)*aux(96) with precondition: [Out=0,V1>=0,V>=0,V2>=0] * Chain [67]: 171*s(2842)+9*s(2843)+9*s(2844)+9*s(2845)+9*s(2846)+36*s(2848)+171*s(2849)+9*s(2854)+9*s(2855)+9*s(2856)+1170*s(2860)+180*s(2861)+2340*s(2862)+216*s(2863)+180*s(2864)+36*s(2865)+247*s(2873)+13*s(2874)+13*s(2875)+13*s(2876)+13*s(2877)+174*s(2879)+247*s(2880)+13*s(2885)+13*s(2886)+13*s(2887)+1690*s(2891)+260*s(2892)+3380*s(2893)+312*s(2894)+260*s(2895)+52*s(2896)+650*s(3054)+56*s(3057)+24*s(3125)+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(2840) =< aux(130) s(2871) =< aux(137) s(3054) =< aux(124) s(3057) =< s(3054)*aux(124) s(2873) =< aux(132) s(2874) =< aux(132) s(2875) =< aux(132) s(2876) =< aux(132) s(2877) =< aux(132) s(2878) =< aux(132) s(2879) =< aux(132) s(2871) =< aux(132) s(2871) =< aux(133) s(2876) =< aux(134) s(2880) =< aux(135) s(2875) =< aux(136) s(2876) =< aux(136) s(2874) =< aux(138) s(2881) =< aux(132)+2 s(2882) =< aux(132)+1 s(2883) =< aux(132) s(2884) =< aux(132)+3 s(2876) =< aux(133)*(1/2)+aux(134) s(2877) =< aux(133)*(1/2)+aux(134) s(2878) =< aux(133)*(1/2)+aux(134) s(2875) =< aux(133)*(1/3)+aux(136) s(2876) =< aux(133)*(1/3)+aux(136) s(2877) =< aux(133)*(1/3)+aux(136) s(2878) =< aux(133)*(1/3)+aux(136) s(2874) =< aux(133)*(3/5)+s(2871)*(1/5)+aux(138) s(2875) =< aux(133)*(3/5)+s(2871)*(1/5)+aux(138) s(2876) =< aux(133)*(3/5)+s(2871)*(1/5)+aux(138) s(2877) =< aux(133)*(3/5)+s(2871)*(1/5)+aux(138) s(2878) =< aux(133)*(3/5)+s(2871)*(1/5)+aux(138) s(2880) =< aux(133)*(1/3)+aux(135) s(2873) =< aux(133)*(1/3)+aux(135) s(2885) =< s(2878)*s(2881) s(2886) =< s(2876)*s(2882) s(2887) =< s(2874)*s(2883) s(2888) =< s(2873)*s(2881) s(2889) =< s(2873)*s(2884) s(2890) =< s(2880)*s(2883) s(2891) =< s(2889) s(2892) =< s(2891)*s(2884) s(2893) =< s(2888) s(2894) =< s(2893)*s(2881) s(2895) =< s(2890) s(2896) =< s(2895)*aux(132) s(2842) =< aux(125) s(2843) =< aux(125) s(2844) =< aux(125) s(2845) =< aux(125) s(2846) =< aux(125) s(2847) =< aux(125) s(2848) =< aux(125) s(2840) =< aux(125) s(2840) =< aux(126) s(2845) =< aux(127) s(2849) =< aux(128) s(2844) =< aux(129) s(2845) =< aux(129) s(2843) =< aux(131) s(2850) =< aux(125)+2 s(2851) =< aux(125)+1 s(2852) =< aux(125) s(2853) =< aux(125)+3 s(2845) =< aux(126)*(1/2)+aux(127) s(2846) =< aux(126)*(1/2)+aux(127) s(2847) =< aux(126)*(1/2)+aux(127) s(2844) =< aux(126)*(1/3)+aux(129) s(2845) =< aux(126)*(1/3)+aux(129) s(2846) =< aux(126)*(1/3)+aux(129) s(2847) =< aux(126)*(1/3)+aux(129) s(2843) =< aux(126)*(3/5)+s(2840)*(1/5)+aux(131) s(2844) =< aux(126)*(3/5)+s(2840)*(1/5)+aux(131) s(2845) =< aux(126)*(3/5)+s(2840)*(1/5)+aux(131) s(2846) =< aux(126)*(3/5)+s(2840)*(1/5)+aux(131) s(2847) =< aux(126)*(3/5)+s(2840)*(1/5)+aux(131) s(2849) =< aux(126)*(1/3)+aux(128) s(2842) =< aux(126)*(1/3)+aux(128) s(2854) =< s(2847)*s(2850) s(2855) =< s(2845)*s(2851) s(2856) =< s(2843)*s(2852) s(2857) =< s(2842)*s(2850) s(2858) =< s(2842)*s(2853) s(2859) =< s(2849)*s(2852) s(2860) =< s(2858) s(2861) =< s(2860)*s(2853) s(2862) =< s(2857) s(2863) =< s(2862)*s(2850) s(2864) =< s(2859) s(2865) =< s(2864)*aux(125) s(3125) =< s(2879)*aux(132) with precondition: [V2=2,Out=0,V1>=0,V>=0] * Chain [66]: 266*s(3612)+14*s(3613)+14*s(3614)+14*s(3615)+14*s(3616)+56*s(3618)+266*s(3619)+14*s(3624)+14*s(3625)+14*s(3626)+1820*s(3630)+280*s(3631)+3640*s(3632)+336*s(3633)+280*s(3634)+56*s(3635)+152*s(3643)+8*s(3644)+8*s(3645)+8*s(3646)+8*s(3647)+129*s(3649)+152*s(3650)+8*s(3655)+8*s(3656)+8*s(3657)+1040*s(3661)+160*s(3662)+2080*s(3663)+192*s(3664)+160*s(3665)+32*s(3666)+259*s(3825)+40*s(3826)+8*s(3961)+83*s(4093)+8*s(4099)+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(3610) =< aux(154) s(3641) =< aux(161) s(3825) =< aux(148) s(3826) =< s(3825)*aux(148) s(3643) =< aux(156) s(3644) =< aux(156) s(3645) =< aux(156) s(3646) =< aux(156) s(3647) =< aux(156) s(3648) =< aux(156) s(3649) =< aux(156) s(3641) =< aux(156) s(3641) =< aux(157) s(3646) =< aux(158) s(3650) =< aux(159) s(3645) =< aux(160) s(3646) =< aux(160) s(3644) =< aux(162) s(3651) =< aux(156)+2 s(3652) =< aux(156)+1 s(3653) =< aux(156) s(3654) =< aux(156)+3 s(3646) =< aux(157)*(1/2)+aux(158) s(3647) =< aux(157)*(1/2)+aux(158) s(3648) =< aux(157)*(1/2)+aux(158) s(3645) =< aux(157)*(1/3)+aux(160) s(3646) =< aux(157)*(1/3)+aux(160) s(3647) =< aux(157)*(1/3)+aux(160) s(3648) =< aux(157)*(1/3)+aux(160) s(3644) =< aux(157)*(3/5)+s(3641)*(1/5)+aux(162) s(3645) =< aux(157)*(3/5)+s(3641)*(1/5)+aux(162) s(3646) =< aux(157)*(3/5)+s(3641)*(1/5)+aux(162) s(3647) =< aux(157)*(3/5)+s(3641)*(1/5)+aux(162) s(3648) =< aux(157)*(3/5)+s(3641)*(1/5)+aux(162) s(3650) =< aux(157)*(1/3)+aux(159) s(3643) =< aux(157)*(1/3)+aux(159) s(3655) =< s(3648)*s(3651) s(3656) =< s(3646)*s(3652) s(3657) =< s(3644)*s(3653) s(3658) =< s(3643)*s(3651) s(3659) =< s(3643)*s(3654) s(3660) =< s(3650)*s(3653) s(3661) =< s(3659) s(3662) =< s(3661)*s(3654) s(3663) =< s(3658) s(3664) =< s(3663)*s(3651) s(3665) =< s(3660) s(3666) =< s(3665)*aux(156) s(3612) =< aux(149) s(3613) =< aux(149) s(3614) =< aux(149) s(3615) =< aux(149) s(3616) =< aux(149) s(3617) =< aux(149) s(3618) =< aux(149) s(3610) =< aux(149) s(3610) =< aux(150) s(3615) =< aux(151) s(3619) =< aux(152) s(3614) =< aux(153) s(3615) =< aux(153) s(3613) =< aux(155) s(3620) =< aux(149)+2 s(3621) =< aux(149)+1 s(3622) =< aux(149) s(3623) =< aux(149)+3 s(3615) =< aux(150)*(1/2)+aux(151) s(3616) =< aux(150)*(1/2)+aux(151) s(3617) =< aux(150)*(1/2)+aux(151) s(3614) =< aux(150)*(1/3)+aux(153) s(3615) =< aux(150)*(1/3)+aux(153) s(3616) =< aux(150)*(1/3)+aux(153) s(3617) =< aux(150)*(1/3)+aux(153) s(3613) =< aux(150)*(3/5)+s(3610)*(1/5)+aux(155) s(3614) =< aux(150)*(3/5)+s(3610)*(1/5)+aux(155) s(3615) =< aux(150)*(3/5)+s(3610)*(1/5)+aux(155) s(3616) =< aux(150)*(3/5)+s(3610)*(1/5)+aux(155) s(3617) =< aux(150)*(3/5)+s(3610)*(1/5)+aux(155) s(3619) =< aux(150)*(1/3)+aux(152) s(3612) =< aux(150)*(1/3)+aux(152) s(3624) =< s(3617)*s(3620) s(3625) =< s(3615)*s(3621) s(3626) =< s(3613)*s(3622) s(3627) =< s(3612)*s(3620) s(3628) =< s(3612)*s(3623) s(3629) =< s(3619)*s(3622) s(3630) =< s(3628) s(3631) =< s(3630)*s(3623) s(3632) =< s(3627) s(3633) =< s(3632)*s(3620) s(3634) =< s(3629) s(3635) =< s(3634)*aux(149) s(3961) =< s(3649)*aux(156) s(4093) =< aux(147) s(4099) =< s(4093)*aux(147) with precondition: [V=2,Out=0,V1>=0,V2>=0] #### Cost of chains of fun1(Out): * Chain [70]: 0 with precondition: [Out=0] * Chain [69]: 0 with precondition: [Out=2] #### Cost of chains of fun2(V1,V,V2,Out): * Chain [73]: 152*s(4533)+8*s(4534)+8*s(4535)+8*s(4536)+8*s(4537)+32*s(4539)+152*s(4540)+8*s(4545)+8*s(4546)+8*s(4547)+1040*s(4551)+160*s(4552)+2080*s(4553)+192*s(4554)+160*s(4555)+32*s(4556)+190*s(4564)+10*s(4565)+10*s(4566)+10*s(4567)+10*s(4568)+160*s(4570)+190*s(4571)+10*s(4576)+10*s(4577)+10*s(4578)+1300*s(4582)+200*s(4583)+2600*s(4584)+240*s(4585)+200*s(4586)+40*s(4587)+228*s(4595)+12*s(4596)+12*s(4597)+12*s(4598)+12*s(4599)+549*s(4601)+228*s(4602)+12*s(4607)+12*s(4608)+12*s(4609)+1560*s(4613)+240*s(4614)+3120*s(4615)+288*s(4616)+240*s(4617)+48*s(4618)+24*s(4623)+48*s(4624)+141*s(5296)+20*s(5297)+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(4531) =< aux(207) s(4562) =< aux(214) s(4593) =< aux(221) s(5296) =< aux(201) s(5297) =< s(5296)*aux(201) s(4601) =< aux(216) s(4624) =< s(4601)*aux(216) s(4595) =< aux(216) s(4596) =< aux(216) s(4597) =< aux(216) s(4598) =< aux(216) s(4599) =< aux(216) s(4600) =< aux(216) s(4593) =< aux(216) s(4593) =< aux(217) s(4598) =< aux(218) s(4602) =< aux(219) s(4597) =< aux(220) s(4598) =< aux(220) s(4596) =< aux(222) s(4603) =< aux(216)+2 s(4604) =< aux(216)+1 s(4605) =< aux(216) s(4606) =< aux(216)+3 s(4598) =< aux(217)*(1/2)+aux(218) s(4599) =< aux(217)*(1/2)+aux(218) s(4600) =< aux(217)*(1/2)+aux(218) s(4597) =< aux(217)*(1/3)+aux(220) s(4598) =< aux(217)*(1/3)+aux(220) s(4599) =< aux(217)*(1/3)+aux(220) s(4600) =< aux(217)*(1/3)+aux(220) s(4596) =< aux(217)*(3/5)+s(4593)*(1/5)+aux(222) s(4597) =< aux(217)*(3/5)+s(4593)*(1/5)+aux(222) s(4598) =< aux(217)*(3/5)+s(4593)*(1/5)+aux(222) s(4599) =< aux(217)*(3/5)+s(4593)*(1/5)+aux(222) s(4600) =< aux(217)*(3/5)+s(4593)*(1/5)+aux(222) s(4602) =< aux(217)*(1/3)+aux(219) s(4595) =< aux(217)*(1/3)+aux(219) s(4607) =< s(4600)*s(4603) s(4608) =< s(4598)*s(4604) s(4609) =< s(4596)*s(4605) s(4610) =< s(4595)*s(4603) s(4611) =< s(4595)*s(4606) s(4612) =< s(4602)*s(4605) s(4613) =< s(4611) s(4614) =< s(4613)*s(4606) s(4615) =< s(4610) s(4616) =< s(4615)*s(4603) s(4617) =< s(4612) s(4618) =< s(4617)*aux(216) s(4570) =< aux(209) s(4623) =< s(4570)*aux(209) s(4564) =< aux(209) s(4565) =< aux(209) s(4566) =< aux(209) s(4567) =< aux(209) s(4568) =< aux(209) s(4569) =< aux(209) s(4562) =< aux(209) s(4562) =< aux(210) s(4567) =< aux(211) s(4571) =< aux(212) s(4566) =< aux(213) s(4567) =< aux(213) s(4565) =< aux(215) s(4572) =< aux(209)+2 s(4573) =< aux(209)+1 s(4574) =< aux(209) s(4575) =< aux(209)+3 s(4567) =< aux(210)*(1/2)+aux(211) s(4568) =< aux(210)*(1/2)+aux(211) s(4569) =< aux(210)*(1/2)+aux(211) s(4566) =< aux(210)*(1/3)+aux(213) s(4567) =< aux(210)*(1/3)+aux(213) s(4568) =< aux(210)*(1/3)+aux(213) s(4569) =< aux(210)*(1/3)+aux(213) s(4565) =< aux(210)*(3/5)+s(4562)*(1/5)+aux(215) s(4566) =< aux(210)*(3/5)+s(4562)*(1/5)+aux(215) s(4567) =< aux(210)*(3/5)+s(4562)*(1/5)+aux(215) s(4568) =< aux(210)*(3/5)+s(4562)*(1/5)+aux(215) s(4569) =< aux(210)*(3/5)+s(4562)*(1/5)+aux(215) s(4571) =< aux(210)*(1/3)+aux(212) s(4564) =< aux(210)*(1/3)+aux(212) s(4576) =< s(4569)*s(4572) s(4577) =< s(4567)*s(4573) s(4578) =< s(4565)*s(4574) s(4579) =< s(4564)*s(4572) s(4580) =< s(4564)*s(4575) s(4581) =< s(4571)*s(4574) s(4582) =< s(4580) s(4583) =< s(4582)*s(4575) s(4584) =< s(4579) s(4585) =< s(4584)*s(4572) s(4586) =< s(4581) s(4587) =< s(4586)*aux(209) s(4533) =< aux(202) s(4534) =< aux(202) s(4535) =< aux(202) s(4536) =< aux(202) s(4537) =< aux(202) s(4538) =< aux(202) s(4539) =< aux(202) s(4531) =< aux(202) s(4531) =< aux(203) s(4536) =< aux(204) s(4540) =< aux(205) s(4535) =< aux(206) s(4536) =< aux(206) s(4534) =< aux(208) s(4541) =< aux(202)+2 s(4542) =< aux(202)+1 s(4543) =< aux(202) s(4544) =< aux(202)+3 s(4536) =< aux(203)*(1/2)+aux(204) s(4537) =< aux(203)*(1/2)+aux(204) s(4538) =< aux(203)*(1/2)+aux(204) s(4535) =< aux(203)*(1/3)+aux(206) s(4536) =< aux(203)*(1/3)+aux(206) s(4537) =< aux(203)*(1/3)+aux(206) s(4538) =< aux(203)*(1/3)+aux(206) s(4534) =< aux(203)*(3/5)+s(4531)*(1/5)+aux(208) s(4535) =< aux(203)*(3/5)+s(4531)*(1/5)+aux(208) s(4536) =< aux(203)*(3/5)+s(4531)*(1/5)+aux(208) s(4537) =< aux(203)*(3/5)+s(4531)*(1/5)+aux(208) s(4538) =< aux(203)*(3/5)+s(4531)*(1/5)+aux(208) s(4540) =< aux(203)*(1/3)+aux(205) s(4533) =< aux(203)*(1/3)+aux(205) s(4545) =< s(4538)*s(4541) s(4546) =< s(4536)*s(4542) s(4547) =< s(4534)*s(4543) s(4548) =< s(4533)*s(4541) s(4549) =< s(4533)*s(4544) s(4550) =< s(4540)*s(4543) s(4551) =< s(4549) s(4552) =< s(4551)*s(4544) s(4553) =< s(4548) s(4554) =< s(4553)*s(4541) s(4555) =< s(4550) s(4556) =< s(4555)*aux(202) with precondition: [Out=0,V1>=0,V>=0,V2>=0] * Chain [72]: 76*s(5586)+4*s(5587)+4*s(5588)+4*s(5589)+4*s(5590)+16*s(5592)+76*s(5593)+4*s(5598)+4*s(5599)+4*s(5600)+520*s(5604)+80*s(5605)+1040*s(5606)+96*s(5607)+80*s(5608)+16*s(5609)+95*s(5617)+5*s(5618)+5*s(5619)+5*s(5620)+5*s(5621)+80*s(5623)+95*s(5624)+5*s(5629)+5*s(5630)+5*s(5631)+650*s(5635)+100*s(5636)+1300*s(5637)+120*s(5638)+100*s(5639)+20*s(5640)+420*s(5643)+12*s(5645)+40*s(5646)+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(5584) =< aux(232) s(5615) =< aux(239) s(5643) =< aux(226) s(5623) =< aux(234) s(5645) =< s(5623)*aux(234) s(5646) =< s(5643)*aux(226) s(5617) =< aux(234) s(5618) =< aux(234) s(5619) =< aux(234) s(5620) =< aux(234) s(5621) =< aux(234) s(5622) =< aux(234) s(5615) =< aux(234) s(5615) =< aux(235) s(5620) =< aux(236) s(5624) =< aux(237) s(5619) =< aux(238) s(5620) =< aux(238) s(5618) =< aux(240) s(5625) =< aux(234)+2 s(5626) =< aux(234)+1 s(5627) =< aux(234) s(5628) =< aux(234)+3 s(5620) =< aux(235)*(1/2)+aux(236) s(5621) =< aux(235)*(1/2)+aux(236) s(5622) =< aux(235)*(1/2)+aux(236) s(5619) =< aux(235)*(1/3)+aux(238) s(5620) =< aux(235)*(1/3)+aux(238) s(5621) =< aux(235)*(1/3)+aux(238) s(5622) =< aux(235)*(1/3)+aux(238) s(5618) =< aux(235)*(3/5)+s(5615)*(1/5)+aux(240) s(5619) =< aux(235)*(3/5)+s(5615)*(1/5)+aux(240) s(5620) =< aux(235)*(3/5)+s(5615)*(1/5)+aux(240) s(5621) =< aux(235)*(3/5)+s(5615)*(1/5)+aux(240) s(5622) =< aux(235)*(3/5)+s(5615)*(1/5)+aux(240) s(5624) =< aux(235)*(1/3)+aux(237) s(5617) =< aux(235)*(1/3)+aux(237) s(5629) =< s(5622)*s(5625) s(5630) =< s(5620)*s(5626) s(5631) =< s(5618)*s(5627) s(5632) =< s(5617)*s(5625) s(5633) =< s(5617)*s(5628) s(5634) =< s(5624)*s(5627) s(5635) =< s(5633) s(5636) =< s(5635)*s(5628) s(5637) =< s(5632) s(5638) =< s(5637)*s(5625) s(5639) =< s(5634) s(5640) =< s(5639)*aux(234) s(5586) =< aux(227) s(5587) =< aux(227) s(5588) =< aux(227) s(5589) =< aux(227) s(5590) =< aux(227) s(5591) =< aux(227) s(5592) =< aux(227) s(5584) =< aux(227) s(5584) =< aux(228) s(5589) =< aux(229) s(5593) =< aux(230) s(5588) =< aux(231) s(5589) =< aux(231) s(5587) =< aux(233) s(5594) =< aux(227)+2 s(5595) =< aux(227)+1 s(5596) =< aux(227) s(5597) =< aux(227)+3 s(5589) =< aux(228)*(1/2)+aux(229) s(5590) =< aux(228)*(1/2)+aux(229) s(5591) =< aux(228)*(1/2)+aux(229) s(5588) =< aux(228)*(1/3)+aux(231) s(5589) =< aux(228)*(1/3)+aux(231) s(5590) =< aux(228)*(1/3)+aux(231) s(5591) =< aux(228)*(1/3)+aux(231) s(5587) =< aux(228)*(3/5)+s(5584)*(1/5)+aux(233) s(5588) =< aux(228)*(3/5)+s(5584)*(1/5)+aux(233) s(5589) =< aux(228)*(3/5)+s(5584)*(1/5)+aux(233) s(5590) =< aux(228)*(3/5)+s(5584)*(1/5)+aux(233) s(5591) =< aux(228)*(3/5)+s(5584)*(1/5)+aux(233) s(5593) =< aux(228)*(1/3)+aux(230) s(5586) =< aux(228)*(1/3)+aux(230) s(5598) =< s(5591)*s(5594) s(5599) =< s(5589)*s(5595) s(5600) =< s(5587)*s(5596) s(5601) =< s(5586)*s(5594) s(5602) =< s(5586)*s(5597) s(5603) =< s(5593)*s(5596) s(5604) =< s(5602) s(5605) =< s(5604)*s(5597) s(5606) =< s(5601) s(5607) =< s(5606)*s(5594) s(5608) =< s(5603) s(5609) =< s(5608)*aux(227) with precondition: [V2=2,Out=0,V1>=0,V>=0] * Chain [71]: 114*s(5913)+6*s(5914)+6*s(5915)+6*s(5916)+6*s(5917)+24*s(5919)+114*s(5920)+6*s(5925)+6*s(5926)+6*s(5927)+780*s(5931)+120*s(5932)+1560*s(5933)+144*s(5934)+120*s(5935)+24*s(5936)+57*s(5944)+3*s(5945)+3*s(5946)+3*s(5947)+3*s(5948)+141*s(5950)+57*s(5951)+3*s(5956)+3*s(5957)+3*s(5958)+390*s(5962)+60*s(5963)+780*s(5964)+72*s(5965)+60*s(5966)+12*s(5967)+249*s(5971)+36*s(5972)+12*s(5973)+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(5911) =< aux(252) s(5942) =< aux(259) s(5971) =< aux(246) s(5972) =< s(5971)*aux(246) s(5950) =< aux(254) s(5973) =< s(5950)*aux(254) s(5944) =< aux(254) s(5945) =< aux(254) s(5946) =< aux(254) s(5947) =< aux(254) s(5948) =< aux(254) s(5949) =< aux(254) s(5942) =< aux(254) s(5942) =< aux(255) s(5947) =< aux(256) s(5951) =< aux(257) s(5946) =< aux(258) s(5947) =< aux(258) s(5945) =< aux(260) s(5952) =< aux(254)+2 s(5953) =< aux(254)+1 s(5954) =< aux(254) s(5955) =< aux(254)+3 s(5947) =< aux(255)*(1/2)+aux(256) s(5948) =< aux(255)*(1/2)+aux(256) s(5949) =< aux(255)*(1/2)+aux(256) s(5946) =< aux(255)*(1/3)+aux(258) s(5947) =< aux(255)*(1/3)+aux(258) s(5948) =< aux(255)*(1/3)+aux(258) s(5949) =< aux(255)*(1/3)+aux(258) s(5945) =< aux(255)*(3/5)+s(5942)*(1/5)+aux(260) s(5946) =< aux(255)*(3/5)+s(5942)*(1/5)+aux(260) s(5947) =< aux(255)*(3/5)+s(5942)*(1/5)+aux(260) s(5948) =< aux(255)*(3/5)+s(5942)*(1/5)+aux(260) s(5949) =< aux(255)*(3/5)+s(5942)*(1/5)+aux(260) s(5951) =< aux(255)*(1/3)+aux(257) s(5944) =< aux(255)*(1/3)+aux(257) s(5956) =< s(5949)*s(5952) s(5957) =< s(5947)*s(5953) s(5958) =< s(5945)*s(5954) s(5959) =< s(5944)*s(5952) s(5960) =< s(5944)*s(5955) s(5961) =< s(5951)*s(5954) s(5962) =< s(5960) s(5963) =< s(5962)*s(5955) s(5964) =< s(5959) s(5965) =< s(5964)*s(5952) s(5966) =< s(5961) s(5967) =< s(5966)*aux(254) s(5913) =< aux(247) s(5914) =< aux(247) s(5915) =< aux(247) s(5916) =< aux(247) s(5917) =< aux(247) s(5918) =< aux(247) s(5919) =< aux(247) s(5911) =< aux(247) s(5911) =< aux(248) s(5916) =< aux(249) s(5920) =< aux(250) s(5915) =< aux(251) s(5916) =< aux(251) s(5914) =< aux(253) s(5921) =< aux(247)+2 s(5922) =< aux(247)+1 s(5923) =< aux(247) s(5924) =< aux(247)+3 s(5916) =< aux(248)*(1/2)+aux(249) s(5917) =< aux(248)*(1/2)+aux(249) s(5918) =< aux(248)*(1/2)+aux(249) s(5915) =< aux(248)*(1/3)+aux(251) s(5916) =< aux(248)*(1/3)+aux(251) s(5917) =< aux(248)*(1/3)+aux(251) s(5918) =< aux(248)*(1/3)+aux(251) s(5914) =< aux(248)*(3/5)+s(5911)*(1/5)+aux(253) s(5915) =< aux(248)*(3/5)+s(5911)*(1/5)+aux(253) s(5916) =< aux(248)*(3/5)+s(5911)*(1/5)+aux(253) s(5917) =< aux(248)*(3/5)+s(5911)*(1/5)+aux(253) s(5918) =< aux(248)*(3/5)+s(5911)*(1/5)+aux(253) s(5920) =< aux(248)*(1/3)+aux(250) s(5913) =< aux(248)*(1/3)+aux(250) s(5925) =< s(5918)*s(5921) s(5926) =< s(5916)*s(5922) s(5927) =< s(5914)*s(5923) s(5928) =< s(5913)*s(5921) s(5929) =< s(5913)*s(5924) s(5930) =< s(5920)*s(5923) s(5931) =< s(5929) s(5932) =< s(5931)*s(5924) s(5933) =< s(5928) s(5934) =< s(5933)*s(5921) s(5935) =< s(5930) s(5936) =< s(5935)*aux(247) with precondition: [V=2,Out=0,V1>=0,V2>=0] #### Cost of chains of fun3(V1,V,Out): * Chain [79]: 38*s(6406)+2*s(6407)+2*s(6408)+2*s(6409)+2*s(6410)+8*s(6412)+38*s(6413)+2*s(6418)+2*s(6419)+2*s(6420)+260*s(6424)+40*s(6425)+520*s(6426)+48*s(6427)+40*s(6428)+8*s(6429)+57*s(6437)+3*s(6438)+3*s(6439)+3*s(6440)+3*s(6441)+15*s(6443)+57*s(6444)+3*s(6449)+3*s(6450)+3*s(6451)+390*s(6455)+60*s(6456)+780*s(6457)+72*s(6458)+60*s(6459)+12*s(6460)+1*s(6526)+0 Such that:s(6526) =< 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(6404) =< aux(284) s(6435) =< aux(291) s(6443) =< aux(286) s(6437) =< aux(286) s(6438) =< aux(286) s(6439) =< aux(286) s(6440) =< aux(286) s(6441) =< aux(286) s(6442) =< aux(286) s(6435) =< aux(286) s(6435) =< aux(287) s(6440) =< aux(288) s(6444) =< aux(289) s(6439) =< aux(290) s(6440) =< aux(290) s(6438) =< aux(292) s(6445) =< aux(286)+2 s(6446) =< aux(286)+1 s(6447) =< aux(286) s(6448) =< aux(286)+3 s(6440) =< aux(287)*(1/2)+aux(288) s(6441) =< aux(287)*(1/2)+aux(288) s(6442) =< aux(287)*(1/2)+aux(288) s(6439) =< aux(287)*(1/3)+aux(290) s(6440) =< aux(287)*(1/3)+aux(290) s(6441) =< aux(287)*(1/3)+aux(290) s(6442) =< aux(287)*(1/3)+aux(290) s(6438) =< aux(287)*(3/5)+s(6435)*(1/5)+aux(292) s(6439) =< aux(287)*(3/5)+s(6435)*(1/5)+aux(292) s(6440) =< aux(287)*(3/5)+s(6435)*(1/5)+aux(292) s(6441) =< aux(287)*(3/5)+s(6435)*(1/5)+aux(292) s(6442) =< aux(287)*(3/5)+s(6435)*(1/5)+aux(292) s(6444) =< aux(287)*(1/3)+aux(289) s(6437) =< aux(287)*(1/3)+aux(289) s(6449) =< s(6442)*s(6445) s(6450) =< s(6440)*s(6446) s(6451) =< s(6438)*s(6447) s(6452) =< s(6437)*s(6445) s(6453) =< s(6437)*s(6448) s(6454) =< s(6444)*s(6447) s(6455) =< s(6453) s(6456) =< s(6455)*s(6448) s(6457) =< s(6452) s(6458) =< s(6457)*s(6445) s(6459) =< s(6454) s(6460) =< s(6459)*aux(286) s(6406) =< aux(279) s(6407) =< aux(279) s(6408) =< aux(279) s(6409) =< aux(279) s(6410) =< aux(279) s(6411) =< aux(279) s(6412) =< aux(279) s(6404) =< aux(279) s(6404) =< aux(280) s(6409) =< aux(281) s(6413) =< aux(282) s(6408) =< aux(283) s(6409) =< aux(283) s(6407) =< aux(285) s(6414) =< aux(279)+2 s(6415) =< aux(279)+1 s(6416) =< aux(279) s(6417) =< aux(279)+3 s(6409) =< aux(280)*(1/2)+aux(281) s(6410) =< aux(280)*(1/2)+aux(281) s(6411) =< aux(280)*(1/2)+aux(281) s(6408) =< aux(280)*(1/3)+aux(283) s(6409) =< aux(280)*(1/3)+aux(283) s(6410) =< aux(280)*(1/3)+aux(283) s(6411) =< aux(280)*(1/3)+aux(283) s(6407) =< aux(280)*(3/5)+s(6404)*(1/5)+aux(285) s(6408) =< aux(280)*(3/5)+s(6404)*(1/5)+aux(285) s(6409) =< aux(280)*(3/5)+s(6404)*(1/5)+aux(285) s(6410) =< aux(280)*(3/5)+s(6404)*(1/5)+aux(285) s(6411) =< aux(280)*(3/5)+s(6404)*(1/5)+aux(285) s(6413) =< aux(280)*(1/3)+aux(282) s(6406) =< aux(280)*(1/3)+aux(282) s(6418) =< s(6411)*s(6414) s(6419) =< s(6409)*s(6415) s(6420) =< s(6407)*s(6416) s(6421) =< s(6406)*s(6414) s(6422) =< s(6406)*s(6417) s(6423) =< s(6413)*s(6416) s(6424) =< s(6422) s(6425) =< s(6424)*s(6417) s(6426) =< s(6421) s(6427) =< s(6426)*s(6414) s(6428) =< s(6423) s(6429) =< s(6428)*aux(279) with precondition: [Out=0,V1>=0,V>=0] * Chain [78]: 57*s(6568)+3*s(6569)+3*s(6570)+3*s(6571)+3*s(6572)+12*s(6574)+57*s(6575)+3*s(6580)+3*s(6581)+3*s(6582)+390*s(6586)+60*s(6587)+780*s(6588)+72*s(6589)+60*s(6590)+12*s(6591)+76*s(6599)+4*s(6600)+4*s(6601)+4*s(6602)+4*s(6603)+17*s(6605)+76*s(6606)+4*s(6611)+4*s(6612)+4*s(6613)+520*s(6617)+80*s(6618)+1040*s(6619)+96*s(6620)+80*s(6621)+16*s(6622)+2*s(6748)+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(6748) =< aux(294) s(6566) =< aux(300) s(6597) =< aux(307) s(6599) =< aux(302) s(6600) =< aux(302) s(6601) =< aux(302) s(6602) =< aux(302) s(6603) =< aux(302) s(6604) =< aux(302) s(6605) =< aux(302) s(6597) =< aux(302) s(6597) =< aux(303) s(6602) =< aux(304) s(6606) =< aux(305) s(6601) =< aux(306) s(6602) =< aux(306) s(6600) =< aux(308) s(6607) =< aux(302)+2 s(6608) =< aux(302)+1 s(6609) =< aux(302) s(6610) =< aux(302)+3 s(6602) =< aux(303)*(1/2)+aux(304) s(6603) =< aux(303)*(1/2)+aux(304) s(6604) =< aux(303)*(1/2)+aux(304) s(6601) =< aux(303)*(1/3)+aux(306) s(6602) =< aux(303)*(1/3)+aux(306) s(6603) =< aux(303)*(1/3)+aux(306) s(6604) =< aux(303)*(1/3)+aux(306) s(6600) =< aux(303)*(3/5)+s(6597)*(1/5)+aux(308) s(6601) =< aux(303)*(3/5)+s(6597)*(1/5)+aux(308) s(6602) =< aux(303)*(3/5)+s(6597)*(1/5)+aux(308) s(6603) =< aux(303)*(3/5)+s(6597)*(1/5)+aux(308) s(6604) =< aux(303)*(3/5)+s(6597)*(1/5)+aux(308) s(6606) =< aux(303)*(1/3)+aux(305) s(6599) =< aux(303)*(1/3)+aux(305) s(6611) =< s(6604)*s(6607) s(6612) =< s(6602)*s(6608) s(6613) =< s(6600)*s(6609) s(6614) =< s(6599)*s(6607) s(6615) =< s(6599)*s(6610) s(6616) =< s(6606)*s(6609) s(6617) =< s(6615) s(6618) =< s(6617)*s(6610) s(6619) =< s(6614) s(6620) =< s(6619)*s(6607) s(6621) =< s(6616) s(6622) =< s(6621)*aux(302) s(6568) =< aux(295) s(6569) =< aux(295) s(6570) =< aux(295) s(6571) =< aux(295) s(6572) =< aux(295) s(6573) =< aux(295) s(6574) =< aux(295) s(6566) =< aux(295) s(6566) =< aux(296) s(6571) =< aux(297) s(6575) =< aux(298) s(6570) =< aux(299) s(6571) =< aux(299) s(6569) =< aux(301) s(6576) =< aux(295)+2 s(6577) =< aux(295)+1 s(6578) =< aux(295) s(6579) =< aux(295)+3 s(6571) =< aux(296)*(1/2)+aux(297) s(6572) =< aux(296)*(1/2)+aux(297) s(6573) =< aux(296)*(1/2)+aux(297) s(6570) =< aux(296)*(1/3)+aux(299) s(6571) =< aux(296)*(1/3)+aux(299) s(6572) =< aux(296)*(1/3)+aux(299) s(6573) =< aux(296)*(1/3)+aux(299) s(6569) =< aux(296)*(3/5)+s(6566)*(1/5)+aux(301) s(6570) =< aux(296)*(3/5)+s(6566)*(1/5)+aux(301) s(6571) =< aux(296)*(3/5)+s(6566)*(1/5)+aux(301) s(6572) =< aux(296)*(3/5)+s(6566)*(1/5)+aux(301) s(6573) =< aux(296)*(3/5)+s(6566)*(1/5)+aux(301) s(6575) =< aux(296)*(1/3)+aux(298) s(6568) =< aux(296)*(1/3)+aux(298) s(6580) =< s(6573)*s(6576) s(6581) =< s(6571)*s(6577) s(6582) =< s(6569)*s(6578) s(6583) =< s(6568)*s(6576) s(6584) =< s(6568)*s(6579) s(6585) =< s(6575)*s(6578) s(6586) =< s(6584) s(6587) =< s(6586)*s(6579) s(6588) =< s(6583) s(6589) =< s(6588)*s(6576) s(6590) =< s(6585) s(6591) =< s(6590)*aux(295) with precondition: [Out=1,V1>=0,V>=0] * Chain [77]: 57*s(6788)+3*s(6789)+3*s(6790)+3*s(6791)+3*s(6792)+12*s(6794)+57*s(6795)+3*s(6800)+3*s(6801)+3*s(6802)+390*s(6806)+60*s(6807)+780*s(6808)+72*s(6809)+60*s(6810)+12*s(6811)+76*s(6819)+4*s(6820)+4*s(6821)+4*s(6822)+4*s(6823)+17*s(6825)+76*s(6826)+4*s(6831)+4*s(6832)+4*s(6833)+520*s(6837)+80*s(6838)+1040*s(6839)+96*s(6840)+80*s(6841)+16*s(6842)+1*s(6999)+1 Such that:s(6999) =< 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(6786) =< aux(315) s(6817) =< aux(322) s(6819) =< aux(317) s(6820) =< aux(317) s(6821) =< aux(317) s(6822) =< aux(317) s(6823) =< aux(317) s(6824) =< aux(317) s(6825) =< aux(317) s(6817) =< aux(317) s(6817) =< aux(318) s(6822) =< aux(319) s(6826) =< aux(320) s(6821) =< aux(321) s(6822) =< aux(321) s(6820) =< aux(323) s(6827) =< aux(317)+2 s(6828) =< aux(317)+1 s(6829) =< aux(317) s(6830) =< aux(317)+3 s(6822) =< aux(318)*(1/2)+aux(319) s(6823) =< aux(318)*(1/2)+aux(319) s(6824) =< aux(318)*(1/2)+aux(319) s(6821) =< aux(318)*(1/3)+aux(321) s(6822) =< aux(318)*(1/3)+aux(321) s(6823) =< aux(318)*(1/3)+aux(321) s(6824) =< aux(318)*(1/3)+aux(321) s(6820) =< aux(318)*(3/5)+s(6817)*(1/5)+aux(323) s(6821) =< aux(318)*(3/5)+s(6817)*(1/5)+aux(323) s(6822) =< aux(318)*(3/5)+s(6817)*(1/5)+aux(323) s(6823) =< aux(318)*(3/5)+s(6817)*(1/5)+aux(323) s(6824) =< aux(318)*(3/5)+s(6817)*(1/5)+aux(323) s(6826) =< aux(318)*(1/3)+aux(320) s(6819) =< aux(318)*(1/3)+aux(320) s(6831) =< s(6824)*s(6827) s(6832) =< s(6822)*s(6828) s(6833) =< s(6820)*s(6829) s(6834) =< s(6819)*s(6827) s(6835) =< s(6819)*s(6830) s(6836) =< s(6826)*s(6829) s(6837) =< s(6835) s(6838) =< s(6837)*s(6830) s(6839) =< s(6834) s(6840) =< s(6839)*s(6827) s(6841) =< s(6836) s(6842) =< s(6841)*aux(317) s(6788) =< aux(310) s(6789) =< aux(310) s(6790) =< aux(310) s(6791) =< aux(310) s(6792) =< aux(310) s(6793) =< aux(310) s(6794) =< aux(310) s(6786) =< aux(310) s(6786) =< aux(311) s(6791) =< aux(312) s(6795) =< aux(313) s(6790) =< aux(314) s(6791) =< aux(314) s(6789) =< aux(316) s(6796) =< aux(310)+2 s(6797) =< aux(310)+1 s(6798) =< aux(310) s(6799) =< aux(310)+3 s(6791) =< aux(311)*(1/2)+aux(312) s(6792) =< aux(311)*(1/2)+aux(312) s(6793) =< aux(311)*(1/2)+aux(312) s(6790) =< aux(311)*(1/3)+aux(314) s(6791) =< aux(311)*(1/3)+aux(314) s(6792) =< aux(311)*(1/3)+aux(314) s(6793) =< aux(311)*(1/3)+aux(314) s(6789) =< aux(311)*(3/5)+s(6786)*(1/5)+aux(316) s(6790) =< aux(311)*(3/5)+s(6786)*(1/5)+aux(316) s(6791) =< aux(311)*(3/5)+s(6786)*(1/5)+aux(316) s(6792) =< aux(311)*(3/5)+s(6786)*(1/5)+aux(316) s(6793) =< aux(311)*(3/5)+s(6786)*(1/5)+aux(316) s(6795) =< aux(311)*(1/3)+aux(313) s(6788) =< aux(311)*(1/3)+aux(313) s(6800) =< s(6793)*s(6796) s(6801) =< s(6791)*s(6797) s(6802) =< s(6789)*s(6798) s(6803) =< s(6788)*s(6796) s(6804) =< s(6788)*s(6799) s(6805) =< s(6795)*s(6798) s(6806) =< s(6804) s(6807) =< s(6806)*s(6799) s(6808) =< s(6803) s(6809) =< s(6808)*s(6796) s(6810) =< s(6805) s(6811) =< s(6810)*aux(310) with precondition: [Out=2,V1>=1,V>=0] * Chain [76]: 19*s(7007)+1*s(7008)+1*s(7009)+1*s(7010)+1*s(7011)+4*s(7013)+19*s(7014)+1*s(7019)+1*s(7020)+1*s(7021)+130*s(7025)+20*s(7026)+260*s(7027)+24*s(7028)+20*s(7029)+4*s(7030)+2*s(7031)+0 Such that:s(7000) =< V1 s(7001) =< 2*V1+1 s(7002) =< V1/2 s(7003) =< V1/3 s(7004) =< 2/3*V1 s(7005) =< 2/3*V1+1/3 s(7006) =< 2/5*V1 aux(324) =< 2 s(7031) =< aux(324) s(7007) =< s(7000) s(7008) =< s(7000) s(7009) =< s(7000) s(7010) =< s(7000) s(7011) =< s(7000) s(7012) =< s(7000) s(7013) =< s(7000) s(7005) =< s(7000) s(7005) =< s(7001) s(7010) =< s(7002) s(7014) =< s(7003) s(7009) =< s(7004) s(7010) =< s(7004) s(7008) =< s(7006) s(7015) =< s(7000)+2 s(7016) =< s(7000)+1 s(7017) =< s(7000) s(7018) =< s(7000)+3 s(7010) =< s(7001)*(1/2)+s(7002) s(7011) =< s(7001)*(1/2)+s(7002) s(7012) =< s(7001)*(1/2)+s(7002) s(7009) =< s(7001)*(1/3)+s(7004) s(7010) =< s(7001)*(1/3)+s(7004) s(7011) =< s(7001)*(1/3)+s(7004) s(7012) =< s(7001)*(1/3)+s(7004) s(7008) =< s(7001)*(3/5)+s(7005)*(1/5)+s(7006) s(7009) =< s(7001)*(3/5)+s(7005)*(1/5)+s(7006) s(7010) =< s(7001)*(3/5)+s(7005)*(1/5)+s(7006) s(7011) =< s(7001)*(3/5)+s(7005)*(1/5)+s(7006) s(7012) =< s(7001)*(3/5)+s(7005)*(1/5)+s(7006) s(7014) =< s(7001)*(1/3)+s(7003) s(7007) =< s(7001)*(1/3)+s(7003) s(7019) =< s(7012)*s(7015) s(7020) =< s(7010)*s(7016) s(7021) =< s(7008)*s(7017) s(7022) =< s(7007)*s(7015) s(7023) =< s(7007)*s(7018) s(7024) =< s(7014)*s(7017) s(7025) =< s(7023) s(7026) =< s(7025)*s(7018) s(7027) =< s(7022) s(7028) =< s(7027)*s(7015) s(7029) =< s(7024) s(7030) =< s(7029)*s(7000) with precondition: [V=2,Out=0,V1>=0] * Chain [75]: 38*s(7040)+2*s(7041)+2*s(7042)+2*s(7043)+2*s(7044)+9*s(7046)+38*s(7047)+2*s(7052)+2*s(7053)+2*s(7054)+260*s(7058)+40*s(7059)+520*s(7060)+48*s(7061)+40*s(7062)+8*s(7063)+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(7038) =< aux(331) s(7040) =< aux(326) s(7041) =< aux(326) s(7042) =< aux(326) s(7043) =< aux(326) s(7044) =< aux(326) s(7045) =< aux(326) s(7046) =< aux(326) s(7038) =< aux(326) s(7038) =< aux(327) s(7043) =< aux(328) s(7047) =< aux(329) s(7042) =< aux(330) s(7043) =< aux(330) s(7041) =< aux(332) s(7048) =< aux(326)+2 s(7049) =< aux(326)+1 s(7050) =< aux(326) s(7051) =< aux(326)+3 s(7043) =< aux(327)*(1/2)+aux(328) s(7044) =< aux(327)*(1/2)+aux(328) s(7045) =< aux(327)*(1/2)+aux(328) s(7042) =< aux(327)*(1/3)+aux(330) s(7043) =< aux(327)*(1/3)+aux(330) s(7044) =< aux(327)*(1/3)+aux(330) s(7045) =< aux(327)*(1/3)+aux(330) s(7041) =< aux(327)*(3/5)+s(7038)*(1/5)+aux(332) s(7042) =< aux(327)*(3/5)+s(7038)*(1/5)+aux(332) s(7043) =< aux(327)*(3/5)+s(7038)*(1/5)+aux(332) s(7044) =< aux(327)*(3/5)+s(7038)*(1/5)+aux(332) s(7045) =< aux(327)*(3/5)+s(7038)*(1/5)+aux(332) s(7047) =< aux(327)*(1/3)+aux(329) s(7040) =< aux(327)*(1/3)+aux(329) s(7052) =< s(7045)*s(7048) s(7053) =< s(7043)*s(7049) s(7054) =< s(7041)*s(7050) s(7055) =< s(7040)*s(7048) s(7056) =< s(7040)*s(7051) s(7057) =< s(7047)*s(7050) s(7058) =< s(7056) s(7059) =< s(7058)*s(7051) s(7060) =< s(7055) s(7061) =< s(7060)*s(7048) s(7062) =< s(7057) s(7063) =< s(7062)*aux(326) with precondition: [V=2,Out=1,V1>=0] * Chain [74]: 19*s(7103)+1*s(7104)+1*s(7105)+1*s(7106)+1*s(7107)+4*s(7109)+19*s(7110)+1*s(7115)+1*s(7116)+1*s(7117)+130*s(7121)+20*s(7122)+260*s(7123)+24*s(7124)+20*s(7125)+4*s(7126)+1*s(7127)+1 Such that:s(7127) =< 2 s(7096) =< V1 s(7097) =< 2*V1+1 s(7098) =< V1/2 s(7099) =< V1/3 s(7100) =< 2/3*V1 s(7101) =< 2/3*V1+1/3 s(7102) =< 2/5*V1 s(7103) =< s(7096) s(7104) =< s(7096) s(7105) =< s(7096) s(7106) =< s(7096) s(7107) =< s(7096) s(7108) =< s(7096) s(7109) =< s(7096) s(7101) =< s(7096) s(7101) =< s(7097) s(7106) =< s(7098) s(7110) =< s(7099) s(7105) =< s(7100) s(7106) =< s(7100) s(7104) =< s(7102) s(7111) =< s(7096)+2 s(7112) =< s(7096)+1 s(7113) =< s(7096) s(7114) =< s(7096)+3 s(7106) =< s(7097)*(1/2)+s(7098) s(7107) =< s(7097)*(1/2)+s(7098) s(7108) =< s(7097)*(1/2)+s(7098) s(7105) =< s(7097)*(1/3)+s(7100) s(7106) =< s(7097)*(1/3)+s(7100) s(7107) =< s(7097)*(1/3)+s(7100) s(7108) =< s(7097)*(1/3)+s(7100) s(7104) =< s(7097)*(3/5)+s(7101)*(1/5)+s(7102) s(7105) =< s(7097)*(3/5)+s(7101)*(1/5)+s(7102) s(7106) =< s(7097)*(3/5)+s(7101)*(1/5)+s(7102) s(7107) =< s(7097)*(3/5)+s(7101)*(1/5)+s(7102) s(7108) =< s(7097)*(3/5)+s(7101)*(1/5)+s(7102) s(7110) =< s(7097)*(1/3)+s(7099) s(7103) =< s(7097)*(1/3)+s(7099) s(7115) =< s(7108)*s(7111) s(7116) =< s(7106)*s(7112) s(7117) =< s(7104)*s(7113) s(7118) =< s(7103)*s(7111) s(7119) =< s(7103)*s(7114) s(7120) =< s(7110)*s(7113) s(7121) =< s(7119) s(7122) =< s(7121)*s(7114) s(7123) =< s(7118) s(7124) =< s(7123)*s(7111) s(7125) =< s(7120) s(7126) =< s(7125)*s(7096) with precondition: [V=2,Out=2,V1>=3] #### Cost of chains of fun4(V1,Out): * Chain [82]: 19*s(7428)+1*s(7429)+1*s(7430)+1*s(7431)+1*s(7432)+4*s(7434)+19*s(7435)+1*s(7440)+1*s(7441)+1*s(7442)+130*s(7446)+20*s(7447)+260*s(7448)+24*s(7449)+20*s(7450)+4*s(7451)+0 Such that:s(7421) =< V1 s(7422) =< 2*V1+1 s(7423) =< V1/2 s(7424) =< V1/3 s(7425) =< 2/3*V1 s(7426) =< 2/3*V1+1/3 s(7427) =< 2/5*V1 s(7428) =< s(7421) s(7429) =< s(7421) s(7430) =< s(7421) s(7431) =< s(7421) s(7432) =< s(7421) s(7433) =< s(7421) s(7434) =< s(7421) s(7426) =< s(7421) s(7426) =< s(7422) s(7431) =< s(7423) s(7435) =< s(7424) s(7430) =< s(7425) s(7431) =< s(7425) s(7429) =< s(7427) s(7436) =< s(7421)+2 s(7437) =< s(7421)+1 s(7438) =< s(7421) s(7439) =< s(7421)+3 s(7431) =< s(7422)*(1/2)+s(7423) s(7432) =< s(7422)*(1/2)+s(7423) s(7433) =< s(7422)*(1/2)+s(7423) s(7430) =< s(7422)*(1/3)+s(7425) s(7431) =< s(7422)*(1/3)+s(7425) s(7432) =< s(7422)*(1/3)+s(7425) s(7433) =< s(7422)*(1/3)+s(7425) s(7429) =< s(7422)*(3/5)+s(7426)*(1/5)+s(7427) s(7430) =< s(7422)*(3/5)+s(7426)*(1/5)+s(7427) s(7431) =< s(7422)*(3/5)+s(7426)*(1/5)+s(7427) s(7432) =< s(7422)*(3/5)+s(7426)*(1/5)+s(7427) s(7433) =< s(7422)*(3/5)+s(7426)*(1/5)+s(7427) s(7435) =< s(7422)*(1/3)+s(7424) s(7428) =< s(7422)*(1/3)+s(7424) s(7440) =< s(7433)*s(7436) s(7441) =< s(7431)*s(7437) s(7442) =< s(7429)*s(7438) s(7443) =< s(7428)*s(7436) s(7444) =< s(7428)*s(7439) s(7445) =< s(7435)*s(7438) s(7446) =< s(7444) s(7447) =< s(7446)*s(7439) s(7448) =< s(7443) s(7449) =< s(7448)*s(7436) s(7450) =< s(7445) s(7451) =< s(7450)*s(7421) with precondition: [Out=0,V1>=0] * Chain [81]: 19*s(7459)+1*s(7460)+1*s(7461)+1*s(7462)+1*s(7463)+4*s(7465)+19*s(7466)+1*s(7471)+1*s(7472)+1*s(7473)+130*s(7477)+20*s(7478)+260*s(7479)+24*s(7480)+20*s(7481)+4*s(7482)+1 Such that:s(7452) =< V1 s(7453) =< 2*V1+1 s(7454) =< V1/2 s(7455) =< V1/3 s(7456) =< 2/3*V1 s(7457) =< 2/3*V1+1/3 s(7458) =< 2/5*V1 s(7459) =< s(7452) s(7460) =< s(7452) s(7461) =< s(7452) s(7462) =< s(7452) s(7463) =< s(7452) s(7464) =< s(7452) s(7465) =< s(7452) s(7457) =< s(7452) s(7457) =< s(7453) s(7462) =< s(7454) s(7466) =< s(7455) s(7461) =< s(7456) s(7462) =< s(7456) s(7460) =< s(7458) s(7467) =< s(7452)+2 s(7468) =< s(7452)+1 s(7469) =< s(7452) s(7470) =< s(7452)+3 s(7462) =< s(7453)*(1/2)+s(7454) s(7463) =< s(7453)*(1/2)+s(7454) s(7464) =< s(7453)*(1/2)+s(7454) s(7461) =< s(7453)*(1/3)+s(7456) s(7462) =< s(7453)*(1/3)+s(7456) s(7463) =< s(7453)*(1/3)+s(7456) s(7464) =< s(7453)*(1/3)+s(7456) s(7460) =< s(7453)*(3/5)+s(7457)*(1/5)+s(7458) s(7461) =< s(7453)*(3/5)+s(7457)*(1/5)+s(7458) s(7462) =< s(7453)*(3/5)+s(7457)*(1/5)+s(7458) s(7463) =< s(7453)*(3/5)+s(7457)*(1/5)+s(7458) s(7464) =< s(7453)*(3/5)+s(7457)*(1/5)+s(7458) s(7466) =< s(7453)*(1/3)+s(7455) s(7459) =< s(7453)*(1/3)+s(7455) s(7471) =< s(7464)*s(7467) s(7472) =< s(7462)*s(7468) s(7473) =< s(7460)*s(7469) s(7474) =< s(7459)*s(7467) s(7475) =< s(7459)*s(7470) s(7476) =< s(7466)*s(7469) s(7477) =< s(7475) s(7478) =< s(7477)*s(7470) s(7479) =< s(7474) s(7480) =< s(7479)*s(7467) s(7481) =< s(7476) s(7482) =< s(7481)*s(7452) with precondition: [Out=2,V1>=1] * Chain [80]: 19*s(7490)+1*s(7491)+1*s(7492)+1*s(7493)+1*s(7494)+4*s(7496)+19*s(7497)+1*s(7502)+1*s(7503)+1*s(7504)+130*s(7508)+20*s(7509)+260*s(7510)+24*s(7511)+20*s(7512)+4*s(7513)+1 Such that:s(7483) =< V1 s(7484) =< 2*V1+1 s(7485) =< V1/2 s(7486) =< V1/3 s(7487) =< 2/3*V1 s(7488) =< 2/3*V1+1/3 s(7489) =< 2/5*V1 s(7490) =< s(7483) s(7491) =< s(7483) s(7492) =< s(7483) s(7493) =< s(7483) s(7494) =< s(7483) s(7495) =< s(7483) s(7496) =< s(7483) s(7488) =< s(7483) s(7488) =< s(7484) s(7493) =< s(7485) s(7497) =< s(7486) s(7492) =< s(7487) s(7493) =< s(7487) s(7491) =< s(7489) s(7498) =< s(7483)+2 s(7499) =< s(7483)+1 s(7500) =< s(7483) s(7501) =< s(7483)+3 s(7493) =< s(7484)*(1/2)+s(7485) s(7494) =< s(7484)*(1/2)+s(7485) s(7495) =< s(7484)*(1/2)+s(7485) s(7492) =< s(7484)*(1/3)+s(7487) s(7493) =< s(7484)*(1/3)+s(7487) s(7494) =< s(7484)*(1/3)+s(7487) s(7495) =< s(7484)*(1/3)+s(7487) s(7491) =< s(7484)*(3/5)+s(7488)*(1/5)+s(7489) s(7492) =< s(7484)*(3/5)+s(7488)*(1/5)+s(7489) s(7493) =< s(7484)*(3/5)+s(7488)*(1/5)+s(7489) s(7494) =< s(7484)*(3/5)+s(7488)*(1/5)+s(7489) s(7495) =< s(7484)*(3/5)+s(7488)*(1/5)+s(7489) s(7497) =< s(7484)*(1/3)+s(7486) s(7490) =< s(7484)*(1/3)+s(7486) s(7502) =< s(7495)*s(7498) s(7503) =< s(7493)*s(7499) s(7504) =< s(7491)*s(7500) s(7505) =< s(7490)*s(7498) s(7506) =< s(7490)*s(7501) s(7507) =< s(7497)*s(7500) s(7508) =< s(7506) s(7509) =< s(7508)*s(7501) s(7510) =< s(7505) s(7511) =< s(7510)*s(7498) s(7512) =< s(7507) s(7513) =< s(7512)*s(7483) with precondition: [Out=1,V1>=0] #### Cost of chains of fun5(Out): * Chain [84]: 0 with precondition: [Out=0] * Chain [83]: 0 with precondition: [Out=1] #### Cost of chains of fun6(V1,Out): * Chain [86]: 19*s(7521)+1*s(7522)+1*s(7523)+1*s(7524)+1*s(7525)+4*s(7527)+19*s(7528)+1*s(7533)+1*s(7534)+1*s(7535)+130*s(7539)+20*s(7540)+260*s(7541)+24*s(7542)+20*s(7543)+4*s(7544)+1 Such that:s(7514) =< V1 s(7515) =< 2*V1+1 s(7516) =< V1/2 s(7517) =< V1/3 s(7518) =< 2/3*V1 s(7519) =< 2/3*V1+1/3 s(7520) =< 2/5*V1 s(7521) =< s(7514) s(7522) =< s(7514) s(7523) =< s(7514) s(7524) =< s(7514) s(7525) =< s(7514) s(7526) =< s(7514) s(7527) =< s(7514) s(7519) =< s(7514) s(7519) =< s(7515) s(7524) =< s(7516) s(7528) =< s(7517) s(7523) =< s(7518) s(7524) =< s(7518) s(7522) =< s(7520) s(7529) =< s(7514)+2 s(7530) =< s(7514)+1 s(7531) =< s(7514) s(7532) =< s(7514)+3 s(7524) =< s(7515)*(1/2)+s(7516) s(7525) =< s(7515)*(1/2)+s(7516) s(7526) =< s(7515)*(1/2)+s(7516) s(7523) =< s(7515)*(1/3)+s(7518) s(7524) =< s(7515)*(1/3)+s(7518) s(7525) =< s(7515)*(1/3)+s(7518) s(7526) =< s(7515)*(1/3)+s(7518) s(7522) =< s(7515)*(3/5)+s(7519)*(1/5)+s(7520) s(7523) =< s(7515)*(3/5)+s(7519)*(1/5)+s(7520) s(7524) =< s(7515)*(3/5)+s(7519)*(1/5)+s(7520) s(7525) =< s(7515)*(3/5)+s(7519)*(1/5)+s(7520) s(7526) =< s(7515)*(3/5)+s(7519)*(1/5)+s(7520) s(7528) =< s(7515)*(1/3)+s(7517) s(7521) =< s(7515)*(1/3)+s(7517) s(7533) =< s(7526)*s(7529) s(7534) =< s(7524)*s(7530) s(7535) =< s(7522)*s(7531) s(7536) =< s(7521)*s(7529) s(7537) =< s(7521)*s(7532) s(7538) =< s(7528)*s(7531) s(7539) =< s(7537) s(7540) =< s(7539)*s(7532) s(7541) =< s(7536) s(7542) =< s(7541)*s(7529) s(7543) =< s(7538) s(7544) =< s(7543)*s(7514) with precondition: [Out=0,V1>=0] * Chain [85]: 19*s(7552)+1*s(7553)+1*s(7554)+1*s(7555)+1*s(7556)+4*s(7558)+19*s(7559)+1*s(7564)+1*s(7565)+1*s(7566)+130*s(7570)+20*s(7571)+260*s(7572)+24*s(7573)+20*s(7574)+4*s(7575)+1 Such that:s(7545) =< V1 s(7546) =< 2*V1+1 s(7547) =< V1/2 s(7548) =< V1/3 s(7549) =< 2/3*V1 s(7550) =< 2/3*V1+1/3 s(7551) =< 2/5*V1 s(7552) =< s(7545) s(7553) =< s(7545) s(7554) =< s(7545) s(7555) =< s(7545) s(7556) =< s(7545) s(7557) =< s(7545) s(7558) =< s(7545) s(7550) =< s(7545) s(7550) =< s(7546) s(7555) =< s(7547) s(7559) =< s(7548) s(7554) =< s(7549) s(7555) =< s(7549) s(7553) =< s(7551) s(7560) =< s(7545)+2 s(7561) =< s(7545)+1 s(7562) =< s(7545) s(7563) =< s(7545)+3 s(7555) =< s(7546)*(1/2)+s(7547) s(7556) =< s(7546)*(1/2)+s(7547) s(7557) =< s(7546)*(1/2)+s(7547) s(7554) =< s(7546)*(1/3)+s(7549) s(7555) =< s(7546)*(1/3)+s(7549) s(7556) =< s(7546)*(1/3)+s(7549) s(7557) =< s(7546)*(1/3)+s(7549) s(7553) =< s(7546)*(3/5)+s(7550)*(1/5)+s(7551) s(7554) =< s(7546)*(3/5)+s(7550)*(1/5)+s(7551) s(7555) =< s(7546)*(3/5)+s(7550)*(1/5)+s(7551) s(7556) =< s(7546)*(3/5)+s(7550)*(1/5)+s(7551) s(7557) =< s(7546)*(3/5)+s(7550)*(1/5)+s(7551) s(7559) =< s(7546)*(1/3)+s(7548) s(7552) =< s(7546)*(1/3)+s(7548) s(7564) =< s(7557)*s(7560) s(7565) =< s(7555)*s(7561) s(7566) =< s(7553)*s(7562) s(7567) =< s(7552)*s(7560) s(7568) =< s(7552)*s(7563) s(7569) =< s(7559)*s(7562) s(7570) =< s(7568) s(7571) =< s(7570)*s(7563) s(7572) =< s(7567) s(7573) =< s(7572)*s(7560) s(7574) =< s(7569) s(7575) =< s(7574)*s(7545) with precondition: [Out>=0,V1>=Out+1] #### Cost of chains of fun8(V1,Out): * Chain [89]: 19*s(7583)+1*s(7584)+1*s(7585)+1*s(7586)+1*s(7587)+4*s(7589)+19*s(7590)+1*s(7595)+1*s(7596)+1*s(7597)+130*s(7601)+20*s(7602)+260*s(7603)+24*s(7604)+20*s(7605)+4*s(7606)+0 Such that:s(7576) =< V1 s(7577) =< 2*V1+1 s(7578) =< V1/2 s(7579) =< V1/3 s(7580) =< 2/3*V1 s(7581) =< 2/3*V1+1/3 s(7582) =< 2/5*V1 s(7583) =< s(7576) s(7584) =< s(7576) s(7585) =< s(7576) s(7586) =< s(7576) s(7587) =< s(7576) s(7588) =< s(7576) s(7589) =< s(7576) s(7581) =< s(7576) s(7581) =< s(7577) s(7586) =< s(7578) s(7590) =< s(7579) s(7585) =< s(7580) s(7586) =< s(7580) s(7584) =< s(7582) s(7591) =< s(7576)+2 s(7592) =< s(7576)+1 s(7593) =< s(7576) s(7594) =< s(7576)+3 s(7586) =< s(7577)*(1/2)+s(7578) s(7587) =< s(7577)*(1/2)+s(7578) s(7588) =< s(7577)*(1/2)+s(7578) s(7585) =< s(7577)*(1/3)+s(7580) s(7586) =< s(7577)*(1/3)+s(7580) s(7587) =< s(7577)*(1/3)+s(7580) s(7588) =< s(7577)*(1/3)+s(7580) s(7584) =< s(7577)*(3/5)+s(7581)*(1/5)+s(7582) s(7585) =< s(7577)*(3/5)+s(7581)*(1/5)+s(7582) s(7586) =< s(7577)*(3/5)+s(7581)*(1/5)+s(7582) s(7587) =< s(7577)*(3/5)+s(7581)*(1/5)+s(7582) s(7588) =< s(7577)*(3/5)+s(7581)*(1/5)+s(7582) s(7590) =< s(7577)*(1/3)+s(7579) s(7583) =< s(7577)*(1/3)+s(7579) s(7595) =< s(7588)*s(7591) s(7596) =< s(7586)*s(7592) s(7597) =< s(7584)*s(7593) s(7598) =< s(7583)*s(7591) s(7599) =< s(7583)*s(7594) s(7600) =< s(7590)*s(7593) s(7601) =< s(7599) s(7602) =< s(7601)*s(7594) s(7603) =< s(7598) s(7604) =< s(7603)*s(7591) s(7605) =< s(7600) s(7606) =< s(7605)*s(7576) with precondition: [V1>=1,Out>=1,V1+1>=Out] * Chain [88]: 0 with precondition: [Out=0,V1>=0] * Chain [87]: 0 with precondition: [Out=1,V1>=0] #### Cost of chains of start(V1,V,V2): * Chain [90]: 1937*s(7609)+156*s(7612)+982*s(7616)+132*s(7617)+318*s(7657)+1501*s(7666)+79*s(7667)+79*s(7668)+79*s(7669)+79*s(7670)+1501*s(7673)+79*s(7678)+79*s(7679)+79*s(7680)+10270*s(7684)+1580*s(7685)+20540*s(7686)+1896*s(7687)+1580*s(7688)+316*s(7689)+1984*s(7715)+232*s(7716)+1026*s(7717)+54*s(7718)+54*s(7719)+54*s(7720)+54*s(7721)+1026*s(7724)+54*s(7729)+54*s(7730)+54*s(7731)+7020*s(7735)+1080*s(7736)+14040*s(7737)+1296*s(7738)+1080*s(7739)+216*s(7740)+167*s(7766)+16*s(7767)+1273*s(7769)+67*s(7770)+67*s(7771)+67*s(7772)+67*s(7773)+1273*s(7776)+67*s(7781)+67*s(7782)+67*s(7783)+8710*s(7787)+1340*s(7788)+17420*s(7789)+1608*s(7790)+1340*s(7791)+268*s(7792)+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(7766) =< aux(359) s(7715) =< aux(360) s(7657) =< aux(361) s(7664) =< aux(366) s(7616) =< aux(368) s(7714) =< aux(380) s(7716) =< s(7715)*aux(360) s(7717) =< aux(375) s(7718) =< aux(375) s(7719) =< aux(375) s(7720) =< aux(375) s(7721) =< aux(375) s(7722) =< aux(375) s(7609) =< aux(375) s(7714) =< aux(375) s(7714) =< aux(376) s(7720) =< aux(377) s(7724) =< aux(378) s(7719) =< aux(379) s(7720) =< aux(379) s(7718) =< aux(381) s(7725) =< aux(375)+2 s(7726) =< aux(375)+1 s(7727) =< aux(375) s(7728) =< aux(375)+3 s(7720) =< aux(376)*(1/2)+aux(377) s(7721) =< aux(376)*(1/2)+aux(377) s(7722) =< aux(376)*(1/2)+aux(377) s(7719) =< aux(376)*(1/3)+aux(379) s(7720) =< aux(376)*(1/3)+aux(379) s(7721) =< aux(376)*(1/3)+aux(379) s(7722) =< aux(376)*(1/3)+aux(379) s(7718) =< aux(376)*(3/5)+s(7714)*(1/5)+aux(381) s(7719) =< aux(376)*(3/5)+s(7714)*(1/5)+aux(381) s(7720) =< aux(376)*(3/5)+s(7714)*(1/5)+aux(381) s(7721) =< aux(376)*(3/5)+s(7714)*(1/5)+aux(381) s(7722) =< aux(376)*(3/5)+s(7714)*(1/5)+aux(381) s(7724) =< aux(376)*(1/3)+aux(378) s(7717) =< aux(376)*(1/3)+aux(378) s(7729) =< s(7722)*s(7725) s(7730) =< s(7720)*s(7726) s(7731) =< s(7718)*s(7727) s(7732) =< s(7717)*s(7725) s(7733) =< s(7717)*s(7728) s(7734) =< s(7724)*s(7727) s(7735) =< s(7733) s(7736) =< s(7735)*s(7728) s(7737) =< s(7732) s(7738) =< s(7737)*s(7725) s(7739) =< s(7734) s(7740) =< s(7739)*aux(375) s(7666) =< aux(361) s(7667) =< aux(361) s(7668) =< aux(361) s(7669) =< aux(361) s(7670) =< aux(361) s(7671) =< aux(361) s(7664) =< aux(361) s(7664) =< aux(362) s(7669) =< aux(363) s(7673) =< aux(364) s(7668) =< aux(365) s(7669) =< aux(365) s(7667) =< aux(367) s(7674) =< aux(361)+2 s(7675) =< aux(361)+1 s(7676) =< aux(361) s(7677) =< aux(361)+3 s(7669) =< aux(362)*(1/2)+aux(363) s(7670) =< aux(362)*(1/2)+aux(363) s(7671) =< aux(362)*(1/2)+aux(363) s(7668) =< aux(362)*(1/3)+aux(365) s(7669) =< aux(362)*(1/3)+aux(365) s(7670) =< aux(362)*(1/3)+aux(365) s(7671) =< aux(362)*(1/3)+aux(365) s(7667) =< aux(362)*(3/5)+s(7664)*(1/5)+aux(367) s(7668) =< aux(362)*(3/5)+s(7664)*(1/5)+aux(367) s(7669) =< aux(362)*(3/5)+s(7664)*(1/5)+aux(367) s(7670) =< aux(362)*(3/5)+s(7664)*(1/5)+aux(367) s(7671) =< aux(362)*(3/5)+s(7664)*(1/5)+aux(367) s(7673) =< aux(362)*(1/3)+aux(364) s(7666) =< aux(362)*(1/3)+aux(364) s(7678) =< s(7671)*s(7674) s(7679) =< s(7669)*s(7675) s(7680) =< s(7667)*s(7676) s(7681) =< s(7666)*s(7674) s(7682) =< s(7666)*s(7677) s(7683) =< s(7673)*s(7676) s(7684) =< s(7682) s(7685) =< s(7684)*s(7677) s(7686) =< s(7681) s(7687) =< s(7686)*s(7674) s(7688) =< s(7683) s(7689) =< s(7688)*aux(361) s(7612) =< s(7609)*aux(375) s(7767) =< s(7766)*aux(359) s(7768) =< aux(373) s(7769) =< aux(368) s(7770) =< aux(368) s(7771) =< aux(368) s(7772) =< aux(368) s(7773) =< aux(368) s(7774) =< aux(368) s(7768) =< aux(368) s(7768) =< aux(369) s(7772) =< aux(370) s(7776) =< aux(371) s(7771) =< aux(372) s(7772) =< aux(372) s(7770) =< aux(374) s(7777) =< aux(368)+2 s(7778) =< aux(368)+1 s(7779) =< aux(368) s(7780) =< aux(368)+3 s(7772) =< aux(369)*(1/2)+aux(370) s(7773) =< aux(369)*(1/2)+aux(370) s(7774) =< aux(369)*(1/2)+aux(370) s(7771) =< aux(369)*(1/3)+aux(372) s(7772) =< aux(369)*(1/3)+aux(372) s(7773) =< aux(369)*(1/3)+aux(372) s(7774) =< aux(369)*(1/3)+aux(372) s(7770) =< aux(369)*(3/5)+s(7768)*(1/5)+aux(374) s(7771) =< aux(369)*(3/5)+s(7768)*(1/5)+aux(374) s(7772) =< aux(369)*(3/5)+s(7768)*(1/5)+aux(374) s(7773) =< aux(369)*(3/5)+s(7768)*(1/5)+aux(374) s(7774) =< aux(369)*(3/5)+s(7768)*(1/5)+aux(374) s(7776) =< aux(369)*(1/3)+aux(371) s(7769) =< aux(369)*(1/3)+aux(371) s(7781) =< s(7774)*s(7777) s(7782) =< s(7772)*s(7778) s(7783) =< s(7770)*s(7779) s(7784) =< s(7769)*s(7777) s(7785) =< s(7769)*s(7780) s(7786) =< s(7776)*s(7779) s(7787) =< s(7785) s(7788) =< s(7787)*s(7780) s(7789) =< s(7784) s(7790) =< s(7789)*s(7777) s(7791) =< s(7786) s(7792) =< s(7791)*aux(368) s(7617) =< s(7616)*aux(368) with precondition: [] Closed-form bounds of start(V1,V,V2): ------------------------------------- * Chain [90] with precondition: [] - Upper bound: nat(V1)*96066+5098+nat(V1)*48111*nat(V1)+nat(V1)*3476*nat(V1)*nat(V1)+nat(V1)*316*nat(V1)*nat(V1/3)+nat(V1)*1580*nat(V1/3)+nat(V)*82186+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)*67385+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)*1501+nat(V/3)*1273+nat(V2/3)*1026 - Complexity: n^3 ### Maximum cost of start(V1,V,V2): nat(V1)*96066+5098+nat(V1)*48111*nat(V1)+nat(V1)*3476*nat(V1)*nat(V1)+nat(V1)*316*nat(V1)*nat(V1/3)+nat(V1)*1580*nat(V1/3)+nat(V)*82186+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)*67385+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)*1501+nat(V/3)*1273+nat(V2/3)*1026 Asymptotic class: n^3 * Total analysis performed in 37696 ms. ---------------------------------------- (14) BOUNDS(1, n^3) ---------------------------------------- (15) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (16) Obligation: Analyzing the following TRS for decreasing loops: 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(gr0(x), y, y) cond2(false, x, y) -> cond1(gr0(x), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) gr0(0) -> false gr0(s(x)) -> true p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(false) -> false encArg(0) -> 0 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_gr0(x_1)) -> gr0(encArg(x_1)) 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_gr0(x_1) -> gr0(encArg(x_1)) encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (17) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence gr(s(x), s(y)) ->^+ gr(x, y) gives rise to a decreasing loop by considering the right hand sides subterm at position []. The pumping substitution is [x / s(x), y / s(y)]. The result substitution is [ ]. ---------------------------------------- (18) Complex Obligation (BEST) ---------------------------------------- (19) Obligation: Proved the lower bound n^1 for the following 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(gr0(x), y, y) cond2(false, x, y) -> cond1(gr0(x), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) gr0(0) -> false gr0(s(x)) -> true p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(false) -> false encArg(0) -> 0 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_gr0(x_1)) -> gr0(encArg(x_1)) 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_gr0(x_1) -> gr0(encArg(x_1)) encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (20) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (21) BOUNDS(n^1, INF) ---------------------------------------- (22) Obligation: Analyzing the following TRS for decreasing loops: 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(gr0(x), y, y) cond2(false, x, y) -> cond1(gr0(x), p(x), y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) gr0(0) -> false gr0(s(x)) -> true p(0) -> 0 p(s(x)) -> x The (relative) TRS S consists of the following rules: encArg(true) -> true encArg(false) -> false encArg(0) -> 0 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_gr0(x_1)) -> gr0(encArg(x_1)) 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_gr0(x_1) -> gr0(encArg(x_1)) encode_false -> false encode_p(x_1) -> p(encArg(x_1)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) Rewrite Strategy: INNERMOST